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<div class="vector-toc-text"> <span class="vector-toc-numb">1.3.1</span> <span>Students</span> </div> </a> <ul id="toc-Students-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Death" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Death"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Death</span> </div> </a> <ul id="toc-Death-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Work" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Work"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Work</span> </div> </a> <button aria-controls="toc-Work-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Work subsection</span> </button> <ul id="toc-Work-sublist" class="vector-toc-list"> <li id="toc-Summary" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Summary"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Summary</span> </div> </a> <ul id="toc-Summary-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Three-body_problem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Three-body_problem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Three-body problem</span> </div> </a> <ul id="toc-Three-body_problem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Work_on_relativity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Work_on_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Work on relativity</span> </div> </a> <ul id="toc-Work_on_relativity-sublist" class="vector-toc-list"> <li id="toc-Local_time" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Local_time"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.1</span> <span>Local time</span> </div> </a> <ul id="toc-Local_time-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Principle_of_relativity_and_Lorentz_transformations" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Principle_of_relativity_and_Lorentz_transformations"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.2</span> <span>Principle of relativity and Lorentz transformations</span> </div> </a> <ul id="toc-Principle_of_relativity_and_Lorentz_transformations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mass–energy_relation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Mass–energy_relation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.3</span> <span>Mass–energy relation</span> </div> </a> <ul id="toc-Mass–energy_relation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gravitational_waves" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Gravitational_waves"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.4</span> <span>Gravitational waves</span> </div> </a> <ul id="toc-Gravitational_waves-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Poincaré_and_Einstein" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Poincaré_and_Einstein"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.5</span> <span>Poincaré and Einstein</span> </div> </a> <ul id="toc-Poincaré_and_Einstein-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Assessments_on_Poincaré_and_relativity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Assessments_on_Poincaré_and_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.6</span> <span>Assessments on Poincaré and relativity</span> </div> </a> <ul id="toc-Assessments_on_Poincaré_and_relativity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Algebra_and_number_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Algebra_and_number_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Algebra and number theory</span> </div> </a> <ul id="toc-Algebra_and_number_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Topology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Topology"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Topology</span> </div> </a> <ul id="toc-Topology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Astronomy_and_celestial_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Astronomy_and_celestial_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Astronomy and celestial mechanics</span> </div> </a> <ul id="toc-Astronomy_and_celestial_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Differential_equations_and_mathematical_physics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Differential_equations_and_mathematical_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Differential equations and mathematical physics</span> </div> </a> <ul id="toc-Differential_equations_and_mathematical_physics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Character" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Character"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Character</span> </div> </a> <button aria-controls="toc-Character-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Character subsection</span> </button> <ul id="toc-Character-sublist" class="vector-toc-list"> <li id="toc-Toulouse's_characterisation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Toulouse's_characterisation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Toulouse's characterisation</span> </div> </a> <ul id="toc-Toulouse's_characterisation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Publications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Publications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Publications</span> </div> </a> <ul id="toc-Publications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Honours" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Honours"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Honours</span> </div> </a> <ul id="toc-Honours-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Philosophy" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Philosophy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Philosophy</span> </div> </a> <button aria-controls="toc-Philosophy-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Philosophy subsection</span> </button> <ul id="toc-Philosophy-sublist" class="vector-toc-list"> <li id="toc-Free_will" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Free_will"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Free will</span> </div> </a> <ul id="toc-Free_will-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Bibliography</span> </div> </a> <button aria-controls="toc-Bibliography-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Bibliography subsection</span> </button> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> <li id="toc-Poincaré's_writings_in_English_translation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Poincaré's_writings_in_English_translation"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Poincaré's writings in English translation</span> </div> </a> <ul id="toc-Poincaré's_writings_in_English_translation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <button aria-controls="toc-See_also-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle See also subsection</span> </button> <ul id="toc-See_also-sublist" class="vector-toc-list"> <li id="toc-Concepts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Concepts"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Concepts</span> </div> </a> <ul id="toc-Concepts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theorems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Theorems"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Theorems</span> </div> </a> <ul id="toc-Theorems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Other</span> </div> </a> <ul id="toc-Other-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Further reading</span> </div> </a> <button aria-controls="toc-Further_reading-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Further reading subsection</span> </button> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> <li id="toc-Secondary_sources_to_work_on_relativity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Secondary_sources_to_work_on_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Secondary sources to work on relativity</span> </div> </a> <ul id="toc-Secondary_sources_to_work_on_relativity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-mainstream_sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-mainstream_sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.2</span> <span>Non-mainstream sources</span> </div> </a> <ul id="toc-Non-mainstream_sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Henri Poincaré</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 94 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-94" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">94 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ady mw-list-item"><a href="https://ady.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D0%B8_%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D0%B5" title="Анри Пуанкаре – Adyghe" lang="ady" hreflang="ady" data-title="Анри Пуанкаре" data-language-autonym="Адыгабзэ" data-language-local-name="Adyghe" class="interlanguage-link-target"><span>Адыгабзэ</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Afrikaans" lang="af" hreflang="af" data-title="Henri Poincaré" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Alemannic" lang="gsw" hreflang="gsw" data-title="Henri Poincaré" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D9%86%D8%B1%D9%8A_%D8%A8%D9%88%D8%A7%D9%86%D9%83%D8%A7%D8%B1%D9%8A%D9%87" title="هنري بوانكاريه – Arabic" lang="ar" hreflang="ar" data-title="هنري بوانكاريه" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Asturian" lang="ast" hreflang="ast" data-title="Henri Poincaré" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Anri_Puankare" title="Anri Puankare – Azerbaijani" lang="az" hreflang="az" data-title="Anri Puankare" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A2%D9%86%D8%B1%DB%8C_%D9%BE%D9%88%D8%A7%D9%86%DA%A9%D8%A7%D8%B1%D9%87" title="آنری پوانکاره – South Azerbaijani" lang="azb" hreflang="azb" data-title="آنری پوانکاره" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%81%E0%A6%B0%E0%A6%BF_%E0%A6%AA%E0%A7%8B%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%81%E0%A6%95%E0%A6%BE%E0%A6%B0%E0%A7%87" title="অঁরি পোয়াঁকারে – Bangla" lang="bn" hreflang="bn" data-title="অঁরি পোয়াঁকারে" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Minnan" lang="nan" hreflang="nan" data-title="Henri Poincaré" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D1%8B_%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D1%8D" title="Анры Пуанкарэ – Belarusian" lang="be" hreflang="be" data-title="Анры Пуанкарэ" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D0%B8_%D0%9F%D0%BE%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D0%B5" title="Анри Поанкаре – Bulgarian" lang="bg" hreflang="bg" data-title="Анри Поанкаре" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Bosnian" lang="bs" hreflang="bs" data-title="Henri Poincaré" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Catalan" lang="ca" hreflang="ca" data-title="Henri Poincaré" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D0%B5,_%D0%90%D0%BD%D1%80%D0%B8" title="Пуанкаре, Анри – Chuvash" lang="cv" hreflang="cv" data-title="Пуанкаре, Анри" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Czech" lang="cs" hreflang="cs" data-title="Henri Poincaré" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Danish" lang="da" hreflang="da" data-title="Henri Poincaré" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – German" lang="de" hreflang="de" data-title="Henri Poincaré" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Estonian" lang="et" hreflang="et" data-title="Henri Poincaré" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BD%CF%81%CE%AF_%CE%A0%CE%BF%CF%85%CE%B1%CE%BD%CE%BA%CE%B1%CF%81%CE%AD" title="Ανρί Πουανκαρέ – Greek" lang="el" hreflang="el" data-title="Ανρί Πουανκαρέ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Spanish" lang="es" hreflang="es" data-title="Henri Poincaré" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Esperanto" lang="eo" hreflang="eo" data-title="Henri Poincaré" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Basque" lang="eu" hreflang="eu" data-title="Henri Poincaré" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D9%86%D8%B1%DB%8C_%D9%BE%D9%88%D8%A7%D9%86%DA%A9%D8%A7%D8%B1%D9%87" title="آنری پوانکاره – Persian" lang="fa" hreflang="fa" data-title="آنری پوانکاره" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – French" lang="fr" hreflang="fr" data-title="Henri Poincaré" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Western Frisian" lang="fy" hreflang="fy" data-title="Henri Poincaré" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Irish" lang="ga" hreflang="ga" data-title="Henri Poincaré" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Galician" lang="gl" hreflang="gl" data-title="Henri Poincaré" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E8%88%AC%E5%8A%A0%E9%BB%91" title="般加黑 – Gan" lang="gan" hreflang="gan" data-title="般加黑" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%99%EB%A6%AC_%ED%91%B8%EC%95%B5%EC%B9%B4%EB%A0%88" title="앙리 푸앵카레 – Korean" lang="ko" hreflang="ko" data-title="앙리 푸앵카레" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Hausa" lang="ha" hreflang="ha" data-title="Henri Poincaré" data-language-autonym="Hausa" data-language-local-name="Hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B6%D6%80%D5%AB_%D5%8A%D5%B8%D6%82%D5%A1%D5%B6%D5%AF%D5%A1%D6%80%D5%A5" title="Անրի Պուանկարե – Armenian" lang="hy" hreflang="hy" data-title="Անրի Պուանկարե" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%86%E0%A4%A8%E0%A5%8D%E0%A4%B0%E0%A5%80_%E0%A4%AA%E0%A4%BE%E0%A4%82%E0%A4%95%E0%A4%B0%E0%A5%87" title="आन्री पांकरे – Hindi" lang="hi" hreflang="hi" data-title="आन्री पांकरे" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Croatian" lang="hr" hreflang="hr" data-title="Henri Poincaré" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Ido" lang="io" hreflang="io" data-title="Henri Poincaré" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Indonesian" lang="id" hreflang="id" data-title="Henri Poincaré" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Italian" lang="it" hreflang="it" data-title="Henri Poincaré" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A0%D7%A8%D7%99_%D7%A4%D7%95%D7%90%D7%A0%D7%A7%D7%A8%D7%94" title="אנרי פואנקרה – Hebrew" lang="he" hreflang="he" data-title="אנרי פואנקרה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Kabiye" lang="kbp" hreflang="kbp" data-title="Henri Poincaré" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B9%E0%B3%86%E0%B2%A8%E0%B3%8D%E0%B2%B0%E0%B2%BF_%E0%B2%AA%E0%B3%8D%E0%B2%B5%E0%B2%BE%E0%B2%A8%E0%B3%8D%E2%80%8D%E0%B2%95%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%B0%E0%B3%87" title="ಹೆನ್ರಿ ಪ್ವಾನ್‍ಕ್ಯಾರೇ – Kannada" lang="kn" hreflang="kn" data-title="ಹೆನ್ರಿ ಪ್ವಾನ್‍ಕ್ಯಾರೇ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9F%E1%83%98%E1%83%A3%E1%83%9A_%E1%83%90%E1%83%9C%E1%83%A0%E1%83%98_%E1%83%9E%E1%83%A3%E1%83%90%E1%83%9C%E1%83%99%E1%83%90%E1%83%A0%E1%83%94" title="ჟიულ ანრი პუანკარე – Georgian" lang="ka" hreflang="ka" data-title="ჟიულ ანრი პუანკარე" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D0%B8_%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D0%B5" title="Анри Пуанкаре – Kazakh" lang="kk" hreflang="kk" data-title="Анри Пуанкаре" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Haitian Creole" lang="ht" hreflang="ht" data-title="Henri Poincaré" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Henricus_Poincar%C3%A9" title="Henricus Poincaré – Latin" lang="la" hreflang="la" data-title="Henricus Poincaré" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Anr%C4%AB_Puankar%C4%93" title="Anrī Puankarē – Latvian" lang="lv" hreflang="lv" data-title="Anrī Puankarē" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Luxembourgish" lang="lb" hreflang="lb" data-title="Henri Poincaré" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Lithuanian" lang="lt" hreflang="lt" data-title="Henri Poincaré" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/aris.puakares" title="aris.puakares – Lojban" lang="jbo" hreflang="jbo" data-title="aris.puakares" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Hungarian" lang="hu" hreflang="hu" data-title="Henri Poincaré" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D0%B8_%D0%9F%D0%BE%D0%B5%D0%BD%D0%BA%D0%B0%D1%80%D0%B5" title="Анри Поенкаре – Macedonian" lang="mk" hreflang="mk" data-title="Анри Поенкаре" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Malagasy" lang="mg" hreflang="mg" data-title="Henri Poincaré" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%90%E1%83%9C%E1%83%A0%E1%83%98_%E1%83%9E%E1%83%A3%E1%83%90%E1%83%9C%E1%83%99%E1%83%90%E1%83%A0%E1%83%94" title="ანრი პუანკარე – Mingrelian" lang="xmf" hreflang="xmf" data-title="ანრი პუანკარე" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%87%D9%86%D8%B1%D9%89_%D8%A8%D9%88%D8%A7%D9%86%D9%83%D8%A7%D8%B1%D9%8A%D9%87" title="هنرى بوانكاريه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="هنرى بوانكاريه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Mirandese" lang="mwl" hreflang="mwl" data-title="Henri Poincaré" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D0%B8_%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D1%8D" title="Анри Пуанкарэ – Mongolian" lang="mn" hreflang="mn" data-title="Анри Пуанкарэ" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%BD%E1%80%94%E1%80%BA%E1%80%9B%E1%80%AD_%E1%80%95%E1%80%BD%E1%80%94%E1%80%BA%E1%80%80%E1%80%AC%E1%80%9B%E1%80%B1" title="အွန်ရိ ပွန်ကာရေ – Burmese" lang="my" hreflang="my" data-title="အွန်ရိ ပွန်ကာရေ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Dutch" lang="nl" hreflang="nl" data-title="Henri Poincaré" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%83%B3%E3%83%AA%E3%83%BB%E3%83%9D%E3%82%A2%E3%83%B3%E3%82%AB%E3%83%AC" title="アンリ・ポアンカレ – Japanese" lang="ja" hreflang="ja" data-title="アンリ・ポアンカレ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Henri Poincaré" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Henri Poincaré" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Occitan" lang="oc" hreflang="oc" data-title="Henri Poincaré" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Uzbek" lang="uz" hreflang="uz" data-title="Henri Poincaré" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%9C%E0%A9%82%E0%A8%B2%E0%A8%9C%E0%A8%BC_%E0%A8%94%E0%A8%A8%E0%A8%B0%E0%A9%80_%E0%A8%AA%E0%A9%8B%E0%A8%87%E0%A8%A8%E0%A8%95%E0%A8%B0%E0%A9%87" title="ਜੂਲਜ਼ ਔਨਰੀ ਪੋਇਨਕਰੇ – Punjabi" lang="pa" hreflang="pa" data-title="ਜੂਲਜ਼ ਔਨਰੀ ਪੋਇਨਕਰੇ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%87%D9%8A%D9%86%D8%B1%D9%8A_%D9%BE%D9%88%D8%A7%D9%8A%D9%86%DA%A9%D8%B1%DB%8C" title="هينري پواينکری – Pashto" lang="ps" hreflang="ps" data-title="هينري پواينکری" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Henri Poincaré" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Piedmontese" lang="pms" hreflang="pms" data-title="Henri Poincaré" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Polish" lang="pl" hreflang="pl" data-title="Henri Poincaré" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Portuguese" lang="pt" hreflang="pt" data-title="Henri Poincaré" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Romanian" lang="ro" hreflang="ro" data-title="Henri Poincaré" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Quechua" lang="qu" hreflang="qu" data-title="Henri Poincaré" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D0%B5,_%D0%90%D0%BD%D1%80%D0%B8" title="Пуанкаре, Анри – Russian" lang="ru" hreflang="ru" data-title="Пуанкаре, Анри" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D0%B8_%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D0%B5" title="Анри Пуанкаре – Yakut" lang="sah" hreflang="sah" data-title="Анри Пуанкаре" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Scots" lang="sco" hreflang="sco" data-title="Henri Poincaré" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Henri_Poincare" title="Henri Poincare – Albanian" lang="sq" hreflang="sq" data-title="Henri Poincare" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%84%E0%B7%99%E0%B6%B1%E0%B7%8A%E0%B6%BB%E0%B7%92_%E0%B6%B4%E0%B7%9C%E0%B6%BA%E0%B7%92%E0%B6%B1%E0%B7%8A%E0%B6%9A%E0%B7%8F%E0%B6%BB%E0%B7%9A" title="හෙන්රි පොයින්කාරේ – Sinhala" lang="si" hreflang="si" data-title="හෙන්රි පොයින්කාරේ" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Simple English" lang="en-simple" hreflang="en-simple" data-title="Henri Poincaré" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Slovak" lang="sk" hreflang="sk" data-title="Henri Poincaré" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Slovenian" lang="sl" hreflang="sl" data-title="Henri Poincaré" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%BE%DB%8E%D9%86%D8%B1%DB%8C_%D9%BE%DB%86%DB%8C%D9%86%DA%A9%D8%A7%D8%B1%DB%8E" title="ھێنری پۆینکارێ – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ھێنری پۆینکارێ" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D0%B8_%D0%9F%D0%BE%D0%B5%D0%BD%D0%BA%D0%B0%D1%80%D0%B5" title="Анри Поенкаре – Serbian" lang="sr" hreflang="sr" data-title="Анри Поенкаре" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Henri Poincaré" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Finnish" lang="fi" hreflang="fi" data-title="Henri Poincaré" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Swedish" lang="sv" hreflang="sv" data-title="Henri Poincaré" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Tagalog" lang="tl" hreflang="tl" data-title="Henri Poincaré" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B9%87%E0%B8%AD%E0%B8%87%E0%B8%A3%E0%B8%B5_%E0%B8%9B%E0%B8%A7%E0%B8%87%E0%B8%81%E0%B8%B2%E0%B9%80%E0%B8%A3" title="อ็องรี ปวงกาเร – Thai" lang="th" hreflang="th" data-title="อ็องรี ปวงกาเร" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Turkish" lang="tr" hreflang="tr" data-title="Henri Poincaré" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BD%D1%80%D1%96_%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D0%B5" title="Анрі Пуанкаре – Ukrainian" lang="uk" hreflang="uk" data-title="Анрі Пуанкаре" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DB%81%D9%86%D8%B1%DB%8C_%D9%BE%D9%88%D8%A7%D8%A6%D9%86%DA%A9%DB%8C%D8%B1%DB%92" title="ہنری پوائنکیرے – Urdu" lang="ur" hreflang="ur" data-title="ہنری پوائنکیرے" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Vietnamese" lang="vi" hreflang="vi" data-title="Henri Poincaré" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E9%BE%90%E5%8A%A0%E8%90%8A" title="龐加萊 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="龐加萊" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Waray" lang="war" hreflang="war" data-title="Henri Poincaré" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%84%92%E5%8B%92%C2%B7%E6%98%82%E5%88%A9%C2%B7%E5%BA%9E%E5%8A%A0%E8%8E%B1" title="儒勒·昂利·庞加莱 – Wu" lang="wuu" hreflang="wuu" data-title="儒勒·昂利·庞加莱" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré – Yoruba" lang="yo" hreflang="yo" data-title="Henri Poincaré" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%BE%90%E5%8A%A0%E8%90%8A" title="龐加萊 – Cantonese" lang="yue" hreflang="yue" data-title="龐加萊" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BA%A8%E5%88%A9%C2%B7%E9%BE%90%E5%8A%A0%E8%90%8A" title="亨利·龐加萊 – Chinese" lang="zh" hreflang="zh" data-title="亨利·龐加萊" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q81082#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Henri_Poincar%C3%A9" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a 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Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Henri+Poincar%C3%A9%22">"Henri Poincaré"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Henri+Poincar%C3%A9%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Henri+Poincar%C3%A9%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Henri+Poincar%C3%A9%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Henri+Poincar%C3%A9%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Henri+Poincar%C3%A9%22&acc=on&wc=on">JSTOR</a></span></small></span> <span 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div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Henri Poincaré</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:PSM_V82_D416_Henri_Poincare.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/PSM_V82_D416_Henri_Poincare.png/220px-PSM_V82_D416_Henri_Poincare.png" decoding="async" width="220" height="282" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/PSM_V82_D416_Henri_Poincare.png/330px-PSM_V82_D416_Henri_Poincare.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/PSM_V82_D416_Henri_Poincare.png/440px-PSM_V82_D416_Henri_Poincare.png 2x" data-file-width="1692" data-file-height="2165" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1854-04-29</span>)</span>29 April 1854<br /><div style="display:inline" class="birthplace"><a href="/wiki/Nancy,_France" title="Nancy, France">Nancy</a>, <a href="/wiki/Meurthe-et-Moselle" title="Meurthe-et-Moselle">Meurthe-et-Moselle</a>, France</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">17 July 1912<span style="display:none">(1912-07-17)</span> (aged 58)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Paris" title="Paris">Paris</a>, France</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category">French</td></tr><tr><th scope="row" class="infobox-label">Other names</th><td class="infobox-data nickname">Jules Henri Poincaré</td></tr><tr><th scope="row" class="infobox-label">Education</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li>Lycée Nancy (now <a href="/w/index.php?title=Lyc%C3%A9e_Henri-Poincar%C3%A9&action=edit&redlink=1" class="new" title="Lycée Henri-Poincaré (page does not exist)">Lycée Henri-Poincaré</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://fr.wikipedia.org/wiki/Lyc%C3%A9e_Henri-Poincar%C3%A9" class="extiw" title="fr:Lycée Henri-Poincaré">fr</a>]</span>)</li> <li><a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a></li> <li><a href="/wiki/%C3%89cole_des_Mines" class="mw-redirect" title="École des Mines">École des Mines</a></li> <li><a href="/wiki/University_of_Paris" title="University of Paris">University of Paris</a> (<a href="/wiki/Doctorat" class="mw-redirect" title="Doctorat">Dr</a>, 1879)</li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Poincar%C3%A9_conjecture" title="Poincaré conjecture">Poincaré conjecture</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Bendixson_theorem" title="Poincaré–Bendixson theorem">Poincaré–Bendixson theorem</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Lindstedt_method" title="Poincaré–Lindstedt method">Poincaré–Lindstedt method</a></li> <li><a href="/wiki/Poincar%C3%A9_recurrence_theorem" title="Poincaré recurrence theorem">Poincaré recurrence theorem</a></li> <li><a href="/wiki/Kelvin%27s_circulation_theorem#Poincaré–Bjerknes_circulation_theorem" title="Kelvin's circulation theorem">Poincaré–Bjerknes circulation theorem</a></li> <li><a href="/wiki/Poincar%C3%A9_group" title="Poincaré group">Poincaré group</a></li> <li><a href="/wiki/Poincar%C3%A9_gauge" class="mw-redirect" title="Poincaré gauge">Poincaré gauge</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Hopf_theorem" title="Poincaré–Hopf theorem">Poincaré–Hopf theorem</a></li> <li><a href="/wiki/Poincar%C3%A9_duality" title="Poincaré duality">Poincaré duality</a></li> <li><span class="nowrap"><a href="/wiki/Poincar%C3%A9%E2%80%93Birkhoff%E2%80%93Witt_theorem" title="Poincaré–Birkhoff–Witt theorem">Poincaré–Birkhoff–Witt theorem</a></span></li> <li><a href="/wiki/Poincar%C3%A9_inequality" title="Poincaré inequality">Poincaré inequality</a></li> <li><a href="/wiki/Hilbert%E2%80%93Poincar%C3%A9_series" title="Hilbert–Poincaré series">Hilbert–Poincaré series</a></li> <li><a href="/wiki/Poincar%C3%A9_series_(modular_form)" title="Poincaré series (modular form)">Poincaré series</a></li> <li><a href="/wiki/Poincar%C3%A9_metric" title="Poincaré metric">Poincaré metric</a></li> <li><a href="/wiki/Automorphic_form" title="Automorphic form">Automorphic form</a></li> <li><a href="/wiki/Betti_number" title="Betti number">Coining the term "Betti number"</a></li> <li><a href="/wiki/Brouwer_fixed-point_theorem" title="Brouwer fixed-point theorem">Brouwer fixed-point theorem</a></li> <li><a href="/wiki/Bifurcation_theory" title="Bifurcation theory">Bifurcation theory</a></li> <li><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></li> <li><a href="/wiki/Dynamical_system" title="Dynamical system">Dynamical system theory</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/French_historical_epistemology" class="mw-redirect" title="French historical epistemology">French historical epistemology</a></li> <li><a href="/wiki/Fundamental_group" title="Fundamental group">Fundamental group</a></li> <li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational wave</a></li> <li><a href="/wiki/Hairy_ball_theorem" title="Hairy ball theorem">Hairy ball theorem</a></li> <li><a href="/wiki/Homological_algebra" title="Homological algebra">Homological algebra</a></li> <li><a href="/wiki/Limit_cycle" title="Limit cycle">Limit cycle</a></li> <li><a href="/wiki/Phase_space" title="Phase space">Phase space</a></li> <li><a href="/wiki/Preintuitionism" class="mw-redirect" title="Preintuitionism">Preintuitionism</a>/<a href="/wiki/Conventionalism" title="Conventionalism">conventionalism</a></li> <li><a href="/wiki/Predicativism" class="mw-redirect" title="Predicativism">Predicativism</a></li> <li><a href="/wiki/Qualitative_theory_of_differential_equations" title="Qualitative theory of differential equations">Qualitative theory of differential equations</a></li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li> <li><a href="/wiki/Sphere-world" title="Sphere-world">Sphere-world</a></li> <li><a href="/wiki/Rotation_number" title="Rotation number">Rotation number</a></li> <li><a href="/wiki/Uniformization_theorem" title="Uniformization theorem">Uniformization theorem</a></li> <li><a href="/wiki/Three-body_problem" title="Three-body problem">Three-body problem</a></li> <li><a href="/wiki/Topology" title="Topology">Topology</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Spouse</th><td class="infobox-data">Jeanne-Louise Poulain d'Andecy</td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><span class="nowrap"><a href="/wiki/Gold_Medal_of_the_Royal_Astronomical_Society" title="Gold Medal of the Royal Astronomical Society">RAS Gold Medal</a> (1900)</span></li> <li><a href="/wiki/Sylvester_Medal" title="Sylvester Medal">Sylvester Medal</a> (1901)</li> <li><a href="/wiki/Matteucci_Medal" title="Matteucci Medal">Matteucci Medal</a> (1905)</li> <li><a href="/wiki/Bolyai_Prize" title="Bolyai Prize">Bolyai Prize</a> (1905)</li> <li><a href="/wiki/Bruce_Medal" title="Bruce Medal">Bruce Medal</a> (1911)</li></ul> </div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"> <ul><li>Mathematics</li> <li><a href="/wiki/Physics" title="Physics">physics</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Corps_des_Mines" class="mw-redirect" title="Corps des Mines">Corps des Mines</a></li> <li><a href="/wiki/Caen_University" class="mw-redirect" title="Caen University">Caen University</a></li> <li><a href="/wiki/University_of_Paris" title="University of Paris">La Sorbonne</a></li> <li><a href="/wiki/Bureau_des_Longitudes" title="Bureau des Longitudes">Bureau des Longitudes</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160506152142/https://iris.univ-lille1.fr/handle/1908/458">Sur les propriétés des fonctions définies par les équations différences</a></i> <span style="font-size:97%;">(1879)</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Charles_Hermite" title="Charles Hermite">Charles Hermite</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Louis_Bachelier" title="Louis Bachelier">Louis Bachelier</a></li> <li><a href="/wiki/Jean_Bosler" title="Jean Bosler">Jean Bosler</a></li> <li><a href="/wiki/Dimitrie_Pompeiu" title="Dimitrie Pompeiu">Dimitrie Pompeiu</a></li> <li><a href="/wiki/Mihailo_Petrovi%C4%87_Alas" title="Mihailo Petrović Alas">Mihailo Petrović Alas</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Other notable students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Tobias_Dantzig" title="Tobias Dantzig">Tobias Dantzig</a></li> <li><a href="/wiki/Th%C3%A9ophile_de_Donder" title="Théophile de Donder">Théophile de Donder</a></li></ul> </div></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th colspan="2" class="infobox-header">Signature</th></tr><tr><td colspan="2" class="infobox-full-data"><span class="infobox-signature skin-invert" typeof="mw:File"><a href="/wiki/File:Henri_Poincar%C3%A9_Signature.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Henri_Poincar%C3%A9_Signature.svg/150px-Henri_Poincar%C3%A9_Signature.svg.png" decoding="async" width="150" height="81" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Henri_Poincar%C3%A9_Signature.svg/225px-Henri_Poincar%C3%A9_Signature.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Henri_Poincar%C3%A9_Signature.svg/300px-Henri_Poincar%C3%A9_Signature.svg.png 2x" data-file-width="276" data-file-height="149" /></a></span></td></tr><tr><th colspan="2" class="infobox-header">Notes</th></tr><tr><td colspan="2" class="infobox-full-data"><div style="text-align: left;">He was an uncle of <a href="/wiki/Pierre_Boutroux" title="Pierre Boutroux">Pierre Boutroux</a>.</div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 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a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></th></tr><tr><td class="sidebar-image"><span class="notpageimage" typeof="mw:File"><a href="/wiki/File:World_line.svg" class="mw-file-description" title="The world line: a diagrammatic representation of spacetime"><img alt="The world line: a diagrammatic representation of spacetime" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/200px-World_line.svg.png" decoding="async" width="200" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/300px-World_line.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/400px-World_line.svg.png 2x" data-file-width="481" data-file-height="491" /></a></span></td></tr><tr><td class="sidebar-content" style="padding-bottom:0.6em;"> <ul><li><a href="/wiki/Principle_of_relativity" title="Principle of relativity">Principle of relativity</a></li> <li><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li> <li><a href="/wiki/Formulations_of_special_relativity" title="Formulations of special relativity">Formulations</a></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">Foundations</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Postulates_of_special_relativity" title="Postulates of special relativity">Einstein's postulates</a></li> <li><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial frame of reference</a></li> <li><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a></li> <li><a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">Consequences</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Length_contraction" title="Length contraction">Length contraction</a></li> <li><a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity">Relativistic mass</a></li> <li><a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence</a></li> <li><a href="/wiki/Relativity_of_simultaneity" title="Relativity of simultaneity">Relativity of simultaneity</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li> <li><a href="/wiki/Thomas_precession" title="Thomas precession">Thomas precession</a></li> <li><a href="/wiki/Relativistic_disk" title="Relativistic disk">Relativistic disk</a></li> <li><a href="/wiki/Bell%27s_spaceship_paradox" title="Bell's spaceship paradox">Bell's spaceship paradox</a></li> <li><a href="/wiki/Ehrenfest_paradox" title="Ehrenfest paradox">Ehrenfest paradox</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%"><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski spacetime</a></li> <li><a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Spacetime diagram</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Light_cone" title="Light cone">Light cone</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%"><a href="/wiki/Dynamics_(mechanics)" class="mw-redirect" title="Dynamics (mechanics)">Dynamics</a></span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Invariant_mass" title="Invariant mass">Proper mass</a></li> <li><a href="/wiki/Four-momentum" title="Four-momentum">Four-momentum</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist" style="font-size:110%;"><ul><li><a href="/wiki/History_of_special_relativity" title="History of special relativity">History</a></li><li>Precursors</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Galilean_invariance" title="Galilean invariance">Galilean relativity</a></li> <li><a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformation</a></li> <li><a href="/wiki/Aether_theories" title="Aether theories">Aether theories</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">People</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"><div class="hlist"> <ul><li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a></li> <li><a href="/wiki/Albert_A._Michelson" title="Albert A. Michelson">Michelson</a></li> <li><a href="/wiki/Edward_W._Morley" title="Edward W. Morley">Morley</a></li> <li><a href="/wiki/George_Francis_FitzGerald" title="George Francis FitzGerald">FitzGerald</a></li> <li><a href="/wiki/Gustav_Herglotz" title="Gustav Herglotz">Herglotz</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a class="mw-selflink selflink">Poincaré</a></li> <li><a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Minkowski</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Max_Abraham" title="Max Abraham">Abraham</a></li> <li><a href="/wiki/Max_Born" title="Max Born">Born</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/Max_von_Laue" title="Max von Laue">von Laue</a></li> <li><a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Ehrenfest</a></li> <li><a href="/wiki/Richard_C._Tolman" title="Richard C. Tolman">Tolman</a></li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, 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Henri Poincaré</b> (<span class="rt-commentedText nowrap"><style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small"><a href="/wiki/British_English" title="British English">UK</a>: </span><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'p' in 'pie'">p</span><span title="'w' in 'wind'">w</span><span title="/æ̃/: nasal 'in' in 'vin blanc'">æ̃</span><span title="'k' in 'kind'">k</span><span title="/ɑːr/: 'ar' in 'far'">ɑːr</span><span title="/eɪ/: 'a' in 'face'">eɪ</span></span>/</a></span></span>, <span class="rt-commentedText nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991"><span class="IPA-label IPA-label-small"><a href="/wiki/American_English" title="American English">US</a>: </span><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˌ/: secondary stress follows">ˌ</span><span title="'p' in 'pie'">p</span><span title="'w' in 'wind'">w</span><span title="/æ̃/: nasal 'in' in 'vin blanc'">æ̃</span><span title="'k' in 'kind'">k</span><span title="/ɑː/: 'a' in 'father'">ɑː</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="'r' in 'rye'">r</span><span title="/eɪ/: 'a' in 'face'">eɪ</span></span>/</a></span></span>; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1177148991"><span class="IPA-label IPA-label-small">French:</span> <span class="IPA nowrap" lang="fr-Latn-fonipa"><a href="/wiki/Help:IPA/French" title="Help:IPA/French">[ɑ̃ʁi<span class="wrap"> </span>pwɛ̃kaʁe]</a></span> <span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-1" class="ext-phonos-PhonosButton noexcerpt ext-phonos-PhonosButton-emptylabel oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/7\/70\/Fr-Henri_Poincar%C3%A9.ogg\/Fr-Henri_Poincar%C3%A9.ogg.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"Fr-Henri Poincar\u00e9.ogg"},"classes":["ext-phonos-PhonosButton","noexcerpt","ext-phonos-PhonosButton-emptylabel"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/7/70/Fr-Henri_Poincar%C3%A9.ogg/Fr-Henri_Poincar%C3%A9.ogg.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label"></span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:Fr-Henri_Poincar%C3%A9.ogg" title="File:Fr-Henri Poincaré.ogg">ⓘ</a></sup></span></span>;<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-forvo_2-0" class="reference"><a href="#cite_note-forvo-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-pronouncekiwi_3-0" class="reference"><a href="#cite_note-pronouncekiwi-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> 29 April 1854 – 17 July 1912) was a French <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physicist</a>, engineer, and <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosopher of science</a>. He is often described as a <a href="/wiki/Polymath" title="Polymath">polymath</a>, and in mathematics as "The Last Universalist",<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> since he excelled in all fields of the discipline as it existed during his lifetime. Due to his scientific success, influence and his discoveries, he has been deemed "the philosopher par excellence of modern science."<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>As a mathematician and <a href="/wiki/Physicist" title="Physicist">physicist</a>, he made many original fundamental contributions to <a href="/wiki/Pure_mathematics" title="Pure mathematics">pure</a> and <a href="/wiki/Applied_mathematics" title="Applied mathematics">applied mathematics</a>, <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>, and <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> In his research on the <a href="/wiki/Three-body_problem" title="Three-body problem">three-body problem</a>, Poincaré became the first person to discover a chaotic <a href="/wiki/Deterministic_system" title="Deterministic system">deterministic system</a> which laid the foundations of modern <a href="/wiki/Chaos_theory" title="Chaos theory">chaos theory</a>. He is also considered to be one of the founders of the field of <a href="/wiki/Topology" title="Topology">topology</a>. </p><p>Poincaré made clear the importance of paying attention to the <a href="/wiki/Invariant_(mathematics)" title="Invariant (mathematics)">invariance</a> of laws of physics under different transformations, and was the first to present the <a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformations</a> in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Hendrik Lorentz</a> in 1905. Thus he obtained perfect invariance of all of <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a>, an important step in the formulation of the theory of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>. In 1905, Poincaré first proposed <a href="/wiki/Gravitational_wave" title="Gravitational wave">gravitational waves</a> (<i>ondes gravifiques</i>) emanating from a body and propagating at the speed of light as being required by the Lorentz transformations.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In 1912, he wrote an influential paper which provided a mathematical argument for <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>.<sup id="cite_ref-McCormmach_8-0" class="reference"><a href="#cite_note-McCormmach-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Poincar%C3%A9_group" title="Poincaré group">Poincaré group</a> used in physics and mathematics was named after him. </p><p>Early in the 20th century he formulated the <a href="/wiki/Poincar%C3%A9_conjecture" title="Poincaré conjecture">Poincaré conjecture</a>, which became, over time, one of the famous <a href="/wiki/List_of_unsolved_problems_in_mathematics" title="List of unsolved problems in mathematics">unsolved problems in mathematics</a>. It was solved in 2002–2003 by <a href="/wiki/Grigori_Perelman" title="Grigori Perelman">Grigori Perelman</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Life">Life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=1" title="Edit section: Life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Poincaré was born on 29 April 1854 in Cité Ducale neighborhood, <a href="/wiki/Nancy,_Meurthe-et-Moselle" class="mw-redirect" title="Nancy, Meurthe-et-Moselle">Nancy, Meurthe-et-Moselle</a>, into an influential French family.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> His father Léon Poincaré (1828–1892) was a professor of medicine at the <a href="/wiki/University_of_Nancy" class="mw-redirect" title="University of Nancy">University of Nancy</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> His younger sister Aline married the spiritual philosopher <a href="/wiki/%C3%89mile_Boutroux" title="Émile Boutroux">Émile Boutroux</a>. Another notable member of Henri's family was his cousin, <a href="/wiki/Raymond_Poincar%C3%A9" title="Raymond Poincaré">Raymond Poincaré</a>, a fellow member of the <a href="/wiki/Acad%C3%A9mie_fran%C3%A7aise" class="mw-redirect" title="Académie française">Académie française</a>, who was <a href="/wiki/President_of_France" title="President of France">President of France</a> from 1913 to 1920, and three-time <a href="/wiki/Prime_Minister_of_France" title="Prime Minister of France">Prime Minister of France</a> between 1913 and 1929.<sup id="cite_ref-IEP_12-0" class="reference"><a href="#cite_note-IEP-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Education">Education</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=2" title="Edit section: Education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Henri_Poincar%C3%A9_maison_natale_Nancy_plaque.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Henri_Poincar%C3%A9_maison_natale_Nancy_plaque.jpg/200px-Henri_Poincar%C3%A9_maison_natale_Nancy_plaque.jpg" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Henri_Poincar%C3%A9_maison_natale_Nancy_plaque.jpg/300px-Henri_Poincar%C3%A9_maison_natale_Nancy_plaque.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Henri_Poincar%C3%A9_maison_natale_Nancy_plaque.jpg/400px-Henri_Poincar%C3%A9_maison_natale_Nancy_plaque.jpg 2x" data-file-width="2560" data-file-height="1920" /></a><figcaption> Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy</figcaption></figure> <p>During his childhood he was seriously ill for a time with <a href="/wiki/Diphtheria" title="Diphtheria">diphtheria</a> and received special instruction from his mother, Eugénie Launois (1830–1897). </p><p>In 1862, Henri entered the Lycée in <a href="/wiki/Nancy,_Meurthe-et-Moselle" class="mw-redirect" title="Nancy, Meurthe-et-Moselle">Nancy</a> (now renamed the <a href="/w/index.php?title=Lyc%C3%A9e_Henri-Poincar%C3%A9&action=edit&redlink=1" class="new" title="Lycée Henri-Poincaré (page does not exist)">Lycée Henri-Poincaré</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://fr.wikipedia.org/wiki/Lyc%C3%A9e_Henri-Poincar%C3%A9" class="extiw" title="fr:Lycée Henri-Poincaré">fr</a>]</span> in his honour, along with <a href="/wiki/Henri_Poincar%C3%A9_University" title="Henri Poincaré University">Henri Poincaré University</a>, also in Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the <a href="/wiki/Concours_g%C3%A9n%C3%A9ral" title="Concours général">concours général</a>, a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best".<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> However, poor eyesight and a tendency towards absentmindedness may explain these difficulties.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> He graduated from the Lycée in 1871 with a <a href="/wiki/Baccalaur%C3%A9at" title="Baccalauréat">baccalauréat</a> in both letters and sciences. </p><p>During the <a href="/wiki/Franco-Prussian_War" title="Franco-Prussian War">Franco-Prussian War</a> of 1870, he served alongside his father in the <a href="/wiki/Ambulance_Corps" class="mw-redirect" title="Ambulance Corps">Ambulance Corps</a>. </p><p>Poincaré entered the <a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a> as the top qualifier in 1873 and graduated in 1875. There he studied mathematics as a student of <a href="/wiki/Charles_Hermite" title="Charles Hermite">Charles Hermite</a>, continuing to excel and publishing his first paper (<i>Démonstration nouvelle des propriétés de l'indicatrice d'une surface</i>) in 1874. From November 1875 to June 1878 he studied at the <a href="/wiki/%C3%89cole_des_Mines" class="mw-redirect" title="École des Mines">École des Mines</a>, while continuing the study of mathematics in addition to the <a href="/wiki/Mining_engineering" title="Mining engineering">mining engineering</a> syllabus, and received the degree of ordinary mining engineer in March 1879.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>As a graduate of the École des Mines, he joined the <a href="/wiki/Corps_des_Mines" class="mw-redirect" title="Corps des Mines">Corps des Mines</a> as an inspector for the <a href="/wiki/Vesoul" title="Vesoul">Vesoul</a> region in northeast France. He was on the scene of a mining disaster at <a href="/wiki/Magny-l%C3%A8s-Jussey" title="Magny-lès-Jussey">Magny</a> in August 1879 in which 18 miners died. He carried out the official investigation into the accident in a characteristically thorough and humane way. </p><p>At the same time, Poincaré was preparing for his <a href="/wiki/Doctorate_in_Science" class="mw-redirect" title="Doctorate in Science">Doctorate in Science</a> in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of <a href="/wiki/Differential_equations" class="mw-redirect" title="Differential equations">differential equations</a>. It was named <i>Sur les propriétés des fonctions définies par les équations aux différences partielles</i>. Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the <a href="/wiki/Solar_System" title="Solar System">Solar System</a>. Poincaré graduated from the <a href="/wiki/University_of_Paris" title="University of Paris">University of Paris</a> in 1879. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Young_Poincare.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Young_Poincare.jpg/170px-Young_Poincare.jpg" decoding="async" width="170" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Young_Poincare.jpg/255px-Young_Poincare.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/d/db/Young_Poincare.jpg 2x" data-file-width="283" data-file-height="388" /></a><figcaption>The young Henri Poincaré in 1887 at the age of 33</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="First_scientific_achievements">First scientific achievements</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=3" title="Edit section: First scientific achievements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After receiving his degree, Poincaré began teaching as junior <a href="/wiki/Lecturer" title="Lecturer">lecturer</a> in mathematics at the <a href="/wiki/Caen_University" class="mw-redirect" title="Caen University">University of Caen</a> in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of <a href="/wiki/Automorphic_function" title="Automorphic function">automorphic functions</a>. </p><p>There, in <a href="/wiki/Caen" title="Caen">Caen</a>, he met his future wife, Louise Poulain d'Andecy (1857–1934), granddaughter of <a href="/wiki/Isidore_Geoffroy_Saint-Hilaire" title="Isidore Geoffroy Saint-Hilaire">Isidore Geoffroy Saint-Hilaire</a> and great-granddaughter of <a href="/wiki/%C3%89tienne_Geoffroy_Saint-Hilaire" title="Étienne Geoffroy Saint-Hilaire">Étienne Geoffroy Saint-Hilaire</a> and on 20 April 1881, they married.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893). </p><p>Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the <a href="/wiki/University_of_Paris" title="University of Paris">University of Paris</a>; he accepted the invitation. During the years 1883 to 1897, he taught <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">mathematical analysis</a> in the <a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a>. </p><p>In 1881–1882, Poincaré created a new branch of mathematics: <a href="/wiki/Qualitative_theory_of_differential_equations" title="Qualitative theory of differential equations">qualitative theory of differential equations</a>. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a> and <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Career">Career</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=4" title="Edit section: Career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>He never fully abandoned his career in the mining administration to mathematics. He worked at the <a href="/w/index.php?title=Ministry_of_Public_Services&action=edit&redlink=1" class="new" title="Ministry of Public Services (page does not exist)">Ministry of Public Services</a> as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the <a href="/wiki/Corps_des_Mines" class="mw-redirect" title="Corps des Mines">Corps des Mines</a> in 1893 and inspector general in 1910. </p><p>Beginning in 1881 and for the rest of his career, he taught at the <a href="/wiki/University_of_Paris" title="University of Paris">University of Paris</a> (the <a href="/wiki/University_of_Paris" title="University of Paris">Sorbonne</a>). He was initially appointed as the <i>maître de conférences d'analyse</i> (associate professor of analysis).<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability,<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> and Celestial Mechanics and Astronomy. </p><p>In 1887, at the young age of 32, Poincaré was elected to the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a>. He became its president in 1906, and was elected to the <a href="/wiki/Acad%C3%A9mie_fran%C3%A7aise" class="mw-redirect" title="Académie française">Académie française</a> on 5 March 1908. </p><p>In 1887, he won <a href="/wiki/Oscar_II_of_Sweden" class="mw-redirect" title="Oscar II of Sweden">Oscar II, King of Sweden</a>'s mathematical competition for a resolution of the <a href="/wiki/Three-body_problem" title="Three-body problem">three-body problem</a> concerning the free motion of multiple orbiting bodies. (See <a href="#Three-body_problem">three-body problem</a> section below.) </p><p>In 1893, Poincaré joined the French <a href="/wiki/Bureau_des_Longitudes" title="Bureau des Longitudes">Bureau des Longitudes</a>, which engaged him in the <a href="/wiki/Clock_synchronization" title="Clock synchronization">synchronisation of time</a> around the world. In 1897 Poincaré backed an unsuccessful proposal for the <a href="/wiki/Decimal_degrees" title="Decimal degrees">decimalisation of circular measure</a>, and hence time and <a href="/wiki/Longitude" title="Longitude">longitude</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See <a href="#Work_on_relativity">work on relativity</a> section below.) </p><p>In 1904, he intervened in the <a href="/wiki/Dreyfus_affair" title="Dreyfus affair">trials</a> of <a href="/wiki/Alfred_Dreyfus" title="Alfred Dreyfus">Alfred Dreyfus</a>, attacking the spurious scientific claims regarding evidence brought against Dreyfus. </p><p>Poincaré was the President of the <a href="/wiki/Soci%C3%A9t%C3%A9_astronomique_de_France" title="Société astronomique de France">Société Astronomique de France (SAF)</a>, the French astronomical society, from 1901 to 1903.<sup id="cite_ref-BSAF1911_20-0" class="reference"><a href="#cite_note-BSAF1911-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Students">Students</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=5" title="Edit section: Students"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Poincaré had two notable doctoral students at the University of Paris, <a href="/wiki/Louis_Bachelier" title="Louis Bachelier">Louis Bachelier</a> (1900) and <a href="/wiki/Dimitrie_Pompeiu" title="Dimitrie Pompeiu">Dimitrie Pompeiu</a> (1905).<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Death">Death</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=6" title="Edit section: Death"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1912, Poincaré underwent surgery for a <a href="/wiki/Prostate" title="Prostate">prostate</a> problem and subsequently died from an <a href="/wiki/Embolism" title="Embolism">embolism</a> on 17 July 1912, in Paris. He was 58 years of age. He is buried in the Poincaré family vault in the <a href="/wiki/Cimeti%C3%A8re_du_Montparnasse" class="mw-redirect" title="Cimetière du Montparnasse">Cemetery of Montparnasse</a>, Paris, in section 16 close to the gate Rue Émile-Richard. </p><p> A former French Minister of Education, <a href="/wiki/Claude_All%C3%A8gre" title="Claude Allègre">Claude Allègre</a>, proposed in 2004 that Poincaré be reburied in the <a href="/wiki/Panth%C3%A9on,_Paris" class="mw-redirect" title="Panthéon, Paris">Panthéon</a> in Paris, which is reserved for French citizens of the highest honour.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Poincar%C3%A9_gravestone.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Poincar%C3%A9_gravestone.jpg/170px-Poincar%C3%A9_gravestone.jpg" decoding="async" width="170" height="267" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Poincar%C3%A9_gravestone.jpg/255px-Poincar%C3%A9_gravestone.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Poincar%C3%A9_gravestone.jpg/340px-Poincar%C3%A9_gravestone.jpg 2x" data-file-width="2326" data-file-height="3648" /></a><figcaption>The Poincaré family grave at the <a href="/wiki/Cimeti%C3%A8re_du_Montparnasse" class="mw-redirect" title="Cimetière du Montparnasse">Cimetière du Montparnasse</a></figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Work">Work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=7" title="Edit section: Work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Summary">Summary</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=8" title="Edit section: Summary"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Poincaré made many contributions to different fields of pure and applied mathematics such as: <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a>, <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a>, <a href="/wiki/Optics" title="Optics">optics</a>, <a href="/wiki/Electricity" title="Electricity">electricity</a>, <a href="/wiki/Telegraphy" title="Telegraphy">telegraphy</a>, <a href="/wiki/Capillarity" class="mw-redirect" title="Capillarity">capillarity</a>, <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elasticity</a>, <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>, <a href="/wiki/Potential_theory" title="Potential theory">potential theory</a>, <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a>, <a href="/wiki/Theory_of_relativity" title="Theory of relativity">theory of relativity</a> and <a href="/wiki/Physical_cosmology" title="Physical cosmology">physical cosmology</a>. </p><p>He was also a popularizer of mathematics and physics and wrote several books for the lay public. </p><p>Among the specific topics he contributed to are the following: </p> <ul><li><a href="/wiki/Algebraic_topology" title="Algebraic topology">algebraic topology</a> (a field that Poincaré virtually invented)</li> <li>the theory of analytic functions of <a href="/wiki/Several_complex_variables" class="mw-redirect" title="Several complex variables">several complex variables</a></li> <li><a href="/wiki/Abelian_variety" title="Abelian variety">the theory of abelian functions</a></li> <li><a href="/wiki/Algebraic_geometry" title="Algebraic geometry">algebraic geometry</a></li> <li>the <a href="/wiki/Poincar%C3%A9_conjecture" title="Poincaré conjecture">Poincaré conjecture</a>, proven in 2003 by <a href="/wiki/Grigori_Perelman" title="Grigori Perelman">Grigori Perelman</a>.</li> <li><a href="/wiki/Poincar%C3%A9_recurrence_theorem" title="Poincaré recurrence theorem">Poincaré recurrence theorem</a></li> <li><a href="/wiki/Hyperbolic_geometry" title="Hyperbolic geometry">hyperbolic geometry</a></li> <li><a href="/wiki/Number_theory" title="Number theory">number theory</a></li> <li>the <a href="/wiki/Three-body_problem" title="Three-body problem">three-body problem</a></li> <li>the theory of <a href="/wiki/Diophantine_equation" title="Diophantine equation">diophantine equations</a></li> <li><a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a></li> <li><a href="/wiki/Special_relativity" title="Special relativity">special relativity</a></li> <li>the <a href="/wiki/Fundamental_group" title="Fundamental group">fundamental group</a></li> <li>In the field of <a href="/wiki/Differential_equations" class="mw-redirect" title="Differential equations">differential equations</a> Poincaré has given many results that are critical for the qualitative theory of differential equations, for example the <a href="/wiki/Poincar%C3%A9_homology_sphere" class="mw-redirect" title="Poincaré homology sphere">Poincaré sphere</a> and the <a href="/wiki/Poincar%C3%A9_map" title="Poincaré map">Poincaré map</a>.</li> <li>Poincaré on "everybody's belief" in the <a href="https://en.wikiquote.org/wiki/Henri_Poincar%C3%A9" class="extiw" title="q:Henri Poincaré"><i>Normal Law of Errors</i></a> (see <a href="/wiki/Normal_distribution" title="Normal distribution">normal distribution</a> for an account of that "law")</li> <li>Published an influential paper providing a novel mathematical argument in support of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>.<sup id="cite_ref-McCormmach_8-1" class="reference"><a href="#cite_note-McCormmach-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Irons_23-0" class="reference"><a href="#cite_note-Irons-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Three-body_problem">Three-body problem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=9" title="Edit section: Three-body problem"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The problem of finding the general solution to the motion of more than two orbiting bodies in the <a href="/wiki/Solar_System" title="Solar System">Solar System</a> had eluded mathematicians since <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton's</a> time. This was known originally as the three-body problem and later the <a href="/wiki/N-body_problem" title="N-body problem"><i>n</i>-body problem</a>, where <i>n</i> is any number of more than two orbiting bodies. The <i>n</i>-body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, <a href="/wiki/Oscar_II_of_Sweden" class="mw-redirect" title="Oscar II of Sweden">Oscar II, King of Sweden</a>, advised by <a href="/wiki/G%C3%B6sta_Mittag-Leffler" title="Gösta Mittag-Leffler">Gösta Mittag-Leffler</a>, established a prize for anyone who could find the solution to the problem. The announcement was quite specific: </p> <blockquote><p>Given a system of arbitrarily many mass points that attract each according to <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law</a>, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series <a href="/wiki/Uniform_convergence" title="Uniform convergence">converges uniformly</a>.</p></blockquote> <p>In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished <a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a>, said, <i>"This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics."</i> (The first version of his contribution even contained a serious error; for details see the article by Diacu<sup id="cite_ref-diacu_24-0" class="reference"><a href="#cite_note-diacu-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> and the book by <a href="/wiki/June_Barrow-Green" title="June Barrow-Green">Barrow-Green</a><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup>). The version finally printed<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> contained many important ideas which led to the <a href="/wiki/Chaos_theory" title="Chaos theory">theory of chaos</a>. The problem as stated originally was finally solved by <a href="/wiki/Karl_F._Sundman" title="Karl F. Sundman">Karl F. Sundman</a> for <i>n</i> = 3 in 1912 and was generalised to the case of <i>n</i> > 3 bodies by <a href="/wiki/Qiudong_Wang" title="Qiudong Wang">Qiudong Wang</a> in the 1990s. The series solutions have very slow convergence. It would take millions of terms to determine the motion of the particles for even very short intervals of time, so they are unusable in numerical work.<sup id="cite_ref-diacu_24-1" class="reference"><a href="#cite_note-diacu-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Work_on_relativity">Work on relativity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=10" title="Edit section: Work on relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Lorentz_ether_theory" title="Lorentz ether theory">Lorentz ether theory</a> and <a href="/wiki/History_of_special_relativity" title="History of special relativity">History of special relativity</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Curie_and_Poincare_1911_Solvay.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Curie_and_Poincare_1911_Solvay.jpg/220px-Curie_and_Poincare_1911_Solvay.jpg" decoding="async" width="220" height="151" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Curie_and_Poincare_1911_Solvay.jpg/330px-Curie_and_Poincare_1911_Solvay.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Curie_and_Poincare_1911_Solvay.jpg/440px-Curie_and_Poincare_1911_Solvay.jpg 2x" data-file-width="452" data-file-height="310" /></a><figcaption><a href="/wiki/Marie_Curie" title="Marie Curie">Marie Curie</a> and Poincaré talk at the 1911 <a href="/wiki/Solvay_Conference" title="Solvay Conference">Solvay Conference</a>.</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Local_time">Local time</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=11" title="Edit section: Local time"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "<a href="/wiki/Luminiferous_aether" title="Luminiferous aether">luminiferous aether</a>"), could be synchronised. At the same time Dutch theorist <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Hendrik Lorentz</a> was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t^{\prime }=t-vx/c^{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mi>t</mi> <mo>−</mo> <mi>v</mi> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t^{\prime }=t-vx/c^{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fd7716b2d21130688c8f4161f4d66e4d1d7cdba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.371ex; height:3.176ex;" alt="{\displaystyle t^{\prime }=t-vx/c^{2}\,}"></span><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> and introduced the hypothesis of <a href="/wiki/Length_contraction" title="Length contraction">length contraction</a> to explain the failure of optical and electrical experiments to detect motion relative to the aether (see <a href="/wiki/Michelson%E2%80%93Morley_experiment" title="Michelson–Morley experiment">Michelson–Morley experiment</a>).<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In <a href="https://en.wikisource.org/wiki/The_Measure_of_Time" class="extiw" title="s:The Measure of Time">The Measure of Time</a> (1898), Poincaré said, "A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a <a href="/wiki/Postulate" class="mw-redirect" title="Postulate">postulate</a> to give physical theories the simplest form.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronised by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.<sup id="cite_ref-action_30-0" class="reference"><a href="#cite_note-action-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Principle_of_relativity_and_Lorentz_transformations">Principle of relativity and Lorentz transformations</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=12" title="Edit section: Principle of relativity and Lorentz transformations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/History_of_Lorentz_transformations" title="History of Lorentz transformations">History of Lorentz transformations</a></div> <p>In 1881 Poincaré described <a href="/wiki/Hyperbolic_geometry" title="Hyperbolic geometry">hyperbolic geometry</a> in terms of the <a href="/wiki/Hyperboloid_model" title="Hyperboloid model">hyperboloid model</a>, formulating transformations leaving invariant the <a href="/wiki/Lorentz_interval" class="mw-redirect" title="Lorentz interval">Lorentz interval</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}-z^{2}=-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}-z^{2}=-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6614e8b9d05f37ee7ecfa308185207376d91dce7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.493ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}-z^{2}=-1}"></span>, which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> In addition, Poincaré's other models of hyperbolic geometry (<a href="/wiki/Poincar%C3%A9_disk_model" title="Poincaré disk model">Poincaré disk model</a>, <a href="/wiki/Poincar%C3%A9_half-plane_model" title="Poincaré half-plane model">Poincaré half-plane model</a>) as well as the <a href="/wiki/Beltrami%E2%80%93Klein_model" title="Beltrami–Klein model">Beltrami–Klein model</a> can be related to the relativistic velocity space (see <a href="/wiki/Gyrovector_space" title="Gyrovector space">Gyrovector space</a>). </p><p>In 1892 Poincaré developed a <a href="/wiki/Mathematical_theory" class="mw-redirect" title="Mathematical theory">mathematical theory</a> of <a href="/wiki/Light" title="Light">light</a> including <a href="/wiki/Polarization_(waves)" title="Polarization (waves)">polarization</a>. His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the <a href="/wiki/Poincar%C3%A9_sphere_(optics)" class="mw-redirect" title="Poincaré sphere (optics)">Poincaré sphere</a>.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> It was shown that the Poincaré sphere possesses an underlying Lorentzian symmetry, by which it can be used as a geometrical representation of Lorentz transformations and velocity additions.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>He discussed the "principle of relative motion" in two papers in 1900<sup id="cite_ref-action_30-1" class="reference"><a href="#cite_note-action-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> and named it the <a href="/wiki/Principle_of_relativity" title="Principle of relativity">principle of relativity</a> in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest.<sup id="cite_ref-louis_36-0" class="reference"><a href="#cite_note-louis-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance". In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz.<sup id="cite_ref-univ-nantes_37-0" class="reference"><a href="#cite_note-univ-nantes-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law.<sup id="cite_ref-univ-nantes2_38-0" class="reference"><a href="#cite_note-univ-nantes2-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed. In the published version of that he wrote:<sup id="cite_ref-1905_paper_39-0" class="reference"><a href="#cite_note-1905_paper-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <blockquote><p>The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form: </p><dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{\prime }=k\ell \left(x+\varepsilon t\right)\!,\;t^{\prime }=k\ell \left(t+\varepsilon x\right)\!,\;y^{\prime }=\ell y,\;z^{\prime }=\ell z,\;k=1/{\sqrt {1-\varepsilon ^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mi>k</mi> <mi>ℓ</mi> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>+</mo> <mi>ε</mi> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mspace width="negativethinmathspace" /> <mo>,</mo> <mspace width="thickmathspace" /> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mi>k</mi> <mi>ℓ</mi> <mrow> <mo>(</mo> <mrow> <mi>t</mi> <mo>+</mo> <mi>ε</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mspace width="negativethinmathspace" /> <mo>,</mo> <mspace width="thickmathspace" /> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mi>ℓ</mi> <mi>y</mi> <mo>,</mo> <mspace width="thickmathspace" /> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mi>ℓ</mi> <mi>z</mi> <mo>,</mo> <mspace width="thickmathspace" /> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{\prime }=k\ell \left(x+\varepsilon t\right)\!,\;t^{\prime }=k\ell \left(t+\varepsilon x\right)\!,\;y^{\prime }=\ell y,\;z^{\prime }=\ell z,\;k=1/{\sqrt {1-\varepsilon ^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb1cc994ce4b5eb88dfb7500579faad07dd52457" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:67.139ex; height:3.509ex;" alt="{\displaystyle x^{\prime }=k\ell \left(x+\varepsilon t\right)\!,\;t^{\prime }=k\ell \left(t+\varepsilon x\right)\!,\;y^{\prime }=\ell y,\;z^{\prime }=\ell z,\;k=1/{\sqrt {1-\varepsilon ^{2}}}.}"></span></dd></dl></dd></dl></blockquote> <p>and showed that the arbitrary function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell \left(\varepsilon \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell \left(\varepsilon \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/448f79b16b164e60c74eab6721706b460ea5f56f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.25ex; height:2.843ex;" alt="{\displaystyle \ell \left(\varepsilon \right)}"></span> must be unity for all <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }"></span> (Lorentz had set <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell =1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell =1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/942a65b8d58f57930318142ad11ca4be77a53460" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.231ex; height:2.176ex;" alt="{\displaystyle \ell =1}"></span> by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/101d249c29d5d550f759172c0b4dd9dbc1279af1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.219ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}}"></span> is <a href="/wiki/Invariant_(mathematics)" title="Invariant (mathematics)">invariant</a>. He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ct{\sqrt {-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ct{\sqrt {-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd666a0ffc00a10a7f354c27f17cbadf8368e320" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.753ex; height:3.009ex;" alt="{\displaystyle ct{\sqrt {-1}}}"></span> as a fourth imaginary coordinate, and he used an early form of <a href="/wiki/Four-vector" title="Four-vector">four-vectors</a>.<sup id="cite_ref-long_40-0" class="reference"><a href="#cite_note-long-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit.<sup id="cite_ref-Genesis_4-Vectors_41-0" class="reference"><a href="#cite_note-Genesis_4-Vectors-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> So it was <a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Hermann Minkowski</a> who worked out the consequences of this notion in 1907.<sup id="cite_ref-Genesis_4-Vectors_41-1" class="reference"><a href="#cite_note-Genesis_4-Vectors-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Raum_und_Zeit_42-0" class="reference"><a href="#cite_note-Raum_und_Zeit-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Mass–energy_relation"><span id="Mass.E2.80.93energy_relation"></span>Mass–energy relation</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=13" title="Edit section: Mass–energy relation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Like <a href="/wiki/Mass%E2%80%93energy_equivalence#Electromagnetic_mass" title="Mass–energy equivalence">others</a> before, Poincaré (1900) discovered a relation between <a href="/wiki/Mass" title="Mass">mass</a> and <a href="/wiki/Electromagnetic_energy" class="mw-redirect" title="Electromagnetic energy">electromagnetic energy</a>. While studying the conflict between the <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">action/reaction principle</a> and <a href="/wiki/Lorentz_ether_theory" title="Lorentz ether theory">Lorentz ether theory</a>, he tried to determine whether the <a href="/wiki/Center_of_gravity" class="mw-redirect" title="Center of gravity">center of gravity</a> still moves with a uniform velocity when electromagnetic fields are included.<sup id="cite_ref-action_30-2" class="reference"><a href="#cite_note-action-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> He noticed that the action/reaction principle does not hold for matter alone, but that the electromagnetic field has its own momentum. Poincaré concluded that the electromagnetic field energy of an electromagnetic wave behaves like a fictitious <a href="/wiki/Fluid" title="Fluid">fluid</a> (<i>fluide fictif</i>) with a mass density of <i>E</i>/<i>c</i><sup>2</sup>. If the <a href="/wiki/Center_of_mass_frame" class="mw-redirect" title="Center of mass frame">center of mass frame</a> is defined by both the mass of matter <i>and</i> the mass of the fictitious fluid, and if the fictitious fluid is indestructible—<a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">it's neither created or destroyed</a>—then the motion of the center of mass frame remains uniform. But electromagnetic energy can be converted into other forms of energy. So Poincaré assumed that there exists a non-electric energy fluid at each point of space, into which electromagnetic energy can be transformed and which also carries a mass proportional to the energy. In this way, the motion of the center of mass remains uniform. Poincaré said that one should not be too surprised by these assumptions, since they are only mathematical fictions. </p><p>However, Poincaré's resolution led to a <a href="/wiki/Paradox" title="Paradox">paradox</a> when changing frames: if a Hertzian oscillator radiates in a certain direction, it will suffer a <a href="/wiki/Recoil" title="Recoil">recoil</a> from the inertia of the fictitious fluid. Poincaré performed a <a href="/wiki/Lorentz_boost" class="mw-redirect" title="Lorentz boost">Lorentz boost</a> (to order <i>v</i>/<i>c</i>) to the frame of the moving source. He noted that energy conservation holds in both frames, but that the <a href="/wiki/Momentum#Conservation" title="Momentum">law of conservation of momentum</a> is violated. This would allow <a href="/wiki/Perpetual_motion" title="Perpetual motion">perpetual motion</a>, a notion which he abhorred. The laws of nature would have to be different in the <a href="/wiki/Frames_of_reference" class="mw-redirect" title="Frames of reference">frames of reference</a>, and the relativity principle would not hold. Therefore, he argued that also in this case there has to be another compensating mechanism in the <a href="/wiki/Ether" title="Ether">ether</a>. </p><p>Poincaré himself came back to this topic in his St. Louis lecture (1904).<sup id="cite_ref-louis_36-1" class="reference"><a href="#cite_note-louis-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> He rejected<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> the possibility that energy carries mass and criticized his own solution to compensate the above-mentioned problems: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>The apparatus will recoil as if it were a cannon and the projected energy a ball, and that contradicts the principle of Newton, since our present projectile has no mass; it is not matter, it is energy. [..] Shall we say that the space which separates the oscillator from the receiver and which the disturbance must traverse in passing from one to the other, is not empty, but is filled not only with ether, but with air, or even in inter-planetary space with some subtile, yet ponderable fluid; that this matter receives the shock, as does the receiver, at the moment the energy reaches it, and recoils, when the disturbance leaves it? That would save Newton's principle, but it is not true. If the energy during its propagation remained always attached to some material substratum, this matter would carry the light along with it and Fizeau has shown, at least for the air, that there is nothing of the kind. Michelson and Morley have since confirmed this. We might also suppose that the motions of matter proper were exactly compensated by those of the ether; but that would lead us to the same considerations as those made a moment ago. The principle, if thus interpreted, could explain anything, since whatever the visible motions we could imagine hypothetical motions to compensate them. But if it can explain anything, it will allow us to foretell nothing; it will not allow us to choose between the various possible hypotheses, since it explains everything in advance. It therefore becomes useless. </p></blockquote> <p>In the above quote he refers to the Hertz assumption of total aether entrainment that was falsified by the <a href="/wiki/Fizeau_experiment" title="Fizeau experiment">Fizeau experiment</a> but that experiment does indeed show that that light is partially "carried along" with a substance. Finally in 1908<sup id="cite_ref-poinc08_44-0" class="reference"><a href="#cite_note-poinc08-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> he revisits the problem and ends with abandoning the principle of reaction altogether in favor of supporting a solution based in the inertia of aether itself. </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>But we have seen above that Fizeau's experiment does not permit of our retaining the theory of Hertz; it is necessary therefore to adopt the theory of Lorentz, and consequently to renounce the principle of reaction. </p></blockquote> <p>He also discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b16ea3f2c6ac5da9bd10f9b7fb44089f9285d4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.303ex; height:2.176ex;" alt="{\displaystyle \gamma m}"></span>, Abraham's theory of variable mass and <a href="/wiki/Walter_Kaufmann_(physicist)" title="Walter Kaufmann (physicist)">Kaufmann</a>'s experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of <a href="/wiki/Marie_Curie" title="Marie Curie">Marie Curie</a>. </p><p>It was <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>'s concept of <a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">mass–energy equivalence</a> (1905) that a body losing energy as radiation or heat was losing mass of amount <i>m</i> = <i>E</i>/<i>c</i><sup>2</sup> that resolved<sup id="cite_ref-darrigol_45-0" class="reference"><a href="#cite_note-darrigol-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Poincaré's paradox, without using any compensating mechanism within the ether.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> The Hertzian oscillator loses mass in the emission process, and momentum is conserved in any frame. However, concerning Poincaré's solution of the Center of Gravity problem, Einstein noted that Poincaré's formulation and his own from 1906 were mathematically equivalent.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Gravitational_waves">Gravitational waves</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=14" title="Edit section: Gravitational waves"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1905 Poincaré first proposed <a href="/wiki/Gravitational_waves" class="mw-redirect" title="Gravitational waves">gravitational waves</a> (<i>ondes gravifiques</i>) emanating from a body and propagating at the speed of light. He wrote: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>It has become important to examine this hypothesis more closely and in particular to ask in what ways it would require us to modify the laws of gravitation. That is what I have tried to determine; at first I was led to assume that the propagation of gravitation is not instantaneous, but happens with the speed of light.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-1905_paper_39-1" class="reference"><a href="#cite_note-1905_paper-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading4"><h4 id="Poincaré_and_Einstein"><span id="Poincar.C3.A9_and_Einstein"></span>Poincaré and Einstein</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=15" title="Edit section: Poincaré and Einstein"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Einstein's first paper on relativity was published three months after Poincaré's short paper,<sup id="cite_ref-1905_paper_39-2" class="reference"><a href="#cite_note-1905_paper-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> but before Poincaré's longer version.<sup id="cite_ref-long_40-1" class="reference"><a href="#cite_note-long-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> Einstein relied on the principle of relativity to derive the Lorentz transformations and used a similar clock synchronisation procedure (<a href="/wiki/Einstein_synchronisation" title="Einstein synchronisation">Einstein synchronisation</a>) to the one that Poincaré (1900) had described, but Einstein's paper was remarkable in that it contained no references at all. Poincaré never acknowledged Einstein's work on <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>. However, Einstein expressed sympathy with Poincaré's outlook obliquely in a letter to <a href="/wiki/Hans_Vaihinger" title="Hans Vaihinger">Hans Vaihinger</a> on 3 May 1919, when Einstein considered Vaihinger's general outlook to be close to his own and Poincaré's to be close to Vaihinger's.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> In public, Einstein acknowledged Poincaré posthumously in the text of a lecture in 1921 titled "<i>Geometrie und Erfahrung</i> (Geometry and Experience)" in connection with <a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean geometry</a>, but not in connection with special relativity. A few years before his death, Einstein commented on Poincaré as being one of the pioneers of relativity, saying "Lorentz had already recognized that the transformation named after him is essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further ....".<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Assessments_on_Poincaré_and_relativity"><span id="Assessments_on_Poincar.C3.A9_and_relativity"></span>Assessments on Poincaré and relativity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=16" title="Edit section: Assessments on Poincaré and relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/History_of_special_relativity" title="History of special relativity">History of special relativity</a> and <a href="/wiki/Relativity_priority_dispute" title="Relativity priority dispute">Relativity priority dispute</a></div> <p>Poincaré's work in the development of special relativity is well recognised,<sup id="cite_ref-darrigol_45-1" class="reference"><a href="#cite_note-darrigol-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> though most historians stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> Poincaré developed a similar physical interpretation of local time and noticed the connection to signal velocity, but contrary to Einstein he continued to use the ether-concept in his papers and argued that clocks at rest in the ether show the "true" time, and moving clocks show the local time. So Poincaré tried to keep the relativity principle in accordance with classical concepts, while Einstein developed a mathematically equivalent kinematics based on the new physical concepts of the relativity of space and time.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hentschel_PhD_53-0" class="reference"><a href="#cite_note-Hentschel_PhD-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p><p>While this is the view of most historians, a minority go much further, such as <a href="/wiki/E._T._Whittaker" title="E. T. Whittaker">E. T. Whittaker</a>, who held that Poincaré and Lorentz were the true discoverers of relativity.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Algebra_and_number_theory">Algebra and number theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=17" title="Edit section: Algebra and number theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Poincaré introduced <a href="/wiki/Group_theory" title="Group theory">group theory</a> to physics, and was the first to study the group of <a href="/wiki/Lorentz_transformations" class="mw-redirect" title="Lorentz transformations">Lorentz transformations</a>.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Poincaré_Lorentz_l’´electron_59-0" class="reference"><a href="#cite_note-Poincaré_Lorentz_l’´electron-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> He also made major contributions to the theory of discrete groups and their representations. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Mug_and_Torus_morph.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Mug_and_Torus_morph.gif/190px-Mug_and_Torus_morph.gif" decoding="async" width="190" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/26/Mug_and_Torus_morph.gif 1.5x" data-file-width="240" data-file-height="240" /></a><figcaption><div class="center" style="width:auto; margin-left:auto; margin-right:auto;">Topological transformation of a mug into a torus </div></figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Poincar%C3%A9-7.jpg" class="mw-file-description"><img alt="Title page to volume I of Les Méthodes Nouvelles de la Mécanique Céleste (1892)" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Poincar%C3%A9-7.jpg/120px-Poincar%C3%A9-7.jpg" decoding="async" width="120" height="192" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Poincar%C3%A9-7.jpg/180px-Poincar%C3%A9-7.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Poincar%C3%A9-7.jpg/240px-Poincar%C3%A9-7.jpg 2x" data-file-width="2534" data-file-height="4054" /></a><figcaption>Title page to volume I of <i>Les Méthodes Nouvelles de la Mécanique Céleste</i> (1892)</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Topology">Topology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=18" title="Edit section: Topology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The subject is clearly defined by <a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a> in his "Erlangen Program" (1872): the geometry invariants of arbitrary continuous transformation, a kind of geometry. The term "topology" was introduced, as suggested by <a href="/wiki/Johann_Benedict_Listing" title="Johann Benedict Listing">Johann Benedict Listing</a>, instead of previously used "Analysis situs". Some important concepts were introduced by <a href="/wiki/Enrico_Betti" title="Enrico Betti">Enrico Betti</a> and <a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Bernhard Riemann</a>. But the foundation of this science, for a space of any dimension, was created by Poincaré. His first article on this topic appeared in 1894.<sup id="cite_ref-FOOTNOTEStillwell2010419–435_60-0" class="reference"><a href="#cite_note-FOOTNOTEStillwell2010419–435-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p><p>His research in <a href="/wiki/Geometry" title="Geometry">geometry</a> led to the abstract topological definition of <a href="/wiki/Homotopy" title="Homotopy">homotopy</a> and <a href="/wiki/Homology_(mathematics)" title="Homology (mathematics)">homology</a>. He also first introduced the basic concepts and invariants of combinatorial topology, such as <a href="/wiki/Betti_number" title="Betti number">Betti numbers</a> and the <a href="/wiki/Fundamental_group" title="Fundamental group">fundamental group</a>. Poincaré proved a formula relating the number of edges, <a href="/wiki/Triangulated_irregular_network" title="Triangulated irregular network">vertices</a> and faces of <i>n</i>-dimensional <a href="/wiki/Polyhedron" title="Polyhedron">polyhedron</a> (the <a href="/wiki/Euler_characteristic" title="Euler characteristic">Euler–Poincaré theorem</a>) and gave the first precise formulation of the intuitive notion of dimension.<sup id="cite_ref-Aleksandrov_Poincaré_61-0" class="reference"><a href="#cite_note-Aleksandrov_Poincaré-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Astronomy_and_celestial_mechanics">Astronomy and celestial mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=19" title="Edit section: Astronomy and celestial mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Frame"><a href="/wiki/File:N-body_problem_(3).gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/f9/N-body_problem_%283%29.gif" decoding="async" width="182" height="174" class="mw-file-element" data-file-width="182" data-file-height="174" /></a><figcaption><div class="center" style="width:auto; margin-left:auto; margin-right:auto;"> Chaotic motion in three-body problem (computer simulation)</div></figcaption></figure> <p>Poincaré published two now classical monographs, "New Methods of Celestial Mechanics" (1892–1899) and "Lectures on Celestial Mechanics" (1905–1910). In them, he successfully applied the results of their research to the problem of the motion of three bodies and studied in detail the behavior of solutions (frequency, stability, asymptotic, and so on). They introduced the small parameter method, fixed points, integral invariants, variational equations, the convergence of the asymptotic expansions. Generalizing a theory of Bruns (1887), Poincaré showed that the three-body problem is not integrable. In other words, the general solution of the three-body problem can not be expressed in terms of <a href="/wiki/Algebra" title="Algebra">algebraic</a> and <a href="/wiki/Transcendental_functions" class="mw-redirect" title="Transcendental functions">transcendental functions</a> through unambiguous coordinates and velocities of the bodies. His work in this area was the first major achievement in celestial mechanics since <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </p><p>These monographs include an idea of Poincaré, which later became the basis for mathematical "<a href="/wiki/Chaos_theory" title="Chaos theory">chaos theory</a>" (see, in particular, the <a href="/wiki/Poincar%C3%A9_recurrence_theorem" title="Poincaré recurrence theorem">Poincaré recurrence theorem</a>) and the general theory of <a href="/wiki/Dynamical_system" title="Dynamical system">dynamical systems</a>. Poincaré authored important works on <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> for the <a href="/wiki/Hydrostatic_equilibrium" title="Hydrostatic equilibrium">equilibrium figures of a gravitating rotating fluid</a>. He introduced the important concept of <a href="/wiki/Bifurcation_theory" title="Bifurcation theory">bifurcation points</a> and proved the existence of equilibrium figures such as the non-ellipsoids, including ring-shaped and pear-shaped figures, and their stability. For this discovery, Poincaré received the Gold Medal of the Royal Astronomical Society (1900).<sup id="cite_ref-Gold_Medal_to_Poincaré_63-0" class="reference"><a href="#cite_note-Gold_Medal_to_Poincaré-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Differential_equations_and_mathematical_physics">Differential equations and mathematical physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=20" title="Edit section: Differential equations and mathematical physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After defending his doctoral thesis on the study of singular points of the system of <a href="/wiki/Differential_equations" class="mw-redirect" title="Differential equations">differential equations</a>, Poincaré wrote a series of memoirs under the title "On curves defined by differential equations" (1881–1882).<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> In these articles, he built a new branch of mathematics, called "<a href="/wiki/Qualitative_theory_of_differential_equations" title="Qualitative theory of differential equations">qualitative theory of differential equations</a>". Poincaré showed that even if the differential equation can not be solved in terms of known functions, yet from the very form of the equation, a wealth of information about the properties and behavior of the solutions can be found. In particular, Poincaré investigated the nature of the trajectories of the integral curves in the plane, gave a classification of singular points (<a href="/wiki/Saddle_point" title="Saddle point">saddle</a>, <a href="/wiki/Focus_(geometry)" title="Focus (geometry)">focus</a>, <a href="/wiki/Center_(algebra)" title="Center (algebra)">center</a>, <a href="/wiki/Vertex_(graph_theory)" title="Vertex (graph theory)">node</a>), introduced the concept of a <a href="/wiki/Limit_cycle" title="Limit cycle">limit cycle</a> and the <a href="/wiki/Control_flow#Loop_system_cross-reference_table" title="Control flow">loop index</a>, and showed that the number of limit cycles is always finite, except for some special cases. Poincaré also developed a general theory of integral invariants and solutions of the variational equations. For the <a href="/wiki/Finite_difference" title="Finite difference">finite-difference equations</a>, he created a new direction – the <a href="/wiki/Asymptotic" class="mw-redirect" title="Asymptotic">asymptotic</a> analysis of the solutions. He applied all these achievements to study practical problems of <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a> and <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a>, and the methods used were the basis of its topological works.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerycaption">The singular points of the integral curves</li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Phase_Portrait_Sadle.svg" class="mw-file-description" title="Saddle"><img alt="Saddle" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Phase_Portrait_Sadle.svg/120px-Phase_Portrait_Sadle.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Phase_Portrait_Sadle.svg/180px-Phase_Portrait_Sadle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Phase_Portrait_Sadle.svg/240px-Phase_Portrait_Sadle.svg.png 2x" data-file-width="177" data-file-height="177" /></a></span></div> <div class="gallerytext"> Saddle</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Phase_Portrait_Stable_Focus.svg" class="mw-file-description" title="Focus"><img alt="Focus" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Phase_Portrait_Stable_Focus.svg/120px-Phase_Portrait_Stable_Focus.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Phase_Portrait_Stable_Focus.svg/180px-Phase_Portrait_Stable_Focus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Phase_Portrait_Stable_Focus.svg/240px-Phase_Portrait_Stable_Focus.svg.png 2x" data-file-width="177" data-file-height="177" /></a></span></div> <div class="gallerytext"> Focus</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Phase_portrait_center.svg" class="mw-file-description" title="Center"><img alt="Center" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Phase_portrait_center.svg/120px-Phase_portrait_center.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Phase_portrait_center.svg/180px-Phase_portrait_center.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Phase_portrait_center.svg/240px-Phase_portrait_center.svg.png 2x" data-file-width="177" data-file-height="177" /></a></span></div> <div class="gallerytext"> Center</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Phase_Portrait_Stable_Node.svg" class="mw-file-description" title="Node"><img alt="Node" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Phase_Portrait_Stable_Node.svg/120px-Phase_Portrait_Stable_Node.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Phase_Portrait_Stable_Node.svg/180px-Phase_Portrait_Stable_Node.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Phase_Portrait_Stable_Node.svg/240px-Phase_Portrait_Stable_Node.svg.png 2x" data-file-width="177" data-file-height="177" /></a></span></div> <div class="gallerytext"> Node</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Character">Character</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=21" title="Edit section: Character"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Henri_Poincar%C3%A9_by_H_Manuel.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/0/0b/Henri_Poincar%C3%A9_by_H_Manuel.jpg/220px-Henri_Poincar%C3%A9_by_H_Manuel.jpg" decoding="async" width="220" height="322" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/0/0b/Henri_Poincar%C3%A9_by_H_Manuel.jpg/330px-Henri_Poincar%C3%A9_by_H_Manuel.jpg 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/0/0b/Henri_Poincar%C3%A9_by_H_Manuel.jpg/440px-Henri_Poincar%C3%A9_by_H_Manuel.jpg 2x" data-file-width="1956" data-file-height="2865" /></a><figcaption>Photographic portrait of H. Poincaré by Henri Manuel</figcaption></figure> <p>Poincaré's work habits have been compared to a <a href="/wiki/Bee" title="Bee">bee</a> flying from flower to flower. Poincaré was interested in the way his <a href="/wiki/Mind" title="Mind">mind</a> worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in <a href="/wiki/Paris" title="Paris">Paris</a>. He linked his way of <a href="/wiki/Thought" title="Thought">thinking</a> to how he made several discoveries. </p><p>The mathematician <a href="/wiki/Jean_Gaston_Darboux" title="Jean Gaston Darboux">Darboux</a> claimed he was <i>un intuitif</i> (an <a href="/wiki/Intuitive" class="mw-redirect" title="Intuitive">intuitive</a>), arguing that this is demonstrated by the fact that he worked so often by visual representation. <a href="/wiki/Jacques_Hadamard" title="Jacques Hadamard">Jacques Hadamard</a> wrote that Poincaré's research demonstrated marvelous clarity<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> and Poincaré himself wrote that he believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas. </p> <div class="mw-heading mw-heading3"><h3 id="Toulouse's_characterisation"><span id="Toulouse.27s_characterisation"></span>Toulouse's characterisation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=22" title="Edit section: Toulouse's characterisation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Poincaré's mental organisation was interesting not only to Poincaré himself but also to <a href="/wiki/%C3%89douard_Toulouse" title="Édouard Toulouse">Édouard Toulouse</a>, a <a href="/wiki/Psychologist" title="Psychologist">psychologist</a> of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled <i>Henri Poincaré</i> (1910).<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-google_68-0" class="reference"><a href="#cite_note-google-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> In it, he discussed Poincaré's regular schedule: </p> <ul><li>He worked during the same times each day in short periods of time. He undertook mathematical research for four hours a day, between 10 a.m. and noon then again from 5 p.m. to 7 p.m.. He would read articles in journals later in the evening.</li> <li>His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.</li> <li>He was <a href="/wiki/Ambidextrous" class="mw-redirect" title="Ambidextrous">ambidextrous</a> and <a href="/wiki/Nearsighted" class="mw-redirect" title="Nearsighted">nearsighted</a>.</li> <li>His ability to visualise what he heard proved particularly useful when he attended lectures, since his eyesight was so poor that he could not see properly what the lecturer wrote on the blackboard.</li></ul> <p>These abilities were offset to some extent by his shortcomings: </p> <ul><li>He was physically clumsy and <a href="/wiki/Art" title="Art">artistically</a> inept.</li> <li>He was always in a rush and disliked going back for changes or corrections.</li> <li>He never spent a long time on a problem since he believed that the <a href="/wiki/Subconscious" title="Subconscious">subconscious</a> would continue working on the problem <a href="/wiki/Human_multitasking" title="Human multitasking">while he consciously worked on another problem</a>.</li></ul> <p>In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré started from basic principles each time (O'Connor et al., 2002). </p><p>His method of thinking is well summarised as: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p><i>Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire</i> (accustomed to neglecting details and to looking only at mountain tops, he went from one peak to another with surprising rapidity, and the facts he discovered, clustering around their center, were instantly and automatically pigeonholed in his memory).</p><div class="templatequotecite">— <cite>Belliver (1956)</cite></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="Publications">Publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=23" title="Edit section: Publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6569792"><i>Leçons sur la théorie mathématique de la lumière</i></a> (in French). Paris: Carrè. 1889.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Le%C3%A7ons+sur+la+th%C3%A9orie+math%C3%A9matique+de+la+lumi%C3%A8re&rft.place=Paris&rft.pub=Carr%C3%A8&rft.date=1889&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6569792&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=10996590"><i>Solutions periodiques, non-existence des integrales uniformes, solutions asymptotiques</i></a> (in French). Vol. 1. Paris: Gauthier-Villars. 1892.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Solutions+periodiques%2C+non-existence+des+integrales+uniformes%2C+solutions+asymptotiques&rft.place=Paris&rft.pub=Gauthier-Villars&rft.date=1892&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D10996590&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=10997817"><i>Methodes de mm. Newcomb, Gylden, Lindstedt et Bohlin</i></a> (in French). Vol. 2. Paris: Gauthier-Villars. 1893.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Methodes+de+mm.+Newcomb%2C+Gylden%2C+Lindstedt+et+Bohlin&rft.place=Paris&rft.pub=Gauthier-Villars&rft.date=1893&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D10997817&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6571067"><i>Oscillations électriques</i></a> (in French). Paris: Carrè. 1894.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Oscillations+%C3%A9lectriques&rft.place=Paris&rft.pub=Carr%C3%A8&rft.date=1894&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6571067&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=10999338"><i>Invariants integraux, solutions periodiques du deuxieme genre, solutions doublement asymptotiques</i></a> (in French). Vol. 3. Paris: Gauthier-Villars. 1899.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Invariants+integraux%2C+solutions+periodiques+du+deuxieme+genre%2C+solutions+doublement+asymptotiques&rft.place=Paris&rft.pub=Gauthier-Villars&rft.date=1899&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D10999338&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=3901099"><i>Valeur de la science</i></a> (in French). Paris: Flammarion. 1900.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Valeur+de+la+science&rft.place=Paris&rft.pub=Flammarion&rft.date=1900&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D3901099&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=7156481"><i>Electricité et optique</i></a> (in French). Paris: Carrè & Naud. 1901.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electricit%C3%A9+et+optique&rft.place=Paris&rft.pub=Carr%C3%A8+%26+Naud&rft.date=1901&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D7156481&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=3901686"><i>Science et l'hypothèse</i></a> (in French). Paris: Flammarion. 1902.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Science+et+l%27hypoth%C3%A8se&rft.place=Paris&rft.pub=Flammarion&rft.date=1902&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D3901686&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6568325"><i>Thermodynamique</i></a> (in French). Paris: Gauthier-Villars. 1908.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamique&rft.place=Paris&rft.pub=Gauthier-Villars&rft.date=1908&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6568325&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=3902281"><i>Dernières pensées</i></a> (in French). Paris: Flammarion. 1913.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Derni%C3%A8res+pens%C3%A9es&rft.place=Paris&rft.pub=Flammarion&rft.date=1913&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D3902281&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=10947130"><i>Science et méthode</i></a>. London: Nelson and Sons. 1914.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Science+et+m%C3%A9thode&rft.place=London&rft.pub=Nelson+and+Sons&rft.date=1914&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D10947130&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Honours">Honours</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=24" title="Edit section: Honours"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Awards</b> </p> <ul><li>Oscar II, King of Sweden's mathematical competition (1887)</li> <li>Foreign member of the <a href="/wiki/Royal_Netherlands_Academy_of_Arts_and_Sciences" title="Royal Netherlands Academy of Arts and Sciences">Royal Netherlands Academy of Arts and Sciences</a> (1897)<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a> (1899)</li> <li><a href="/wiki/Gold_Medal_of_the_Royal_Astronomical_Society" title="Gold Medal of the Royal Astronomical Society">Gold Medal of the Royal Astronomical Society</a> of London (1900)</li> <li><a href="/wiki/Bolyai_Prize" title="Bolyai Prize">Bolyai Prize</a> (1905)</li> <li><a href="/wiki/Matteucci_Medal" title="Matteucci Medal">Matteucci Medal</a> (1905)</li> <li><a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a> (1906)</li> <li><a href="/wiki/Acad%C3%A9mie_fran%C3%A7aise" class="mw-redirect" title="Académie française">Académie française</a> (1909)</li> <li><a href="/wiki/Bruce_Medal" title="Bruce Medal">Bruce Medal</a> (1911)</li></ul> <p><b>Named after him</b> </p> <ul><li><a href="/wiki/Institut_Henri_Poincar%C3%A9" title="Institut Henri Poincaré">Institut Henri Poincaré</a> (mathematics and theoretical physics centre)</li> <li><a href="/wiki/Poincar%C3%A9_Prize" class="mw-redirect" title="Poincaré Prize">Poincaré Prize</a> (Mathematical Physics International Prize)</li> <li><a href="/wiki/Annales_Henri_Poincar%C3%A9" title="Annales Henri Poincaré">Annales Henri Poincaré</a> (Scientific Journal)</li> <li>Poincaré Seminar (nicknamed "<a href="/wiki/Bourbaphy" class="mw-redirect" title="Bourbaphy">Bourbaphy</a>")</li> <li>The crater <a href="/wiki/Poincar%C3%A9_(crater)" title="Poincaré (crater)">Poincaré</a> on the Moon</li> <li><a href="/wiki/Asteroid" title="Asteroid">Asteroid</a> <a href="/wiki/2021_Poincar%C3%A9" class="mw-redirect" title="2021 Poincaré">2021 Poincaré</a></li> <li><a href="/wiki/List_of_things_named_after_Henri_Poincar%C3%A9" title="List of things named after Henri Poincaré">List of things named after Henri Poincaré</a></li></ul> <p>Henri Poincaré did not receive the <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a>, but he had influential advocates like <a href="/wiki/Henri_Becquerel" title="Henri Becquerel">Henri Becquerel</a> or committee member <a href="/wiki/G%C3%B6sta_Mittag-Leffler" title="Gösta Mittag-Leffler">Gösta Mittag-Leffler</a>.<sup id="cite_ref-gray-biography_70-0" class="reference"><a href="#cite_note-gray-biography-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> The nomination archive reveals that Poincaré received a total of 51 nominations between 1904 and 1912, the year of his death.<sup id="cite_ref-nomination_database_72-0" class="reference"><a href="#cite_note-nomination_database-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> Of the 58 nominations for the 1910 Nobel Prize, 34 named Poincaré.<sup id="cite_ref-nomination_database_72-1" class="reference"><a href="#cite_note-nomination_database-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> Nominators included Nobel laureates <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Hendrik Lorentz</a> and <a href="/wiki/Pieter_Zeeman" title="Pieter Zeeman">Pieter Zeeman</a> (both of 1902), <a href="/wiki/Marie_Curie" title="Marie Curie">Marie Curie</a> (of 1903), <a href="/wiki/Albert_Michelson" class="mw-redirect" title="Albert Michelson">Albert Michelson</a> (of 1907), <a href="/wiki/Gabriel_Lippmann" title="Gabriel Lippmann">Gabriel Lippmann</a> (of 1908) and <a href="/wiki/Guglielmo_Marconi" title="Guglielmo Marconi">Guglielmo Marconi</a> (of 1909).<sup id="cite_ref-nomination_database_72-2" class="reference"><a href="#cite_note-nomination_database-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> </p><p>The fact that renowned <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physicists</a> like Poincaré, <a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Boltzmann</a> or <a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a> were not awarded the <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize</a> is seen as evidence that the Nobel committee had more regard for experimentation than theory.<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> In Poincaré's case, several of those who nominated him pointed out that the greatest problem was to name a specific discovery, invention, or technique.<sup id="cite_ref-gray-biography_70-1" class="reference"><a href="#cite_note-gray-biography-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Philosophy">Philosophy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=25" title="Edit section: Philosophy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Poincar%C3%A9-16.jpg" class="mw-file-description"><img alt="First page of Science and hypothesis (1905)" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Poincar%C3%A9-16.jpg/120px-Poincar%C3%A9-16.jpg" decoding="async" width="120" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Poincar%C3%A9-16.jpg/180px-Poincar%C3%A9-16.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Poincar%C3%A9-16.jpg/240px-Poincar%C3%A9-16.jpg 2x" data-file-width="1926" data-file-height="3225" /></a><figcaption>First page of <i>Science and hypothesis</i> (1905)</figcaption></figure> <p>Poincaré had <a href="/wiki/Philosophical" class="mw-redirect" title="Philosophical">philosophical</a> views opposite to those of <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> and <a href="/wiki/Gottlob_Frege" title="Gottlob Frege">Gottlob Frege</a>, who believed that mathematics was a branch of <a href="/wiki/Logic" title="Logic">logic</a>. Poincaré strongly disagreed, claiming that <a href="/wiki/Intuition_(knowledge)" class="mw-redirect" title="Intuition (knowledge)">intuition</a> was the life of mathematics. Poincaré gives an interesting point of view in his 1902 book <i><a href="/wiki/Science_and_Hypothesis" title="Science and Hypothesis">Science and Hypothesis</a></i>: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.</p></blockquote> <p>Poincaré believed that <a href="/wiki/Arithmetic" title="Arithmetic">arithmetic</a> is <a href="/wiki/Analytic/synthetic_distinction" class="mw-redirect" title="Analytic/synthetic distinction">synthetic</a>. He argued that <a href="/wiki/Peano%27s_axioms" class="mw-redirect" title="Peano's axioms">Peano's axioms</a> cannot be proven non-circularly with the <a href="/wiki/Inductive_reasoning" title="Inductive reasoning">principle of induction</a> (Murzi, 1998), therefore concluding that arithmetic is <i><a href="/wiki/A_priori_and_a_posteriori" title="A priori and a posteriori">a priori</a></i> <a href="/wiki/Analytic%E2%80%93synthetic_distinction" title="Analytic–synthetic distinction">synthetic and not analytic</a>. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were similar to those of <a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Immanuel Kant</a> (Kolak, 2001, Folina 1992). He strongly opposed <a href="/wiki/Cantorian" class="mw-redirect" title="Cantorian">Cantorian</a> <a href="/wiki/Set_theory" title="Set theory">set theory</a>, objecting to its use of <a href="/wiki/Impredicativity" title="Impredicativity">impredicative</a> definitions<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2018)">citation needed</span></a></i>]</sup>. </p><p>However, Poincaré did not share <a href="/wiki/Kantianism" title="Kantianism">Kantian views</a> in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of <a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean space</a> can be known analytically. Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as "<a href="/wiki/Conventionalism" title="Conventionalism">conventionalism</a>".<sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> Poincaré believed that <a href="/wiki/Newton%27s_first_law" class="mw-redirect" title="Newton's first law">Newton's first law</a> was not empirical but is a conventional framework assumption for <a href="/wiki/Mechanics" title="Mechanics">mechanics</a> (Gargani, 2012).<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> He also believed that the geometry of <a href="/wiki/Physical_space" class="mw-redirect" title="Physical space">physical space</a> is conventional. He considered examples in which either the geometry of the physical fields or <a href="/wiki/Gradients" class="mw-redirect" title="Gradients">gradients</a> of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a <a href="/wiki/Euclidean_space" title="Euclidean space">Euclidean space</a> where the rulers are expanded or shrunk by a <a href="/wiki/Variable_(mathematics)" title="Variable (mathematics)">variable</a> heat distribution. However, Poincaré thought that we were so accustomed to <a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a> that we would prefer to change the physical laws to save Euclidean geometry rather than shift to non-Euclidean physical geometry.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Free_will">Free will</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=26" title="Edit section: Free will"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Poincaré's famous lectures before the Société de Psychologie in Paris (published as <i><a href="/wiki/Science_and_Hypothesis" title="Science and Hypothesis">Science and Hypothesis</a></i>, <i><a href="/wiki/The_Value_of_Science" title="The Value of Science">The Value of Science</a></i>, and <i>Science and Method</i>) were cited by <a href="/wiki/Jacques_Hadamard" title="Jacques Hadamard">Jacques Hadamard</a> as the source for the idea that <a href="/wiki/Creativity" title="Creativity">creativity</a> and <a href="/wiki/Innovation" title="Innovation">invention</a> consist of two mental stages, first random combinations of possible solutions to a problem, followed by a <a href="/wiki/Critical_thinking" title="Critical thinking">critical</a> <a href="/wiki/Evaluation" title="Evaluation">evaluation</a>.<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup> </p><p>Although he most often spoke of a <a href="/wiki/Deterministic" class="mw-redirect" title="Deterministic">deterministic</a> <a href="/wiki/Universe" title="Universe">universe</a>, Poincaré said that the <a href="/wiki/Subconscious" title="Subconscious">subconscious</a> generation of new possibilities involves <a href="/wiki/Randomness" title="Randomness">chance</a>. </p> <blockquote> <p>It is certain that the combinations which present themselves to the mind in a kind of sudden illumination after a somewhat prolonged period of unconscious work are generally useful and fruitful combinations... all the combinations are formed as a result of the automatic action of the subliminal ego, but those only which are interesting find their way into the field of consciousness... A few only are harmonious, and consequently at once useful and beautiful, and they will be capable of affecting the geometrician's special sensibility I have been speaking of; which, once aroused, will direct our attention upon them, and will thus give them the opportunity of becoming conscious... In the subliminal ego, on the contrary, there reigns what I would call liberty, if one could give this name to the mere absence of discipline and to disorder born of chance.<sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> </p> </blockquote> <p>Poincaré's two stages—random combinations followed by selection—became the basis for <a href="/wiki/Daniel_Dennett" title="Daniel Dennett">Daniel Dennett</a>'s two-stage model of <a href="/wiki/Free_will" title="Free will">free will</a>.<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=27" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Poincaré's_writings_in_English_translation"><span id="Poincar.C3.A9.27s_writings_in_English_translation"></span>Poincaré's writings in English translation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=28" title="Edit section: Poincaré's writings in English translation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Popular writings on the <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>: </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_Henri1902–1908" class="citation cs2">Poincaré, Henri (1902–1908), <a rel="nofollow" class="external text" href="https://archive.org/details/foundationsscie01poingoog"><i>The Foundations of Science</i></a>, New York: Science Press</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Foundations+of+Science&rft.place=New+York&rft.pub=Science+Press&rft.date=1902%2F1908&rft.au=Poincar%C3%A9%2C+Henri&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffoundationsscie01poingoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>; reprinted in 1921; this book includes the English translations of Science and Hypothesis (1902), The Value of Science (1905), Science and Method (1908).</li> <li>1905. "<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a class="external text" href="https://en.wikisource.org/wiki/Science_and_Hypothesis"><i>Science and Hypothesis</i></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Science+and+Hypothesis&rft_id=https%3A%2F%2Fen.wikisource.org%2Fwiki%2FScience_and_Hypothesis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>", The Walter Scott Publishing Co.</li> <li>1906. "<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a class="external text" href="https://en.wikisource.org/wiki/Translation:The_End_of_Matter"><i>The End of Matter</i></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+End+of+Matter&rft_id=https%3A%2F%2Fen.wikisource.org%2Fwiki%2FTranslation%3AThe_End_of_Matter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>", Athenæum</li> <li>1913. "The New Mechanics", <i>The Monist</i>, Vol. XXIII.</li> <li>1913. "The Relativity of Space", <i>The Monist</i>, Vol. XXIII.</li> <li>1913. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://archive.org/details/mathematicsandsc001861mbp"><i>Last Essays.</i></a>, New York: Dover reprint, 1963</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Last+Essays.&rft.place=New+York&rft.pub=Dover+reprint%2C+1963&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmathematicsandsc001861mbp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li>1956. <i>Chance.</i> In James R. Newman, ed., <i>The World of Mathematics</i> (4 Vols).</li> <li>1958. <i>The Value of Science,</i> New York: Dover.</li></ul> <p>On <a href="/wiki/Algebraic_topology" title="Algebraic topology">algebraic topology</a>: </p> <ul><li>1895. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="http://www.maths.ed.ac.uk/~aar/papers/poincare2009.pdf"><i>Analysis Situs</i></a> <span class="cs1-format">(PDF)</span>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120327043041/http://www.maths.ed.ac.uk/~aar/papers/poincare2009.pdf">archived</a> <span class="cs1-format">(PDF)</span> from the original on 27 March 2012</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Analysis+Situs&rft_id=http%3A%2F%2Fwww.maths.ed.ac.uk%2F~aar%2Fpapers%2Fpoincare2009.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>. The first systematic study of <a href="/wiki/Topology" title="Topology">topology</a>.</li></ul> <p>On <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a>: </p> <ul><li>1890. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré2017" class="citation book cs1">Poincaré, Henri (2017). <i>The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory</i>. Translated by Popp, Bruce D. Cham, Switzerland: Springer International Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-52898-4" title="Special:BookSources/978-3-319-52898-4"><bdi>978-3-319-52898-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+three-body+problem+and+the+equations+of+dynamics%3A+Poincar%C3%A9%27s+foundational+work+on+dynamical+systems+theory&rft.place=Cham%2C+Switzerland&rft.pub=Springer+International+Publishing&rft.date=2017&rft.isbn=978-3-319-52898-4&rft.aulast=Poincar%C3%A9&rft.aufirst=Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li>1892–99. <i>New Methods of Celestial Mechanics</i>, 3 vols. English trans., 1967. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-56396-117-2" title="Special:BookSources/1-56396-117-2">1-56396-117-2</a>.</li> <li>1905. "The Capture Hypothesis of J. J. See", The Monist, Vol. XV.</li> <li>1905–10. <i>Lessons of Celestial Mechanics</i>.</li></ul> <p>On the <a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">philosophy of mathematics</a>: </p> <ul><li>Ewald, William B., ed., 1996. <i>From Kant to Hilbert: A Source Book in the Foundations of Mathematics</i>, 2 vols. Oxford Univ. Press. Contains the following works by Poincaré: <ul><li>1894, "On the Nature of Mathematical Reasoning", 972–981.</li> <li>1898, "On the Foundations of Geometry", 982–1011.</li> <li>1900, "Intuition and Logic in Mathematics", 1012–1020.</li> <li>1905–06, "Mathematics and Logic, I–III", 1021–1070.</li> <li>1910, "On Transfinite Numbers", 1071–1074.</li></ul></li> <li>1905. "The Principles of Mathematical Physics", <i>The Monist</i>, Vol. XV.</li> <li>1910. "The Future of Mathematics", <i>The Monist</i>, Vol. XX.</li> <li>1910. "Mathematical Creation", <i>The Monist</i>, Vol. XX.</li></ul> <p>Other: </p> <ul><li>1904. <i>Maxwell's Theory and Wireless Telegraphy,</i> New York, McGraw Publishing Company.</li> <li>1905. "The New Logics", <i>The Monist</i>, Vol. XV.</li> <li>1905. "The Latest Efforts of the Logisticians", <i>The Monist</i>, Vol. XV.</li></ul> <p>Exhaustive bibliography of English translations: </p> <ul><li>1892–2017. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20200801151000/http://henripoincarepapers.univ-nantes.fr/bibliohp/index.php?a=on&lang=en&action=Chercher"><i>Henri Poincaré Papers</i></a>, archived from <a rel="nofollow" class="external text" href="http://henripoincarepapers.univ-nantes.fr/bibliohp/index.php?a=on&lang=en&action=Chercher">the original</a> on 1 August 2020</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Henri+Poincar%C3%A9+Papers&rft_id=http%3A%2F%2Fhenripoincarepapers.univ-nantes.fr%2Fbibliohp%2Findex.php%3Fa%3Don%26lang%3Den%26action%3DChercher&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=29" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Concepts">Concepts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=30" title="Edit section: Concepts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 21em;"> <ul><li><a href="/wiki/Hopf_bifurcation" title="Hopf bifurcation">Poincaré–Andronov–Hopf bifurcation</a></li> <li><a href="/wiki/Poincar%C3%A9_complex" title="Poincaré complex">Poincaré complex</a> – an abstraction of the singular chain complex of a closed, orientable manifold</li> <li><a href="/wiki/Poincar%C3%A9_duality" title="Poincaré duality">Poincaré duality</a></li> <li><a href="/wiki/Poincar%C3%A9_disk_model" title="Poincaré disk model">Poincaré disk model</a></li> <li><a href="/wiki/Asymptotic_expansion" title="Asymptotic expansion">Poincaré expansion</a></li> <li><a href="/wiki/Gauge_fixing#Multipolar_gauge" title="Gauge fixing">Poincaré gauge</a></li> <li><a href="/wiki/Poincar%C3%A9_group" title="Poincaré group">Poincaré group</a></li> <li><a href="/wiki/Poincar%C3%A9_half-plane_model" title="Poincaré half-plane model">Poincaré half-plane model</a></li> <li><a href="/wiki/Homology_sphere#Poincaré_homology_sphere" title="Homology sphere">Poincaré homology sphere</a></li> <li><a href="/wiki/Poincar%C3%A9_inequality" title="Poincaré inequality">Poincaré inequality</a></li> <li><a href="/wiki/Closed_and_exact_differential_forms#Poincaré_lemma" title="Closed and exact differential forms">Poincaré lemma</a></li> <li><a href="/wiki/Poincar%C3%A9_map" title="Poincaré map">Poincaré map</a></li> <li><a href="/wiki/Poincar%C3%A9_residue" title="Poincaré residue">Poincaré residue</a></li> <li><a href="/wiki/Poincar%C3%A9_series_(modular_form)" title="Poincaré series (modular form)">Poincaré series (modular form)</a></li> <li><a href="/wiki/Poincar%C3%A9_space" title="Poincaré space">Poincaré space</a></li> <li><a href="/wiki/Poincar%C3%A9_metric" title="Poincaré metric">Poincaré metric</a></li> <li><a href="/wiki/Poincar%C3%A9_plot" title="Poincaré plot">Poincaré plot</a></li> <li><a href="/wiki/Betti_number#Poincaré_polynomial" title="Betti number">Poincaré polynomial</a></li> <li><a href="/wiki/Hilbert%E2%80%93Poincar%C3%A9_series" title="Hilbert–Poincaré series">Poincaré series</a></li> <li><a href="/wiki/Poincar%C3%A9_sphere_(optics)" class="mw-redirect" title="Poincaré sphere (optics)">Poincaré sphere</a></li> <li><a href="/wiki/Einstein_synchronisation" title="Einstein synchronisation">Poincaré–Einstein synchronisation</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Lelong_equation" title="Poincaré–Lelong equation">Poincaré–Lelong equation</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Lindstedt_method" title="Poincaré–Lindstedt method">Poincaré–Lindstedt method</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Lindstedt_perturbation_theory" class="mw-redirect" title="Poincaré–Lindstedt perturbation theory">Poincaré–Lindstedt perturbation theory</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Steklov_operator" title="Poincaré–Steklov operator">Poincaré–Steklov operator</a></li> <li><a href="/wiki/Euler_characteristic" title="Euler characteristic">Euler–Poincaré characteristic</a></li> <li><a href="/wiki/Neumann%E2%80%93Poincar%C3%A9_operator" title="Neumann–Poincaré operator">Neumann–Poincaré operator</a></li> <li><a href="/wiki/Reflecting_Function" class="mw-redirect" title="Reflecting Function">Reflecting Function</a></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Theorems">Theorems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=31" title="Edit section: Theorems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Here is a list of theorems proved by Poincaré: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 26em;"> <ul><li><a href="/wiki/Poincar%C3%A9%27s_recurrence_theorem" class="mw-redirect" title="Poincaré's recurrence theorem">Poincaré's recurrence theorem</a>: certain systems will, after a sufficiently long but finite time, return to a state very close to the initial state.</li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Bendixson_theorem" title="Poincaré–Bendixson theorem">Poincaré–Bendixson theorem</a>: a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.</li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Hopf_theorem" title="Poincaré–Hopf theorem">Poincaré–Hopf theorem</a>: a generalization of the hairy-ball theorem, which states that there is no smooth vector field on a sphere having no sources or sinks.</li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Lefschetz_duality_theorem" class="mw-redirect" title="Poincaré–Lefschetz duality theorem">Poincaré–Lefschetz duality theorem</a>: a version of Poincaré duality in geometric topology, applying to a manifold with boundary</li> <li><a href="/wiki/Poincar%C3%A9_separation_theorem" title="Poincaré separation theorem">Poincaré separation theorem</a>: gives the upper and lower bounds of eigenvalues of a real symmetric matrix B'AB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B.</li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Birkhoff_theorem" title="Poincaré–Birkhoff theorem">Poincaré–Birkhoff theorem</a>: every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points.</li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Birkhoff%E2%80%93Witt_theorem" title="Poincaré–Birkhoff–Witt theorem">Poincaré–Birkhoff–Witt theorem</a>: an explicit description of the universal enveloping algebra of a Lie algebra.</li> <li><a href="/wiki/Kelvin%27s_circulation_theorem#Poincaré–Bjerknes_circulation_theorem" title="Kelvin's circulation theorem">Poincaré–Bjerknes circulation theorem</a>: theorem about a conservation of quantity for the rotating frame.</li> <li><a href="/wiki/Poincar%C3%A9_conjecture" title="Poincaré conjecture">Poincaré conjecture</a> (now a theorem): Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.</li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Miranda_theorem" title="Poincaré–Miranda theorem">Poincaré–Miranda theorem</a>: a generalization of the <a href="/wiki/Intermediate_value_theorem" title="Intermediate value theorem">intermediate value theorem</a> to <i>n</i> dimensions.</li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Other">Other</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=32" title="Edit section: Other"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col"> <ul><li><a href="/wiki/French_epistemology" class="mw-redirect" title="French epistemology">French epistemology</a></li> <li><a href="/wiki/History_of_special_relativity" title="History of special relativity">History of special relativity</a></li> <li><a href="/wiki/List_of_things_named_after_Henri_Poincar%C3%A9" title="List of things named after Henri Poincaré">List of things named after Henri Poincaré</a></li> <li><a href="/wiki/Institut_Henri_Poincar%C3%A9" title="Institut Henri Poincaré">Institut Henri Poincaré</a>, Paris</li> <li><a href="/wiki/Brouwer_fixed-point_theorem" title="Brouwer fixed-point theorem">Brouwer fixed-point theorem</a></li> <li><a href="/wiki/Relativity_priority_dispute" title="Relativity priority dispute">Relativity priority dispute</a></li> <li><a href="/wiki/Epistemic_structural_realism" class="mw-redirect" title="Epistemic structural realism">Epistemic structural realism</a><sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=33" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Footnotes">Footnotes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=34" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><link 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font-size:95%; color: var( --color-subtle, #555 )">(Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</span></span> </li> <li id="cite_note-forvo-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-forvo_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://forvo.com/word/poincaré">"Poincaré pronunciation: How to pronounce Poincaré in French"</a>. <i>forvo.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=forvo.com&rft.atitle=Poincar%C3%A9+pronunciation%3A+How+to+pronounce+Poincar%C3%A9+in+French&rft_id=https%3A%2F%2Fforvo.com%2Fword%2Fpoincar%C3%A9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-pronouncekiwi-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-pronouncekiwi_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://pronouncekiwi.com/Henri%20Poincaré">"How To Pronounce Henri Poincaré"</a>. <i>pronouncekiwi.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=pronouncekiwi.com&rft.atitle=How+To+Pronounce+Henri+Poincar%C3%A9&rft_id=https%3A%2F%2Fpronouncekiwi.com%2FHenri%2520Poincar%C3%A9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" 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M.; Gerini, C. (2013). <i>Henri Poincaré: A Biography Through the Daily Papers</i>. <a href="/wiki/World_Scientific" title="World Scientific">World Scientific</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2F8956">10.1142/8956</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-4556-61-3" title="Special:BookSources/978-981-4556-61-3"><bdi>978-981-4556-61-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Henri+Poincar%C3%A9%3A+A+Biography+Through+the+Daily+Papers&rft.pub=World+Scientific&rft.date=2013&rft_id=info%3Adoi%2F10.1142%2F8956&rft.isbn=978-981-4556-61-3&rft.aulast=Ginoux&rft.aufirst=J.+M.&rft.au=Gerini%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoultonJeffries1945" class="citation book cs1"><a href="/wiki/Forest_Ray_Moulton" title="Forest Ray Moulton">Moulton, Forest Ray</a>; Jeffries, Justus J. (1945). <a rel="nofollow" class="external text" href="https://archive.org/details/autobiographyofs0000unse_n5k3/mode/1up"><i>The Autobiography of Science</i></a>. Doubleday & Company. p. 509.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Autobiography+of+Science&rft.pages=509&rft.pub=Doubleday+%26+Company&rft.date=1945&rft.aulast=Moulton&rft.aufirst=Forest+Ray&rft.au=Jeffries%2C+Justus+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fautobiographyofs0000unse_n5k3%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHadamard,_Jacques1922" class="citation journal cs1"><a href="/wiki/Jacques_Hadamard" title="Jacques Hadamard">Hadamard, Jacques</a> (July 1922). <a rel="nofollow" class="external text" href="http://catalog.hathitrust.org/Record/100592035">"The early scientific work of Henri Poincaré"</a>. <i>The Rice Institute Pamphlet</i>. <b>9</b> (3): 111–183.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Rice+Institute+Pamphlet&rft.atitle=The+early+scientific+work+of+Henri+Poincar%C3%A9&rft.volume=9&rft.issue=3&rft.pages=111-183&rft.date=1922-07&rft.au=Hadamard%2C+Jacques&rft_id=http%3A%2F%2Fcatalog.hathitrust.org%2FRecord%2F100592035&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCervantes-CotaGalindo-UribarriSmoot2016" class="citation journal cs1">Cervantes-Cota, Jorge L.; Galindo-Uribarri, Salvador; Smoot, George F. (13 September 2016). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Funiverse2030022">"A Brief History of Gravitational Waves"</a>. <i>Universe</i>. <b>2</b> (3): 22. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1609.09400">1609.09400</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Funiverse2030022">10.3390/universe2030022</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2218-1997">2218-1997</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Universe&rft.atitle=A+Brief+History+of+Gravitational+Waves&rft.volume=2&rft.issue=3&rft.pages=22&rft.date=2016-09-13&rft_id=info%3Aarxiv%2F1609.09400&rft.issn=2218-1997&rft_id=info%3Adoi%2F10.3390%2Funiverse2030022&rft.aulast=Cervantes-Cota&rft.aufirst=Jorge+L.&rft.au=Galindo-Uribarri%2C+Salvador&rft.au=Smoot%2C+George+F.&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Funiverse2030022&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-McCormmach-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-McCormmach_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-McCormmach_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcCormmach1967" class="citation cs2">McCormmach, Russell (Spring 1967), "Henri Poincaré and the Quantum Theory", <i>Isis</i>, <b>58</b> (1): 37–55, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F350182">10.1086/350182</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120934561">120934561</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=Henri+Poincar%C3%A9+and+the+Quantum+Theory&rft.ssn=spring&rft.volume=58&rft.issue=1&rft.pages=37-55&rft.date=1967&rft_id=info%3Adoi%2F10.1086%2F350182&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120934561%23id-name%3DS2CID&rft.aulast=McCormmach&rft.aufirst=Russell&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPrentis1995" class="citation web cs1">Prentis, Jeffrey J. (1 April 1995). <a rel="nofollow" class="external text" href="https://pubs.aip.org/aapt/ajp/article-abstract/63/4/339/1043285/Poincare-s-proof-of-the-quantum-discontinuity-of?redirectedFrom=fulltext">"Poincaré's proof of the quantum discontinuity of nature"</a>. <i>pubs.aip.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">22 October</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=pubs.aip.org&rft.atitle=Poincar%C3%A9%27s+proof+of+the+quantum+discontinuity+of+nature&rft.date=1995-04-01&rft.aulast=Prentis&rft.aufirst=Jeffrey+J.&rft_id=https%3A%2F%2Fpubs.aip.org%2Faapt%2Fajp%2Farticle-abstract%2F63%2F4%2F339%2F1043285%2FPoincare-s-proof-of-the-quantum-discontinuity-of%3FredirectedFrom%3Dfulltext&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Belliver, 1956</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Sagaret, 1911</span> </li> <li id="cite_note-IEP-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-IEP_12-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.utm.edu/research/iep/p/poincare.htm">The Internet Encyclopedia of Philosophy</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20040202060803/http://www.utm.edu/research/iep/p/poincare.htm">Archived</a> 2 February 2004 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> Jules Henri Poincaré article by Mauro Murzi – Retrieved November 2006.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">O'Connor et al., 2002</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Carl, 1968</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">F. Verhulst</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRollet2012" class="citation journal cs1 cs1-prop-foreign-lang-source">Rollet, Laurent (15 November 2012). <a rel="nofollow" class="external text" href="https://journals.openedition.org/sabix/1131">"Jeanne Louise Poulain d'Andecy, épouse Poincaré (1857–1934)"</a>. <i>Bulletin de la Sabix. Société des amis de la Bibliothèque et de l'Histoire de l'École polytechnique</i> (in French) (51): 18–27. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4000%2Fsabix.1131">10.4000/sabix.1131</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0989-3059">0989-3059</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:190028919">190028919</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+de+la+Sabix.+Soci%C3%A9t%C3%A9+des+amis+de+la+Biblioth%C3%A8que+et+de+l%27Histoire+de+l%27%C3%89cole+polytechnique&rft.atitle=Jeanne+Louise+Poulain+d%27Andecy%2C+%C3%A9pouse+Poincar%C3%A9+%281857%E2%80%931934%29&rft.issue=51&rft.pages=18-27&rft.date=2012-11-15&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A190028919%23id-name%3DS2CID&rft.issn=0989-3059&rft_id=info%3Adoi%2F10.4000%2Fsabix.1131&rft.aulast=Rollet&rft.aufirst=Laurent&rft_id=https%3A%2F%2Fjournals.openedition.org%2Fsabix%2F1131&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Sageret, 1911</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMazliak2014" class="citation book cs1">Mazliak, Laurent (14 November 2014). "Poincaré's Odds". In Duplantier, B.; Rivasseau, V. (eds.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=njNpBQAAQBAJ"><i>Poincaré 1912–2012 : Poincaré Seminar 2012</i></a>. Progress in Mathematical Physics. Vol. 67. Basel: Springer. p. 150. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783034808347" title="Special:BookSources/9783034808347"><bdi>9783034808347</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Poincar%C3%A9%E2%80%99s+Odds&rft.btitle=Poincar%C3%A9+1912%E2%80%932012+%3A+Poincar%C3%A9+Seminar+2012&rft.place=Basel&rft.series=Progress+in+Mathematical+Physics&rft.pages=150&rft.pub=Springer&rft.date=2014-11-14&rft.isbn=9783034808347&rft.aulast=Mazliak&rft.aufirst=Laurent&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DnjNpBQAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">see Galison 2003</span> </li> <li id="cite_note-BSAF1911-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-BSAF1911_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k9626551q/f616.item">"<i>Bulletin de la Société astronomique de France</i>, 1911, vol. 25, pp. 581–586"</a>. 1911.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Bulletin+de+la+Soci%C3%A9t%C3%A9+astronomique+de+France%2C+1911%2C+vol.+25%2C+pp.+581%E2%80%93586&rft.date=1911&rft_id=http%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k9626551q%2Ff616.item&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.genealogy.ams.org/id.php?id=34227">Mathematics Genealogy Project</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071005011853/http://www.genealogy.ams.org/id.php?id=34227">Archived</a> 5 October 2007 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> North Dakota State University. Retrieved April 2008.</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20041127160356/http://www.lexpress.fr/idees/tribunes/dossier/allegre/dossier.asp?ida=430274">"Lorentz, Poincaré et Einstein"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.lexpress.fr/idees/tribunes/dossier/allegre/dossier.asp?ida=430274">the original</a> on 27 November 2004.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Lorentz%2C+Poincar%C3%A9+et+Einstein&rft_id=http%3A%2F%2Fwww.lexpress.fr%2Fidees%2Ftribunes%2Fdossier%2Fallegre%2Fdossier.asp%3Fida%3D430274&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-Irons-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-Irons_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIrons2001" class="citation cs2">Irons, F. E. (August 2001), "Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms", <i>American Journal of Physics</i>, <b>69</b> (8): 879–884, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001AmJPh..69..879I">2001AmJPh..69..879I</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1356056">10.1119/1.1356056</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Poincar%C3%A9%27s+1911%E2%80%9312+proof+of+quantum+discontinuity+interpreted+as+applying+to+atoms&rft.volume=69&rft.issue=8&rft.pages=879-884&rft.date=2001-08&rft_id=info%3Adoi%2F10.1119%2F1.1356056&rft_id=info%3Abibcode%2F2001AmJPh..69..879I&rft.aulast=Irons&rft.aufirst=F.+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-diacu-24"><span class="mw-cite-backlink">^ <a href="#cite_ref-diacu_24-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-diacu_24-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDiacu1996" class="citation cs2">Diacu, Florin (1996), "The solution of the <i>n</i>-body Problem", <i>The Mathematical Intelligencer</i>, <b>18</b> (3): 66–70, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF03024313">10.1007/BF03024313</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119728316">119728316</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Mathematical+Intelligencer&rft.atitle=The+solution+of+the+n-body+Problem&rft.volume=18&rft.issue=3&rft.pages=66-70&rft.date=1996&rft_id=info%3Adoi%2F10.1007%2FBF03024313&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119728316%23id-name%3DS2CID&rft.aulast=Diacu&rft.aufirst=Florin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarrow-Green1997" class="citation book cs1">Barrow-Green, June (1997). <a href="/wiki/Poincar%C3%A9_and_the_Three-Body_Problem" title="Poincaré and the Three-Body Problem"><i>Poincaré and the three body problem</i></a>. History of Mathematics. Vol. 11. Providence, RI: <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0821803677" title="Special:BookSources/978-0821803677"><bdi>978-0821803677</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/34357985">34357985</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Poincar%C3%A9+and+the+three+body+problem&rft.place=Providence%2C+RI&rft.series=History+of+Mathematics&rft.pub=American+Mathematical+Society&rft.date=1997&rft_id=info%3Aoclcnum%2F34357985&rft.isbn=978-0821803677&rft.aulast=Barrow-Green&rft.aufirst=June&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré2017" class="citation book cs1">Poincaré, J. Henri (2017). <i>The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory</i>. Popp, Bruce D. (Translator). Cham, Switzerland: Springer International Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319528984" title="Special:BookSources/9783319528984"><bdi>9783319528984</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/987302273">987302273</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+three-body+problem+and+the+equations+of+dynamics%3A+Poincar%C3%A9%27s+foundational+work+on+dynamical+systems+theory&rft.place=Cham%2C+Switzerland&rft.pub=Springer+International+Publishing&rft.date=2017&rft_id=info%3Aoclcnum%2F987302273&rft.isbn=9783319528984&rft.aulast=Poincar%C3%A9&rft.aufirst=J.+Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHsuHsu2006" class="citation cs2">Hsu, Jong-Ping; Hsu, Leonardo (2006), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=amLqckyrvUwC"><i>A broader view of relativity: general implications of Lorentz and Poincaré invariance</i></a>, vol. 10, World Scientific, p. 37, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-256-651-5" title="Special:BookSources/978-981-256-651-5"><bdi>978-981-256-651-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+broader+view+of+relativity%3A+general+implications+of+Lorentz+and+Poincar%C3%A9+invariance&rft.pages=37&rft.pub=World+Scientific&rft.date=2006&rft.isbn=978-981-256-651-5&rft.aulast=Hsu&rft.aufirst=Jong-Ping&rft.au=Hsu%2C+Leonardo&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DamLqckyrvUwC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=amLqckyrvUwC&pg=PA37">Section A5a, p 37</a></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLorentz1895" class="citation cs2"><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz, Hendrik A.</a> (1895), <span class="cs1-ws-icon" title="s:de:Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern"><a class="external text" href="https://en.wikisource.org/wiki/de:Versuch_einer_Theorie_der_electrischen_und_optischen_Erscheinungen_in_bewegten_K%C3%B6rpern"><i>Versuch einer theorie der electrischen und optischen erscheinungen in bewegten Kõrpern</i> </a></span>, Leiden: E.J. Brill</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Versuch+einer+theorie+der+electrischen+und+optischen+erscheinungen+in+bewegten+K%C3%B5rpern&rft.place=Leiden&rft.pub=E.J.+Brill&rft.date=1895&rft.aulast=Lorentz&rft.aufirst=Hendrik+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré1898" class="citation cs2">Poincaré, Henri (1898), <span class="cs1-ws-icon" title="s:The Measure of Time"><a class="external text" href="https://en.wikisource.org/wiki/The_Measure_of_Time">"The Measure of Time" </a></span>, <i>Revue de Métaphysique et de Morale</i>, <b>6</b>: 1–13</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Revue+de+M%C3%A9taphysique+et+de+Morale&rft.atitle=The+Measure+of+Time&rft.volume=6&rft.pages=1-13&rft.date=1898&rft.aulast=Poincar%C3%A9&rft.aufirst=Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-action-30"><span class="mw-cite-backlink">^ <a href="#cite_ref-action_30-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-action_30-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-action_30-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré1900" class="citation cs2">Poincaré, Henri (1900), <span class="cs1-ws-icon" title="s:fr:La théorie de Lorentz et le principe de réaction"><a class="external text" href="https://en.wikisource.org/wiki/fr:La_th%C3%A9orie_de_Lorentz_et_le_principe_de_r%C3%A9action">"La théorie de Lorentz et le principe de réaction" </a></span>, <i>Archives Néerlandaises des Sciences Exactes et Naturelles</i>, <b>5</b>: 252–278</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archives+N%C3%A9erlandaises+des+Sciences+Exactes+et+Naturelles&rft.atitle=La+th%C3%A9orie+de+Lorentz+et+le+principe+de+r%C3%A9action&rft.volume=5&rft.pages=252-278&rft.date=1900&rft.aulast=Poincar%C3%A9&rft.aufirst=Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>. See also the <a rel="nofollow" class="external text" href="http://www.physicsinsights.org/poincare-1900.pdf">English translation</a></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_H.1881" class="citation journal cs1">Poincaré, H. (1881). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200801124731/http://henripoincarepapers.univ-nantes.fr/chp/hp-pdf/hp1881af.pdf">"Sur les applications de la géométrie non-euclidienne à la théorie des formes quadratiques"</a> <span class="cs1-format">(PDF)</span>. <i>Association Française Pour l'Avancement des Sciences</i>. <b>10</b>: 132–138. Archived from <a rel="nofollow" class="external text" href="http://henripoincarepapers.univ-nantes.fr/chp/hp-pdf/hp1881af.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 1 August 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Association+Fran%C3%A7aise+Pour+l%27Avancement+des+Sciences&rft.atitle=Sur+les+applications+de+la+g%C3%A9om%C3%A9trie+non-euclidienne+%C3%A0+la+th%C3%A9orie+des+formes+quadratiques&rft.volume=10&rft.pages=132-138&rft.date=1881&rft.au=Poincar%C3%A9%2C+H.&rft_id=http%3A%2F%2Fhenripoincarepapers.univ-nantes.fr%2Fchp%2Fhp-pdf%2Fhp1881af.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReynolds,_W._F.1993" class="citation journal cs1">Reynolds, W. F. (1993). "Hyperbolic geometry on a hyperboloid". <i>The American Mathematical Monthly</i>. <b>100</b> (5): 442–455. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00029890.1993.11990430">10.1080/00029890.1993.11990430</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2324297">2324297</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:124088818">124088818</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=Hyperbolic+geometry+on+a+hyperboloid&rft.volume=100&rft.issue=5&rft.pages=442-455&rft.date=1993&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A124088818%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2324297%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1080%2F00029890.1993.11990430&rft.au=Reynolds%2C+W.+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_H.1892" class="citation book cs1">Poincaré, H. (1892). <a rel="nofollow" class="external text" href="https://archive.org/details/thoriemathma00poin">"Chapitre XII: Polarisation rotatoire"</a>. <i>Théorie mathématique de la lumière II</i>. Paris: Georges Carré.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapitre+XII%3A+Polarisation+rotatoire&rft.btitle=Th%C3%A9orie+math%C3%A9matique+de+la+lumi%C3%A8re+II&rft.place=Paris&rft.pub=Georges+Carr%C3%A9&rft.date=1892&rft.au=Poincar%C3%A9%2C+H.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fthoriemathma00poin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTudor,_T.2018" class="citation journal cs1">Tudor, T. (2018). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fsym10030052">"Lorentz Transformation, Poincaré Vectors and Poincaré Sphere in Various Branches of Physics"</a>. <i>Symmetry</i>. <b>10</b> (3): 52. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018Symm...10...52T">2018Symm...10...52T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fsym10030052">10.3390/sym10030052</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Symmetry&rft.atitle=Lorentz+Transformation%2C+Poincar%C3%A9+Vectors+and+Poincar%C3%A9+Sphere+in+Various+Branches+of+Physics&rft.volume=10&rft.issue=3&rft.pages=52&rft.date=2018&rft_id=info%3Adoi%2F10.3390%2Fsym10030052&rft_id=info%3Abibcode%2F2018Symm...10...52T&rft.au=Tudor%2C+T.&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Fsym10030052&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_H.1900" class="citation cs2">Poincaré, H. (1900), <a rel="nofollow" class="external text" href="http://gallica.bnf.fr/ark:/12148/bpt6k17075r/f1167.table">"Les relations entre la physique expérimentale et la physique mathématique"</a>, <i>Revue Générale des Sciences Pures et Appliquées</i>, <b>11</b>: 1163–1175</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Revue+G%C3%A9n%C3%A9rale+des+Sciences+Pures+et+Appliqu%C3%A9es&rft.atitle=Les+relations+entre+la+physique+exp%C3%A9rimentale+et+la+physique+math%C3%A9matique&rft.volume=11&rft.pages=1163-1175&rft.date=1900&rft.au=Poincar%C3%A9%2C+H.&rft_id=http%3A%2F%2Fgallica.bnf.fr%2Fark%3A%2F12148%2Fbpt6k17075r%2Ff1167.table&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>. Reprinted in "Science and Hypothesis", Ch. 9–10.</span> </li> <li id="cite_note-louis-36"><span class="mw-cite-backlink">^ <a href="#cite_ref-louis_36-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-louis_36-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_Henri1913" class="citation cs2">Poincaré, Henri (1913), <span class="cs1-ws-icon" title="s:The Principles of Mathematical Physics"><a class="external text" href="https://en.wikisource.org/wiki/The_Principles_of_Mathematical_Physics">"The Principles of Mathematical Physics" </a></span>, <i>The Foundations of Science (The Value of Science)</i>, New York: Science Press, pp. 297–320; article translated from 1904 original</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Principles+of+Mathematical+Physics&rft.btitle=The+Foundations+of+Science+%28The+Value+of+Science%29&rft.place=New+York&rft.pages=297-320&rft.pub=Science+Press&rft.date=1913&rft.au=Poincar%C3%A9%2C+Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Citation" title="Template:Citation">citation</a>}}</code>: CS1 maint: postscript (<a href="/wiki/Category:CS1_maint:_postscript" title="Category:CS1 maint: postscript">link</a>)</span> available in <a rel="nofollow" class="external text" href="https://books.google.com/books/about/The_Foundations_of_Science.html?id=mBvNabP35zoC&pg=PA297">online chapter from 1913 book</a></span> </li> <li id="cite_note-univ-nantes-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-univ-nantes_37-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_H.2007" class="citation cs2">Poincaré, H. (2007), <a rel="nofollow" class="external text" href="http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz3.html">"38.3, Poincaré to H. A. Lorentz, May 1905"</a>, in Walter, S. A. (ed.), <i>La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs</i>, Basel: Birkhäuser, pp. 255–257</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=38.3%2C+Poincar%C3%A9+to+H.+A.+Lorentz%2C+May+1905&rft.btitle=La+correspondance+entre+Henri+Poincar%C3%A9+et+les+physiciens%2C+chimistes%2C+et+ing%C3%A9nieurs&rft.place=Basel&rft.pages=255-257&rft.pub=Birkh%C3%A4user&rft.date=2007&rft.au=Poincar%C3%A9%2C+H.&rft_id=http%3A%2F%2Fhenripoincarepapers.univ-nantes.fr%2Fchp%2Ftext%2Florentz3.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-univ-nantes2-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-univ-nantes2_38-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_H.2007" class="citation cs2">Poincaré, H. (2007), <a rel="nofollow" class="external text" href="http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz4.html">"38.4, Poincaré to H. A. Lorentz, May 1905"</a>, in Walter, S. A. (ed.), <i>La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs</i>, Basel: Birkhäuser, pp. 257–258</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=38.4%2C+Poincar%C3%A9+to+H.+A.+Lorentz%2C+May+1905&rft.btitle=La+correspondance+entre+Henri+Poincar%C3%A9+et+les+physiciens%2C+chimistes%2C+et+ing%C3%A9nieurs&rft.place=Basel&rft.pages=257-258&rft.pub=Birkh%C3%A4user&rft.date=2007&rft.au=Poincar%C3%A9%2C+H.&rft_id=http%3A%2F%2Fhenripoincarepapers.univ-nantes.fr%2Fchp%2Ftext%2Florentz4.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-1905_paper-39"><span class="mw-cite-backlink">^ <a href="#cite_ref-1905_paper_39-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-1905_paper_39-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-1905_paper_39-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="http://www.academie-sciences.fr/pdf/dossiers/Poincare/Poincare_pdf/Poincare_CR1905.pdf">[1]</a> (PDF) Membres de l'Académie des sciences depuis sa création : Henri Poincare. Sur la dynamique de l' electron. Note de H. Poincaré. C.R. T.140 (1905) 1504–1508.</span> </li> <li id="cite_note-long-40"><span class="mw-cite-backlink">^ <a href="#cite_ref-long_40-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-long_40-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_H.1906" class="citation cs2">Poincaré, H. (1906), <a rel="nofollow" class="external text" href="https://zenodo.org/record/1428444">"Sur la dynamique de l'électron (On the Dynamics of the Electron)"</a>, <i>Rendiconti del Circolo Matematico Rendiconti del Circolo di Palermo</i>, <b>21</b>: 129–176, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1906RCMP...21..129P">1906RCMP...21..129P</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF03013466">10.1007/BF03013466</a>, <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2027%2Fuiug.30112063899089">2027/uiug.30112063899089</a></span>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120211823">120211823</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Rendiconti+del+Circolo+Matematico+Rendiconti+del+Circolo+di+Palermo&rft.atitle=Sur+la+dynamique+de+l%27%C3%A9lectron+%28On+the+Dynamics+of+the+Electron%29&rft.volume=21&rft.pages=129-176&rft.date=1906&rft_id=info%3Ahdl%2F2027%2Fuiug.30112063899089&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120211823%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF03013466&rft_id=info%3Abibcode%2F1906RCMP...21..129P&rft.au=Poincar%C3%A9%2C+H.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1428444&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span> (Wikisource translation)</span> </li> <li id="cite_note-Genesis_4-Vectors-41"><span class="mw-cite-backlink">^ <a href="#cite_ref-Genesis_4-Vectors_41-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Genesis_4-Vectors_41-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalter2007" class="citation book cs1">Walter, Scott (2007). "Breaking in the 4-Vectors: The Four-Dimensional Movement in Gravitation, 1905–1910". <i>The Genesis of General Relativity</i>. Vol. 3. Dordrecht: Springer Netherlands. pp. 1118–1178. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4020-4000-9_18">10.1007/978-1-4020-4000-9_18</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-3999-7" title="Special:BookSources/978-1-4020-3999-7"><bdi>978-1-4020-3999-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Breaking+in+the+4-Vectors%3A+The+Four-Dimensional+Movement+in+Gravitation%2C+1905%E2%80%931910&rft.btitle=The+Genesis+of+General+Relativity&rft.place=Dordrecht&rft.pages=1118-1178&rft.pub=Springer+Netherlands&rft.date=2007&rft_id=info%3Adoi%2F10.1007%2F978-1-4020-4000-9_18&rft.isbn=978-1-4020-3999-7&rft.aulast=Walter&rft.aufirst=Scott&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-Raum_und_Zeit-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-Raum_und_Zeit_42-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMinkowski1908" class="citation journal cs1">Minkowski, Hermann (September 1908). <a rel="nofollow" class="external text" href="https://math.nyu.edu/~tschinke/papers/yuri/14minkowski/raum-und-zeit.pdf">"Raum und Zeit"</a> <span class="cs1-format">(PDF)</span>. <i>Jahresbericht der Deutschen Mathematiker-Vereinigung</i>. <b>18</b>: 75–88<span class="reference-accessdate">. Retrieved <span class="nowrap">11 May</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Jahresbericht+der+Deutschen+Mathematiker-Vereinigung&rft.atitle=Raum+und+Zeit&rft.volume=18&rft.pages=75-88&rft.date=1908-09&rft.aulast=Minkowski&rft.aufirst=Hermann&rft_id=https%3A%2F%2Fmath.nyu.edu%2F~tschinke%2Fpapers%2Fyuri%2F14minkowski%2Fraum-und-zeit.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text">Miller 1981, Secondary sources on relativity</span> </li> <li id="cite_note-poinc08-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-poinc08_44-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré,_Henri1908–1913" class="citation book cs1">Poincaré, Henri (1908–1913). <span class="cs1-ws-icon" title="s:The New Mechanics"><a class="external text" href="https://en.wikisource.org/wiki/The_New_Mechanics">"The New Mechanics" </a></span>. <i>The foundations of science (Science and Method)</i>. New York: Science Press. pp. 486–522.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+New+Mechanics&rft.btitle=The+foundations+of+science+%28Science+and+Method%29&rft.place=New+York&rft.pages=486-522&rft.pub=Science+Press&rft.date=1908%2F1913&rft.au=Poincar%C3%A9%2C+Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-darrigol-45"><span class="mw-cite-backlink">^ <a href="#cite_ref-darrigol_45-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-darrigol_45-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Darrigol 2005, Secondary sources on relativity</span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein,_A.1905b" class="citation cs2">Einstein, A. (1905b), "Ist die Trägheit eines Körpers von dessen Energieinhalt abhängig?", <i>Annalen der Physik</i>, <b>18</b> (13): 639–643, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1905AnP...323..639E">1905AnP...323..639E</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19053231314">10.1002/andp.19053231314</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Ist+die+Tr%C3%A4gheit+eines+K%C3%B6rpers+von+dessen+Energieinhalt+abh%C3%A4ngig%3F&rft.volume=18&rft.issue=13&rft.pages=639-643&rft.date=1905&rft_id=info%3Adoi%2F10.1002%2Fandp.19053231314&rft_id=info%3Abibcode%2F1905AnP...323..639E&rft.au=Einstein%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>. See also <a rel="nofollow" class="external text" href="http://www.fourmilab.ch/etexts/einstein/specrel/www">English translation</a>.</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEinstein,_A.1906" class="citation cs2">Einstein, A. (1906), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060318060830/http://www.physik.uni-augsburg.de/annalen/history/papers/1906_20_627-633.pdf">"Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie"</a> <span class="cs1-format">(PDF)</span>, <i>Annalen der Physik</i>, <b>20</b> (8): 627–633, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1906AnP...325..627E">1906AnP...325..627E</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19063250814">10.1002/andp.19063250814</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120361282">120361282</a>, archived from <a rel="nofollow" class="external text" href="http://www.physik.uni-augsburg.de/annalen/history/papers/1906_20_627-633.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 18 March 2006</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Das+Prinzip+von+der+Erhaltung+der+Schwerpunktsbewegung+und+die+Tr%C3%A4gheit+der+Energie&rft.volume=20&rft.issue=8&rft.pages=627-633&rft.date=1906&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120361282%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1002%2Fandp.19063250814&rft_id=info%3Abibcode%2F1906AnP...325..627E&rft.au=Einstein%2C+A.&rft_id=http%3A%2F%2Fwww.physik.uni-augsburg.de%2Fannalen%2Fhistory%2Fpapers%2F1906_20_627-633.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text">"<i>Il importait d'examiner cette hypothèse de plus près et en particulier de rechercher quelles modifications elle nous obligerait à apporter aux lois de la gravitation. C'est ce que j'ai cherché à déterminer; j'ai été d'abord conduit à supposer que la propagation de la gravitation n'est pas instantanée, mais se fait avec la vitesse de la lumière.</i>"</span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="http://einsteinpapers.press.princeton.edu/vol9-trans/52"><i>The Berlin Years: Correspondence, January 1919 – April 1920 (English translation supplement)</i></a>. The Collected Papers of Albert Einstein. Vol. 9. Princeton U.P. p. 30.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Berlin+Years%3A+Correspondence%2C+January+1919+%E2%80%93+April+1920+%28English+translation+supplement%29&rft.series=The+Collected+Papers+of+Albert+Einstein&rft.pages=30&rft.pub=Princeton+U.P.&rft_id=http%3A%2F%2Feinsteinpapers.press.princeton.edu%2Fvol9-trans%2F52&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span> See also this letter, with commentary, in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSass1979" class="citation journal cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Hans-Martin_Sass" title="Hans-Martin Sass">Sass, Hans-Martin</a> (1979). "Einstein über "wahre Kultur" und die Stellung der Geometrie im Wissenschaftssystem: Ein Brief Albert Einsteins an Hans Vaihinger vom Jahre 1919". <i><a href="/wiki/Zeitschrift_f%C3%BCr_allgemeine_Wissenschaftstheorie" class="mw-redirect" title="Zeitschrift für allgemeine Wissenschaftstheorie">Zeitschrift für allgemeine Wissenschaftstheorie</a></i> (in German). <b>10</b> (2): 316–319. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf01802352">10.1007/bf01802352</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/25170513">25170513</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:170178963">170178963</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Zeitschrift+f%C3%BCr+allgemeine+Wissenschaftstheorie&rft.atitle=Einstein+%C3%BCber+%22wahre+Kultur%22+und+die+Stellung+der+Geometrie+im+Wissenschaftssystem%3A+Ein+Brief+Albert+Einsteins+an+Hans+Vaihinger+vom+Jahre+1919&rft.volume=10&rft.issue=2&rft.pages=316-319&rft.date=1979&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A170178963%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F25170513%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1007%2Fbf01802352&rft.aulast=Sass&rft.aufirst=Hans-Martin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text">Darrigol 2004, Secondary sources on relativity</span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text">Galison 2003 and Kragh 1999, Secondary sources on relativity</span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text">Holton (1988), 196–206</span> </li> <li id="cite_note-Hentschel_PhD-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hentschel_PhD_53-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHentschel1990" class="citation thesis cs1">Hentschel, Klaus (1990). <i>Interpretationen und Fehlinterpretationen der speziellen und der allgemeinen Relativitätstheorie durch Zeitgenossen Albert Einsteins</i> (PhD thesis). University of Hamburg. pp. 3–13.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Interpretationen+und+Fehlinterpretationen+der+speziellen+und+der+allgemeinen+Relativit%C3%A4tstheorie+durch+Zeitgenossen+Albert+Einsteins&rft.degree=PhD&rft.inst=University+of+Hamburg&rft.date=1990&rft.aulast=Hentschel&rft.aufirst=Klaus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text">Miller (1981), 216–217</span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text">Darrigol (2005), 15–18</span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text">Katzir (2005), 286–288</span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text">Whittaker 1953, Secondary sources on relativity</span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text">Poincaré, Selected works in three volumes. page = 682<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (September 2019)">full citation needed</span></a></i>]</sup></span> </li> <li id="cite_note-Poincaré_Lorentz_l’´electron-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-Poincaré_Lorentz_l’´electron_59-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré1905" class="citation journal cs1">Poincaré, Henri (1905). "Sur la dynamique de l'électron". <i>Comptes rendus des séances de l'Académie des Sciences</i>. <b>140</b>: 1504–1508.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Comptes+rendus+des+s%C3%A9ances+de+l%27Acad%C3%A9mie+des+Sciences&rft.atitle=Sur+la+dynamique+de+l%27%C3%A9lectron&rft.volume=140&rft.pages=1504-1508&rft.date=1905&rft.aulast=Poincar%C3%A9&rft.aufirst=Henri&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEStillwell2010419–435-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEStillwell2010419–435_60-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFStillwell2010">Stillwell 2010</a>, pp. 419–435.</span> </li> <li id="cite_note-Aleksandrov_Poincaré-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-Aleksandrov_Poincaré_61-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAleksandrov1972" class="citation journal cs1">Aleksandrov, P S (28 February 1972). "Poincaré and topology". <i>Russian Mathematical Surveys</i>. <b>27</b> (1): 157–168. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1070%2FRM1972v027n01ABEH001365">10.1070/RM1972v027n01ABEH001365</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0036-0279">0036-0279</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Russian+Mathematical+Surveys&rft.atitle=Poincar%C3%A9+and+topology&rft.volume=27&rft.issue=1&rft.pages=157-168&rft.date=1972-02-28&rft_id=info%3Adoi%2F10.1070%2FRM1972v027n01ABEH001365&rft.issn=0036-0279&rft.aulast=Aleksandrov&rft.aufirst=P+S&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text">J. Stillwell, Mathematics and its history, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=V7mxZqjs5yUC&pg=PA254">p. 254</a></span> </li> <li id="cite_note-Gold_Medal_to_Poincaré-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gold_Medal_to_Poincaré_63-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDarwin1900" class="citation journal cs1">Darwin, G.H. (1900). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmnras%2F60.5.406">"Address Delivered by the President, Professor G. H. Darwin, on presenting the Gold Medal of the Society to M. H. Poincaré"</a>. <i>Monthly Notices of the Royal Astronomical Society</i>. <b>60</b> (5): 406–416. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fmnras%2F60.5.406">10.1093/mnras/60.5.406</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0035-8711">0035-8711</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.atitle=Address+Delivered+by+the+President%2C+Professor+G.+H.+Darwin%2C+on+presenting+the+Gold+Medal+of+the+Society+to+M.+H.+Poincar%C3%A9&rft.volume=60&rft.issue=5&rft.pages=406-416&rft.date=1900&rft_id=info%3Adoi%2F10.1093%2Fmnras%2F60.5.406&rft.issn=0035-8711&rft.aulast=Darwin&rft.aufirst=G.H.&rft_id=https%3A%2F%2Fdoi.org%2F10.1093%252Fmnras%252F60.5.406&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text">French: "Mémoire sur les courbes définies par une équation différentielle"</span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKolmogorovYushkevich1998" class="citation book cs1">Kolmogorov, A.N.; Yushkevich, A.P., eds. (24 March 1998). <i>Mathematics of the 19th century</i>. Vol. 3. Springer. pp. 162–174, 283. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3764358457" title="Special:BookSources/978-3764358457"><bdi>978-3764358457</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+of+the+19th+century&rft.pages=162-174%2C+283&rft.pub=Springer&rft.date=1998-03-24&rft.isbn=978-3764358457&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text">J. Hadamard. L'oeuvre de H. Poincaré. Acta Mathematica, 38 (1921), p. 208</span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="http://name.umdl.umich.edu/AAS9989.0001.001"><i>Toulouse, Édouard, 1910. </i>Henri Poincaré<i>, E. Flammarion, Paris</i></a>. 2005.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Toulouse%2C+%C3%89douard%2C+1910.+Henri+Poincar%C3%A9%2C+E.+Flammarion%2C+Paris&rft.date=2005&rft_id=http%3A%2F%2Fname.umdl.umich.edu%2FAAS9989.0001.001&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-google-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-google_68-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToulouse,_E.2013" class="citation book cs1">Toulouse, E. (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=mpjWPQAACAAJ"><i>Henri Poincare</i></a>. MPublishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781418165062" title="Special:BookSources/9781418165062"><bdi>9781418165062</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">10 October</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Henri+Poincare&rft.pub=MPublishing&rft.date=2013&rft.isbn=9781418165062&rft.au=Toulouse%2C+E.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DmpjWPQAACAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-69">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150905152142/http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00002358">"Jules Henri Poincaré (1854–1912)"</a>. Royal Netherlands Academy of Arts and Sciences. 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Retrieved <span class="nowrap">4 August</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Jules+Henri+Poincar%C3%A9+%281854%E2%80%931912%29&rft.pub=Royal+Netherlands+Academy+of+Arts+and+Sciences&rft_id=http%3A%2F%2Fwww.dwc.knaw.nl%2Fbiografie%2Fpmknaw%2F%3Fpagetype%3DauthorDetail%26aId%3DPE00002358&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-gray-biography-70"><span class="mw-cite-backlink">^ <a href="#cite_ref-gray-biography_70-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-gray-biography_70-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGray2013" class="citation book cs1">Gray, Jeremy (2013). "The Campaign for Poincaré". <i>Henri Poincaré: A Scientific Biography</i>. 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"Nobel: Always the Winners, Never the Losers". <i><a href="/wiki/Science_(journal)" title="Science (journal)">Science</a></i>. <b>282</b> (5392): 1256–1257. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1998Sci...282.1256C">1998Sci...282.1256C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.282.5392.1256">10.1126/science.282.5392.1256</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:153619456">153619456</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Nobel%3A+Always+the+Winners%2C+Never+the+Losers&rft.volume=282&rft.issue=5392&rft.pages=1256-1257&rft.date=1998-11-13&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A153619456%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1126%2Fscience.282.5392.1256&rft_id=info%3Abibcode%2F1998Sci...282.1256C&rft.aulast=Crawford&rft.aufirst=Elizabeth&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged July 2016">dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-74"><span class="mw-cite-backlink"><b><a href="#cite_ref-74">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNastasi2013" class="citation journal cs1">Nastasi, Pietro (16 May 2013). <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs40329-013-0005-1">"A Nobel Prize for Poincaré?"</a>. <i>Lettera Matematica</i>. <b>1</b> (1–2): 79–82. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs40329-013-0005-1">10.1007/s40329-013-0005-1</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Lettera+Matematica&rft.atitle=A+Nobel+Prize+for+Poincar%C3%A9%3F&rft.volume=1&rft.issue=1%E2%80%932&rft.pages=79-82&rft.date=2013-05-16&rft_id=info%3Adoi%2F10.1007%2Fs40329-013-0005-1&rft.aulast=Nastasi&rft.aufirst=Pietro&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252Fs40329-013-0005-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-75"><span class="mw-cite-backlink"><b><a href="#cite_ref-75">^</a></b></span> <span class="reference-text">Yemima Ben-Menahem, <i>Conventionalism: From Poincare to Quine</i>, Cambridge University Press, 2006, p. 39.</span> </li> <li id="cite_note-76"><span class="mw-cite-backlink"><b><a href="#cite_ref-76">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGargani_Julien2012" class="citation cs2">Gargani Julien (2012), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304140554/http://www.editions-harmattan.fr/index.asp?navig=catalogue&obj=livre&no=38754"><i>Poincaré, le hasard et l'étude des systèmes complexes</i></a>, L'Harmattan, p. 124, archived from <a rel="nofollow" class="external text" href="http://www.editions-harmattan.fr/index.asp?navig=catalogue&obj=livre&no=38754">the original</a> on 4 March 2016<span class="reference-accessdate">, retrieved <span class="nowrap">5 June</span> 2015</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Poincar%C3%A9%2C+le+hasard+et+l%27%C3%A9tude+des+syst%C3%A8mes+complexes&rft.pages=124&rft.pub=L%27Harmattan&rft.date=2012&rft.au=Gargani+Julien&rft_id=http%3A%2F%2Fwww.editions-harmattan.fr%2Findex.asp%3Fnavig%3Dcatalogue%26obj%3Dlivre%26no%3D38754&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-77"><span class="mw-cite-backlink"><b><a href="#cite_ref-77">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré2007" class="citation cs2">Poincaré, Henri (2007), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=2QXqHaVbkgoC&pg=PA50"><i>Science and Hypothesis</i></a>, Cosimo, Inc. Press, p. 50, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-60206-505-5" title="Special:BookSources/978-1-60206-505-5"><bdi>978-1-60206-505-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Science+and+Hypothesis&rft.pages=50&rft.pub=Cosimo%2C+Inc.+Press&rft.date=2007&rft.isbn=978-1-60206-505-5&rft.aulast=Poincar%C3%A9&rft.aufirst=Henri&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D2QXqHaVbkgoC%26pg%3DPA50&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-78"><span class="mw-cite-backlink"><b><a href="#cite_ref-78">^</a></b></span> <span class="reference-text">Hadamard, Jacques. <i>An Essay on the Psychology of Invention in the Mathematical Field</i>. Princeton Univ Press (1945)</span> </li> <li id="cite_note-79"><span class="mw-cite-backlink"><b><a href="#cite_ref-79">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoincaré1914" class="citation book cs1">Poincaré, Henri (1914). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190904163001/https://ebooks.adelaide.edu.au/p/poincare/henri/science-and-method/book1.3.html">"3: Mathematical Creation"</a>. <i>Science and Method</i>. Archived from <a rel="nofollow" class="external text" href="http://ebooks.adelaide.edu.au/p/poincare/henri/science-and-method/book1.3.html">the original</a> on 4 September 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">4 September</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=3%3A+Mathematical+Creation&rft.btitle=Science+and+Method&rft.date=1914&rft.aulast=Poincar%C3%A9&rft.aufirst=Henri&rft_id=http%3A%2F%2Febooks.adelaide.edu.au%2Fp%2Fpoincare%2Fhenri%2Fscience-and-method%2Fbook1.3.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></span> </li> <li id="cite_note-80"><span class="mw-cite-backlink"><b><a href="#cite_ref-80">^</a></b></span> <span class="reference-text">Dennett, Daniel C. 1978. <i>Brainstorms: Philosophical Essays on Mind and Psychology</i>. The MIT Press, p. 293</span> </li> <li id="cite_note-81"><span class="mw-cite-backlink"><b><a href="#cite_ref-81">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/structural-realism/#Rel">"Structural Realism"</a>: entry by James Ladyman in the <i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=35" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Eric_Temple_Bell" title="Eric Temple Bell">Bell, Eric Temple</a>, 1986. <i>Men of Mathematics</i> (reissue edition). Touchstone Books. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-671-62818-6" title="Special:BookSources/0-671-62818-6">0-671-62818-6</a>.</li> <li>Belliver, André, 1956. <i>Henri Poincaré ou la vocation souveraine</i>. Paris: Gallimard.</li> <li><a href="/wiki/Peter_L._Bernstein" title="Peter L. Bernstein">Bernstein, Peter L</a>, 1996. "Against the Gods: A Remarkable Story of Risk". (pp. 199–200). John Wiley & Sons.</li> <li><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Boyer, B. Carl</a>, 1968. <i>A History of Mathematics: Henri Poincaré</i>, John Wiley & Sons.</li> <li><a href="/wiki/Ivor_Grattan-Guinness" title="Ivor Grattan-Guinness">Grattan-Guinness, Ivor</a>, 2000. <i>The Search for Mathematical Roots 1870–1940.</i> Princeton Uni. Press.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDauben2004" class="citation cs2"><a href="/wiki/Joseph_Dauben" title="Joseph Dauben">Dauben, Joseph</a> (2004) [1993], <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100713115605/http://www.acmsonline.org/journal/2004/Dauben-Cantor.pdf">"Georg Cantor and the Battle for Transfinite Set Theory"</a> <span class="cs1-format">(PDF)</span>, <i>Proceedings of the 9th ACMS Conference (Westmont College, Santa Barbara, CA)</i>, pp. 1–22, archived from <a rel="nofollow" class="external text" href="http://www.acmsonline.org/journal/2004/Dauben-Cantor.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 13 July 2010</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Georg+Cantor+and+the+Battle+for+Transfinite+Set+Theory&rft.btitle=Proceedings+of+the+9th+ACMS+Conference+%28Westmont+College%2C+Santa+Barbara%2C+CA%29&rft.pages=1-22&rft.date=2004&rft.aulast=Dauben&rft.aufirst=Joseph&rft_id=http%3A%2F%2Fwww.acmsonline.org%2Fjournal%2F2004%2FDauben-Cantor.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span>. Internet version published in Journal of the ACMS 2004.</li> <li>Folina, Janet, 1992. <i>Poincaré and the Philosophy of Mathematics.</i> Macmillan, New York.</li> <li><a href="/wiki/Jeremy_Gray" title="Jeremy Gray">Gray, Jeremy</a>, 1986. <i>Linear differential equations and group theory from Riemann to Poincaré</i>, Birkhauser <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8176-3318-9" title="Special:BookSources/0-8176-3318-9">0-8176-3318-9</a></li> <li>Gray, Jeremy, 2013. <i>Henri Poincaré: A scientific biography</i>. Princeton University Press <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-15271-4" title="Special:BookSources/978-0-691-15271-4">978-0-691-15271-4</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJean_Mawhin2005" class="citation cs2"><a href="/wiki/Jean_Mawhin" title="Jean Mawhin">Jean Mawhin</a> (October 2005), <a rel="nofollow" class="external text" href="https://www.ams.org/notices/200509/comm-mawhin.pdf">"Henri Poincaré. A Life in the Service of Science"</a> <span class="cs1-format">(PDF)</span>, <i>Notices of the AMS</i>, <b>52</b> (9): 1036–1044, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070303185921/http://www.ams.org/notices/200509/comm-mawhin.pdf">archived</a> <span class="cs1-format">(PDF)</span> from the original on 3 March 2007</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+AMS&rft.atitle=Henri+Poincar%C3%A9.+A+Life+in+the+Service+of+Science&rft.volume=52&rft.issue=9&rft.pages=1036-1044&rft.date=2005-10&rft.au=Jean+Mawhin&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F200509%2Fcomm-mawhin.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><a href="/wiki/Daniel_Kolak" title="Daniel Kolak">Kolak, Daniel</a>, 2001. <i>Lovers of Wisdom</i>, 2nd ed. Wadsworth.</li> <li>Gargani, Julien, 2012. <i>Poincaré, le hasard et l'étude des systèmes complexes</i>, L'Harmattan.</li> <li>Murzi, 1998. "Henri Poincaré".</li> <li>O'Connor, J. John, and Robertson, F. Edmund, 2002, "Jules Henri Poincaré". University of St. Andrews, Scotland.</li> <li><a href="/wiki/Ivars_Peterson" title="Ivars Peterson">Peterson, Ivars</a>, 1995. <i>Newton's Clock: Chaos in the Solar System</i> (reissue edition). W H Freeman & Co. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-2724-2" title="Special:BookSources/0-7167-2724-2">0-7167-2724-2</a>.</li> <li>Sageret, Jules, 1911. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6Mu4AAAAIAAJ"><i>Henri Poincaré</i></a>. Paris: Mercure de France.</li> <li>Toulouse, E., 1910. <i>Henri Poincaré</i> – (Source biography in French) at University of Michigan Historic Math Collection.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStillwell2010" class="citation book cs1"><a href="/wiki/John_Stillwell" title="John Stillwell">Stillwell, John</a> (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=V7mxZqjs5yUC"><i>Mathematics and Its History</i></a> (3rd, illustrated ed.). Springer Science & Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4419-6052-8" title="Special:BookSources/978-1-4419-6052-8"><bdi>978-1-4419-6052-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+and+Its+History&rft.edition=3rd%2C+illustrated&rft.pub=Springer+Science+%26+Business+Media&rft.date=2010&rft.isbn=978-1-4419-6052-8&rft.aulast=Stillwell&rft.aufirst=John&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DV7mxZqjs5yUC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=_WjVAwAAQBAJ"><i><span></span></i>Papers on Topology: Analysis Situs and Its Five Supplements<i> by Henri Poincaré, translated, with an introduction, by John Stillwell</i></a>. American Mathematical Society. 2010. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-5234-7" title="Special:BookSources/978-0-8218-5234-7"><bdi>978-0-8218-5234-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Papers+on+Topology%3A+Analysis+Situs+and+Its+Five+Supplements+by+Henri+Poincar%C3%A9%2C+translated%2C+with+an+introduction%2C+by+John+Stillwell&rft.pub=American+Mathematical+Society&rft.date=2010&rft.isbn=978-0-8218-5234-7&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D_WjVAwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span> – <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSatzer,_William_J.2011" class="citation web cs1">Satzer, William J. (26 April 2011). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240126002055/https://maa.org/press/maa-reviews/papers-on-topology-ianalysis-situsi-and-its-five-supplements">"Review of <i>Papers on Topology: Analysis Situs and Its Five Supplements</i> by Henri Poincaré, translated and edited by John Stillwell"</a>. <i>MAA Reviews, Mathematical Association of America</i>. Archived from <a rel="nofollow" class="external text" href="https://old.maa.org/press/maa-reviews/papers-on-topology-ianalysis-situsi-and-its-five-supplements">the original</a> on 26 January 2024<span class="reference-accessdate">. Retrieved <span class="nowrap">26 January</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MAA+Reviews%2C+Mathematical+Association+of+America&rft.atitle=Review+of+Papers+on+Topology%3A+Analysis+Situs+and+Its+Five+Supplements+by+Henri+Poincar%C3%A9%2C+translated+and+edited+by+John+Stillwell&rft.date=2011-04-26&rft.au=Satzer%2C+William+J.&rft_id=https%3A%2F%2Fold.maa.org%2Fpress%2Fmaa-reviews%2Fpapers-on-topology-ianalysis-situsi-and-its-five-supplements&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li></ul></li> <li><a href="/w/index.php?title=F._Verhulst&action=edit&redlink=1" class="new" title="F. Verhulst (page does not exist)">Verhulst, Ferdinand</a>, 2012 <i>Henri Poincaré. Impatient Genius</i>. N.Y.: Springer.</li> <li><i>Henri Poincaré, l'œuvre scientifique, l'œuvre philosophique</i>, by Vito Volterra, Jacques Hadamard, Paul Langevin and Pierre Boutroux, Felix Alcan, 1914. <ul><li><i>Henri Poincaré, l'œuvre mathématique</i>, by <a href="/wiki/Vito_Volterra" title="Vito Volterra">Vito Volterra</a>.</li> <li><i>Henri Poincaré, le problème des trois corps</i>, by <a href="/wiki/Jacques_Hadamard" title="Jacques Hadamard">Jacques Hadamard</a>.</li> <li><i>Henri Poincaré, le physicien</i>, by <a href="/wiki/Paul_Langevin" title="Paul Langevin">Paul Langevin</a>.</li> <li><i>Henri Poincaré, l'œuvre philosophique</i>, by <a href="/wiki/Pierre_Boutroux" title="Pierre Boutroux">Pierre Boutroux</a>.</li></ul></li> <li><i>This article incorporates material from Jules Henri Poincaré on <a href="/wiki/PlanetMath" title="PlanetMath">PlanetMath</a>, which is licensed under the <a href="/wiki/Wikipedia:CC-BY-SA" class="mw-redirect" title="Wikipedia:CC-BY-SA">Creative Commons Attribution/Share-Alike License</a>.</i></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=36" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Secondary_sources_to_work_on_relativity">Secondary sources to work on relativity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=37" title="Edit section: Secondary sources to work on relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCuvaj,_Camillo1969" class="citation cs2">Cuvaj, Camillo (1969), "Henri Poincaré's Mathematical Contributions to Relativity and the Poincaré Stresses", <i>American Journal of Physics</i>, <b>36</b> (12): 1102–1113, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1968AmJPh..36.1102C">1968AmJPh..36.1102C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1974373">10.1119/1.1974373</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Henri+Poincar%C3%A9%27s+Mathematical+Contributions+to+Relativity+and+the+Poincar%C3%A9+Stresses&rft.volume=36&rft.issue=12&rft.pages=1102-1113&rft.date=1969&rft_id=info%3Adoi%2F10.1119%2F1.1974373&rft_id=info%3Abibcode%2F1968AmJPh..36.1102C&rft.au=Cuvaj%2C+Camillo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDarrigol,_O.1995" class="citation cs2">Darrigol, O. (1995), "Henri Poincaré's criticism of Fin De Siècle electrodynamics", <i>Studies in History and Philosophy of Science</i>, <b>26</b> (1): 1–44, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1995SHPMP..26....1D">1995SHPMP..26....1D</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F1355-2198%2895%2900003-C">10.1016/1355-2198(95)00003-C</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studies+in+History+and+Philosophy+of+Science&rft.atitle=Henri+Poincar%C3%A9%27s+criticism+of+Fin+De+Si%C3%A8cle+electrodynamics&rft.volume=26&rft.issue=1&rft.pages=1-44&rft.date=1995&rft_id=info%3Adoi%2F10.1016%2F1355-2198%2895%2900003-C&rft_id=info%3Abibcode%2F1995SHPMP..26....1D&rft.au=Darrigol%2C+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDarrigol,_O.2000" class="citation cs2">Darrigol, O. (2000), <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/electrodynamicsf0000darr"><i>Electrodynamics from Ampére to Einstein</i></a></span>, Oxford: Clarendon Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-850594-5" title="Special:BookSources/978-0-19-850594-5"><bdi>978-0-19-850594-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrodynamics+from+Amp%C3%A9re+to+Einstein&rft.place=Oxford&rft.pub=Clarendon+Press&rft.date=2000&rft.isbn=978-0-19-850594-5&rft.au=Darrigol%2C+O.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felectrodynamicsf0000darr&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDarrigol,_O.2004" class="citation cs2">Darrigol, O. (2004), "The Mystery of the Einstein–Poincaré Connection", <i>Isis</i>, <b>95</b> (4): 614–626, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004Isis...95..614D">2004Isis...95..614D</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F430652">10.1086/430652</a>, <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16011297">16011297</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:26997100">26997100</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=The+Mystery+of+the+Einstein%E2%80%93Poincar%C3%A9+Connection&rft.volume=95&rft.issue=4&rft.pages=614-626&rft.date=2004&rft_id=info%3Adoi%2F10.1086%2F430652&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A26997100%23id-name%3DS2CID&rft_id=info%3Apmid%2F16011297&rft_id=info%3Abibcode%2F2004Isis...95..614D&rft.au=Darrigol%2C+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDarrigol,_O.2005" class="citation cs2">Darrigol, O. (2005), <a rel="nofollow" class="external text" href="http://www.bourbaphy.fr/darrigol2.pdf">"The Genesis of the theory of relativity"</a> <span class="cs1-format">(PDF)</span>, <i>Séminaire Poincaré</i>, <b>1</b>: 1–22, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006eins.book....1D">2006eins.book....1D</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F3-7643-7436-5_1">10.1007/3-7643-7436-5_1</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-7643-7435-8" title="Special:BookSources/978-3-7643-7435-8"><bdi>978-3-7643-7435-8</bdi></a>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080228124558/http://www.bourbaphy.fr/darrigol2.pdf">archived</a> <span class="cs1-format">(PDF)</span> from the original on 28 February 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=S%C3%A9minaire+Poincar%C3%A9&rft.atitle=The+Genesis+of+the+theory+of+relativity&rft.volume=1&rft.pages=1-22&rft.date=2005&rft_id=info%3Adoi%2F10.1007%2F3-7643-7436-5_1&rft_id=info%3Abibcode%2F2006eins.book....1D&rft.isbn=978-3-7643-7435-8&rft.au=Darrigol%2C+O.&rft_id=http%3A%2F%2Fwww.bourbaphy.fr%2Fdarrigol2.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGalison,_P.2003" class="citation cs2">Galison, P. (2003), <i>Einstein's Clocks, Poincaré's Maps: Empires of Time</i>, New York: W.W. Norton, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-32604-8" title="Special:BookSources/978-0-393-32604-8"><bdi>978-0-393-32604-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Einstein%27s+Clocks%2C+Poincar%C3%A9%27s+Maps%3A+Empires+of+Time&rft.place=New+York&rft.pub=W.W.+Norton&rft.date=2003&rft.isbn=978-0-393-32604-8&rft.au=Galison%2C+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGiannetto,_E.1998" class="citation cs2">Giannetto, E. 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(1967), "Henri Poincaré and Einstein's Theory of Relativity", <i>American Journal of Physics</i>, <b>35</b> (10): 934–944, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1967AmJPh..35..934G">1967AmJPh..35..934G</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1973643">10.1119/1.1973643</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Henri+Poincar%C3%A9+and+Einstein%27s+Theory+of+Relativity&rft.volume=35&rft.issue=10&rft.pages=934-944&rft.date=1967&rft_id=info%3Adoi%2F10.1119%2F1.1973643&rft_id=info%3Abibcode%2F1967AmJPh..35..934G&rft.au=Goldberg%2C+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoldberg,_S.1970" class="citation cs2">Goldberg, S. 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(1996), "Why did Poincaré not formulate special relativity in 1905?", in Jean-Louis Greffe; Gerhard Heinzmann; Kuno Lorenz (eds.), <i>Henri Poincaré : science et philosophie</i>, Berlin, pp. 69–100</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Why+did+Poincar%C3%A9+not+formulate+special+relativity+in+1905%3F&rft.btitle=Henri+Poincar%C3%A9+%3A+science+et+philosophie&rft.place=Berlin&rft.pages=69-100&rft.date=1996&rft.au=Miller%2C+A.I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Citation" title="Template:Citation">citation</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPopp,_B.D.2020" class="citation cs2">Popp, B.D. (2020), <i>Henri Poincaré: Electrons to Special Relativity</i>, Cham: Springer Nature, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-030-48038-7" title="Special:BookSources/978-3-030-48038-7"><bdi>978-3-030-48038-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Henri+Poincar%C3%A9%3A+Electrons+to+Special+Relativity&rft.place=Cham&rft.pub=Springer+Nature&rft.date=2020&rft.isbn=978-3-030-48038-7&rft.au=Popp%2C+B.D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwartz,_H._M.1971" class="citation cs2">Schwartz, H. M. (1971), "Poincaré's Rendiconti Paper on Relativity. Part I", <i>American Journal of Physics</i>, <b>39</b> (7): 1287–1294, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1971AmJPh..39.1287S">1971AmJPh..39.1287S</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1976641">10.1119/1.1976641</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Poincar%C3%A9%27s+Rendiconti+Paper+on+Relativity.+Part+I&rft.volume=39&rft.issue=7&rft.pages=1287-1294&rft.date=1971&rft_id=info%3Adoi%2F10.1119%2F1.1976641&rft_id=info%3Abibcode%2F1971AmJPh..39.1287S&rft.au=Schwartz%2C+H.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwartz,_H._M.1972" class="citation cs2">Schwartz, H. M. (1972), "Poincaré's Rendiconti Paper on Relativity. Part II", <i>American Journal of Physics</i>, <b>40</b> (6): 862–872, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1972AmJPh..40..862S">1972AmJPh..40..862S</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1986684">10.1119/1.1986684</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Poincar%C3%A9%27s+Rendiconti+Paper+on+Relativity.+Part+II&rft.volume=40&rft.issue=6&rft.pages=862-872&rft.date=1972&rft_id=info%3Adoi%2F10.1119%2F1.1986684&rft_id=info%3Abibcode%2F1972AmJPh..40..862S&rft.au=Schwartz%2C+H.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwartz,_H._M.1972" class="citation cs2">Schwartz, H. M. (1972), "Poincaré's Rendiconti Paper on Relativity. Part III", <i>American Journal of Physics</i>, <b>40</b> (9): 1282–1287, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1972AmJPh..40.1282S">1972AmJPh..40.1282S</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1986815">10.1119/1.1986815</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Poincar%C3%A9%27s+Rendiconti+Paper+on+Relativity.+Part+III&rft.volume=40&rft.issue=9&rft.pages=1282-1287&rft.date=1972&rft_id=info%3Adoi%2F10.1119%2F1.1986815&rft_id=info%3Abibcode%2F1972AmJPh..40.1282S&rft.au=Schwartz%2C+H.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScribner,_C.1964" class="citation cs2">Scribner, C. (1964), "Henri Poincaré and the principle of relativity", <i>American Journal of Physics</i>, <b>32</b> (9): 672–678, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1964AmJPh..32..672S">1964AmJPh..32..672S</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.1970936">10.1119/1.1970936</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=Henri+Poincar%C3%A9+and+the+principle+of+relativity&rft.volume=32&rft.issue=9&rft.pages=672-678&rft.date=1964&rft_id=info%3Adoi%2F10.1119%2F1.1970936&rft_id=info%3Abibcode%2F1964AmJPh..32..672S&rft.au=Scribner%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalter,_S.2005" class="citation cs2">Walter, S. (2005), <a rel="nofollow" class="external text" href="http://scottwalter.free.fr/papers/2005-100authors-poincare-einstein-walter.html">"Henri Poincaré and the theory of relativity"</a>, in Renn, J. (ed.), <i>Albert Einstein, Chief Engineer of the Universe: 100 Authors for Einstein</i>, Berlin: Wiley-VCH, pp. 162–165</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Henri+Poincar%C3%A9+and+the+theory+of+relativity&rft.btitle=Albert+Einstein%2C+Chief+Engineer+of+the+Universe%3A+100+Authors+for+Einstein&rft.place=Berlin&rft.pages=162-165&rft.pub=Wiley-VCH&rft.date=2005&rft.au=Walter%2C+S.&rft_id=http%3A%2F%2Fscottwalter.free.fr%2Fpapers%2F2005-100authors-poincare-einstein-walter.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalter,_S.2007" class="citation cs2">Walter, S. (2007), <a rel="nofollow" class="external text" href="http://scottwalter.free.fr/papers/2007-genesis-walter.html">"Breaking in the 4-vectors: the four-dimensional movement in gravitation, 1905–1910"</a>, in Renn, J. (ed.), <i>The Genesis of General Relativity</i>, vol. 3, Berlin: Springer, pp. 193–252</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Breaking+in+the+4-vectors%3A+the+four-dimensional+movement+in+gravitation%2C+1905%E2%80%931910&rft.btitle=The+Genesis+of+General+Relativity&rft.place=Berlin&rft.pages=193-252&rft.pub=Springer&rft.date=2007&rft.au=Walter%2C+S.&rft_id=http%3A%2F%2Fscottwalter.free.fr%2Fpapers%2F2007-genesis-walter.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhittaker,_E.T.1953" class="citation cs2"><a href="/wiki/E._T._Whittaker" title="E. T. Whittaker">Whittaker, E.T.</a> (1953), "The Relativity Theory of Poincaré and Lorentz", <i><a href="/wiki/A_History_of_the_Theories_of_Aether_and_Electricity" title="A History of the Theories of Aether and Electricity">A History of the Theories of Aether and Electricity: The Modern Theories 1900–1926</a></i>, London: Nelson</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Relativity+Theory+of+Poincar%C3%A9+and+Lorentz&rft.btitle=A+History+of+the+Theories+of+Aether+and+Electricity%3A+The+Modern+Theories+1900%E2%80%931926&rft.place=London&rft.pub=Nelson&rft.date=1953&rft.au=Whittaker%2C+E.T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZahar,_E.2001" class="citation cs2">Zahar, E. (2001), <i>Poincaré's Philosophy: From Conventionalism to Phenomenology</i>, Chicago: Open Court Pub Co, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8126-9435-2" title="Special:BookSources/978-0-8126-9435-2"><bdi>978-0-8126-9435-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Poincar%C3%A9%27s+Philosophy%3A+From+Conventionalism+to+Phenomenology&rft.place=Chicago&rft.pub=Open+Court+Pub+Co&rft.date=2001&rft.isbn=978-0-8126-9435-2&rft.au=Zahar%2C+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Non-mainstream_sources">Non-mainstream sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=38" title="Edit section: Non-mainstream sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeveugle,_J.2004" class="citation cs2">Leveugle, J. (2004), <i>La Relativité et Einstein, Planck, Hilbert – Histoire véridique de la Théorie de la Relativitén</i>, Pars: L'Harmattan</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=La+Relativit%C3%A9+et+Einstein%2C+Planck%2C+Hilbert+%E2%80%93+Histoire+v%C3%A9ridique+de+la+Th%C3%A9orie+de+la+Relativit%C3%A9n&rft.place=Pars&rft.pub=L%27Harmattan&rft.date=2004&rft.au=Leveugle%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLogunov,_A.A.2004" class="citation cs2">Logunov, A.A. (2004), <i>Henri Poincaré and relativity theory</i>, <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/physics/0408077">physics/0408077</a></span>, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004physics...8077L">2004physics...8077L</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-5-02-033964-4" title="Special:BookSources/978-5-02-033964-4"><bdi>978-5-02-033964-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Henri+Poincar%C3%A9+and+relativity+theory&rft.date=2004&rft_id=info%3Aarxiv%2Fphysics%2F0408077&rft_id=info%3Abibcode%2F2004physics...8077L&rft.isbn=978-5-02-033964-4&rft.au=Logunov%2C+A.A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Henri_Poincar%C3%A9&action=edit&section=39" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid 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href="https://archive.org/search.php?query=%28%28subject%3A%22Poincaré%2C%20Henri%22%20OR%20subject%3A%22Henri%20Poincaré%22%20OR%20creator%3A%22Poincaré%2C%20Henri%22%20OR%20creator%3A%22Henri%20Poincaré%22%20OR%20creator%3A%22Poincaré%2C%20H%2E%22%20OR%20title%3A%22Henri%20Poincaré%22%20OR%20description%3A%22Poincaré%2C%20Henri%22%20OR%20description%3A%22Henri%20Poincaré%22%20OR%20%28Henri+Poincar%2A%29%29%20OR%20%28%221854-1912%22%20AND%20%28%22Poincaré%22%20OR%20Poincare%29%29%29%20AND%20%28-mediatype:software%29">Works by or about Henri Poincaré</a> at the <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a></li> <li><a rel="nofollow" class="external text" href="https://librivox.org/author/4281">Works by Henri Poincaré</a> at <a href="/wiki/LibriVox" title="LibriVox">LibriVox</a> (public domain audiobooks) <span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/15px-Speaker_Icon.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/23px-Speaker_Icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/30px-Speaker_Icon.svg.png 2x" data-file-width="500" data-file-height="500" /></span></span></li> <li><a rel="nofollow" class="external text" href="http://henripoincarepapers.univ-nantes.fr/en/bibliohp/">Henri Poincaré's Bibliography</a></li> <li><a href="/wiki/Internet_Encyclopedia_of_Philosophy" title="Internet Encyclopedia of Philosophy">Internet Encyclopedia of Philosophy</a>: "<a rel="nofollow" class="external text" href="http://www.utm.edu/research/iep/p/poincare.htm">Henri Poincaré</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20040202060803/http://www.utm.edu/research/iep/p/poincare.htm">Archived</a> 2 February 2004 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>" – by Mauro Murzi.</li> <li><a href="/wiki/Internet_Encyclopedia_of_Philosophy" title="Internet Encyclopedia of Philosophy">Internet Encyclopedia of Philosophy</a>: "<a rel="nofollow" class="external text" href="http://www.iep.utm.edu/poi-math/">Poincaré’s Philosophy of Mathematics</a>" – by Janet Folina.</li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=34227">Henri Poincaré</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090930005045/https://www.informationphilosopher.com/solutions/scientists/poincare/">Henri Poincaré on Information Philosopher</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Poincare.html">"Henri Poincaré"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Henri+Poincar%C3%A9&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FPoincare.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHenri+Poincar%C3%A9" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://henripoincarepapers.univ-nantes.fr/chronos.php">A timeline of Poincaré's life</a> University of Nantes (in French).</li> <li><a rel="nofollow" class="external text" href="http://henripoincarepapers.univ-nantes.fr">Henri Poincaré Papers</a> University of Nantes (in French).</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060627062431/https://www.phys-astro.sonoma.edu/BruceMedalists/Poincare/index.html">Bruce Medal page</a></li> <li>Collins, Graham P., "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20071017055831/http://www.sciam.com/print_version.cfm?articleID=0003848D-1C61-10C7-9C6183414B7F0000">Henri Poincaré, His Conjecture, Copacabana and Higher Dimensions</a>," <i><a href="/wiki/Scientific_American" title="Scientific American">Scientific American</a></i>, 9 June 2004.</li> <li>BBC in Our Time, "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20090424054425/http://www.bbc.co.uk/radio4/history/inourtime/inourtime.shtml">Discussion of the Poincaré conjecture</a>," 2 November 2006, hosted by <a href="/wiki/Melvyn_Bragg" title="Melvyn Bragg">Melvyn Bragg</a>.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070927190224/http://www.mathpages.com/home/kmath305/kmath305.htm">Poincare Contemplates Copernicus</a> at MathPages</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/user/thedebtgeneration?feature=mhum#p/u/8/5pKrKdNclYs0">High Anxieties – The Mathematics of Chaos</a> (2008) BBC documentary directed by <a href="/wiki/David_Malone_(independent_filmmaker)" title="David Malone (independent filmmaker)">David Malone</a> looking at the influence of Poincaré's discoveries on 20th Century mathematics.</li></ul> <table class="wikitable succession-box noprint" style="margin:0.5em auto; font-size:small;clear:both;"> <tbody><tr> <th colspan="3" style="border-top: 5px solid #99CCFF;">Cultural offices </th></tr> <tr style="text-align:center;"> <td style="width:30%;" rowspan="1">Preceded by<div style="font-weight: bold"><a href="/wiki/Sully_Prudhomme" title="Sully Prudhomme">Sully Prudhomme</a></div> </td> <td style="width: 40%; text-align: center;" rowspan="1"><b> <a href="/wiki/List_of_members_of_the_Acad%C3%A9mie_fran%C3%A7aise#Seat_24" title="List of members of the Académie française">Seat 24</a><br /><a href="/wiki/Acad%C3%A9mie_fran%C3%A7aise" class="mw-redirect" title="Académie française">Académie française</a><br />1908–1912 </b> </td> <td style="width: 30%; text-align: center;" rowspan="1">Succeeded by<div style="font-weight: bold"><a href="/wiki/Alfred_Capus" title="Alfred Capus">Alfred Capus</a></div> </td></tr> </tbody></table> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid 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.navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Philosophy_of_science" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Philosophy_of_science" title="Template:Philosophy of science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Philosophy_of_science" title="Template talk:Philosophy of science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Philosophy_of_science" 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Methods</a></li></ul></li> <li><a href="/wiki/Commensurability_(philosophy_of_science)" title="Commensurability (philosophy of science)">Commensurability</a></li> <li><a href="/wiki/Consilience" title="Consilience">Consilience</a></li> <li><a href="/wiki/Construct_(philosophy)" title="Construct (philosophy)">Construct</a></li> <li><a href="/wiki/Correlation" title="Correlation">Correlation</a> <ul><li><a href="/wiki/Correlation_function" title="Correlation function">function</a></li></ul></li> <li><a href="/wiki/Creative_synthesis" title="Creative synthesis">Creative synthesis</a></li> <li><a href="/wiki/Demarcation_problem" title="Demarcation problem">Demarcation problem</a></li> <li><a href="/wiki/Empirical_evidence" title="Empirical evidence">Empirical evidence</a></li> <li><a href="/wiki/Experiment" title="Experiment">Experiment</a> <ul><li><a href="/wiki/Design_of_experiments" title="Design of experiments">design</a></li></ul></li> <li><a href="/wiki/Explanatory_power" title="Explanatory power">Explanatory power</a></li> <li><a href="/wiki/Fact" title="Fact">Fact</a></li> <li><a href="/wiki/Falsifiability" title="Falsifiability">Falsifiability</a></li> <li><a href="/wiki/Feminist_method" title="Feminist method">Feminist method</a></li> <li><a href="/wiki/Functional_contextualism" title="Functional contextualism">Functional contextualism</a></li> <li><a href="/wiki/Hypothesis" title="Hypothesis">Hypothesis</a> <ul><li><a href="/wiki/Alternative_hypothesis" title="Alternative hypothesis">alternative</a></li> <li><a href="/wiki/Null_hypothesis" title="Null hypothesis">null</a></li></ul></li> <li><i><a href="/wiki/Ignoramus_et_ignorabimus" title="Ignoramus et ignorabimus">Ignoramus et ignorabimus</a></i></li> <li><a href="/wiki/Inductive_reasoning" title="Inductive reasoning">Inductive reasoning</a></li> <li><a href="/wiki/Intertheoretic_reduction" title="Intertheoretic reduction">Intertheoretic reduction</a></li> <li><a href="/wiki/Inquiry" title="Inquiry">Inquiry</a></li> <li><a href="/wiki/Nature_(philosophy)" title="Nature (philosophy)">Nature</a></li> <li><a href="/wiki/Objectivity_(philosophy)" class="mw-redirect" title="Objectivity (philosophy)">Objectivity</a></li> <li><a href="/wiki/Observation" title="Observation">Observation</a></li> <li><a href="/wiki/Paradigm" title="Paradigm">Paradigm</a></li> <li><a href="/wiki/Problem_of_induction" title="Problem of induction">Problem of induction</a></li> <li><a href="/wiki/Scientific_evidence" title="Scientific evidence">Scientific evidence</a> <ul><li><a href="/wiki/Evidence-based_practice" title="Evidence-based practice">Evidence-based practice</a></li></ul></li> <li><a href="/wiki/Scientific_law" title="Scientific law">Scientific law</a></li> <li><a href="/wiki/Scientific_method" title="Scientific method">Scientific method</a></li> <li><a href="/wiki/Scientific_pluralism" title="Scientific pluralism">Scientific pluralism</a></li> <li><a href="/wiki/Scientific_Revolution" title="Scientific Revolution">Scientific Revolution</a></li> <li><a href="/wiki/Testability" title="Testability">Testability</a></li> <li><a href="/wiki/Theory" title="Theory">Theory</a> <ul><li><a href="/wiki/Theory_choice" title="Theory choice">choice</a></li> <li><a href="/wiki/Theory-ladenness" title="Theory-ladenness">ladenness</a></li> <li><a href="/wiki/Scientific_theory" title="Scientific theory">scientific</a></li></ul></li> <li><a href="/wiki/Underdetermination" title="Underdetermination">Underdetermination</a></li> <li><a href="/wiki/Unity_of_science" title="Unity of science">Unity of science</a></li> <li><a href="/wiki/Variable_and_attribute_(research)" title="Variable and attribute (research)">Variable</a> <ul><li><a href="/wiki/Control_variable" title="Control variable">control</a></li> <li><a href="/wiki/Dependent_and_independent_variables" title="Dependent and independent variables">dependent and independent</a></li></ul></li> <li><a href="/wiki/Index_of_philosophy_of_science_articles" title="Index of philosophy of science articles">more...</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coherentism" title="Coherentism">Coherentism</a></li> <li><a href="/wiki/Confirmation_holism" title="Confirmation holism">Confirmation holism</a></li> <li><a href="/wiki/Constructive_empiricism" title="Constructive empiricism">Constructive empiricism</a></li> <li><a href="/wiki/Constructive_realism" title="Constructive realism">Constructive realism</a></li> <li><a href="/wiki/Constructivist_epistemology" class="mw-redirect" title="Constructivist epistemology">Constructivist epistemology</a></li> <li><a href="/wiki/Contextualism" title="Contextualism">Contextualism</a></li> <li><a href="/wiki/Conventionalism" title="Conventionalism">Conventionalism</a></li> <li><a href="/wiki/Deductive-nomological_model" title="Deductive-nomological model">Deductive-nomological model</a></li> <li><a href="/wiki/Epistemological_anarchism" class="mw-redirect" title="Epistemological anarchism">Epistemological anarchism</a></li> <li><a href="/wiki/Evolutionism" title="Evolutionism">Evolutionism</a></li> <li><a href="/wiki/Fallibilism" title="Fallibilism">Fallibilism</a></li> <li><a href="/wiki/Foundationalism" title="Foundationalism">Foundationalism</a></li> <li><a href="/wiki/Hypothetico-deductive_model" title="Hypothetico-deductive model">Hypothetico-deductive model</a></li> <li><a href="/wiki/Inductionism" title="Inductionism">Inductionism</a></li> <li><a href="/wiki/Instrumentalism" title="Instrumentalism">Instrumentalism</a></li> <li><a href="/wiki/Model-dependent_realism" title="Model-dependent realism">Model-dependent realism</a></li> <li><a href="/wiki/Naturalism_(philosophy)" title="Naturalism (philosophy)">Naturalism</a></li> <li><a href="/wiki/Physicalism" title="Physicalism">Physicalism</a></li> <li><a href="/wiki/Positivism" title="Positivism">Positivism</a> / <a href="/wiki/Reductionism" title="Reductionism">Reductionism</a> / <a href="/wiki/Determinism" title="Determinism">Determinism</a></li> <li><a href="/wiki/Pragmatism" title="Pragmatism">Pragmatism</a></li> <li><a href="/wiki/Rationalism" title="Rationalism">Rationalism</a> / <a href="/wiki/Empiricism" title="Empiricism">Empiricism</a></li> <li><a href="/wiki/Received_view_of_theories" title="Received view of theories">Received view</a> / <a href="/wiki/Semantic_view_of_theories" title="Semantic view of theories">Semantic view of theories</a></li> <li><a href="/wiki/Scientific_essentialism" title="Scientific essentialism">Scientific essentialism</a></li> <li><a href="/wiki/Scientific_formalism" title="Scientific formalism">Scientific formalism</a></li> <li><a href="/wiki/Scientific_realism" title="Scientific realism">Scientific realism</a> / <a href="/wiki/Anti-realism" title="Anti-realism">Anti-realism</a></li> <li><a href="/wiki/Scientific_skepticism" title="Scientific skepticism">Scientific skepticism</a></li> <li><a href="/wiki/Scientism" title="Scientism">Scientism</a></li> <li><a href="/wiki/Structuralism_(philosophy_of_science)" title="Structuralism (philosophy of science)">Structuralism</a></li> <li><a href="/wiki/Uniformitarianism" title="Uniformitarianism">Uniformitarianism</a></li> <li><a href="/wiki/Verificationism" title="Verificationism">Verificationism</a></li> <li><a href="/wiki/Vitalism" title="Vitalism">Vitalism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Philosophy of...</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Philosophy_of_biology" title="Philosophy of biology">Biology</a></li> <li><a href="/wiki/Philosophy_of_chemistry" title="Philosophy of chemistry">Chemistry</a></li> <li><a href="/wiki/Philosophy_of_physics" title="Philosophy of physics">Physics</a> <ul><li><a href="/wiki/Philosophy_of_space_and_time" title="Philosophy of space and time">Space and time</a></li></ul></li> <li><a href="/wiki/Philosophy_of_social_science" title="Philosophy of social science">Social science</a> <ul><li><a href="/wiki/Philosophy_of_archaeology" title="Philosophy of archaeology">Archaeology</a></li> <li><a href="/wiki/Philosophy_of_economics" class="mw-redirect" title="Philosophy of economics">Economics‎</a></li> <li><a href="/wiki/Philosophy_of_geography" title="Philosophy of geography">Geography</a></li> <li><a href="/wiki/Philosophy_of_history" title="Philosophy of history">History</a></li> <li><a href="/wiki/Philosophy_of_linguistics" title="Philosophy of linguistics">Linguistics</a></li> <li><a href="/wiki/Philosophy_of_psychology" title="Philosophy of psychology">Psychology</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Criticism_of_science" title="Criticism of science">Criticism of science</a></li> <li><a href="/wiki/Descriptive_research" title="Descriptive research">Descriptive science</a></li> <li><a href="/wiki/Epistemology" title="Epistemology">Epistemology</a></li> <li><a href="/wiki/Exact_sciences" title="Exact sciences">Exact sciences</a></li> <li><a href="/wiki/Faith_and_rationality" title="Faith and rationality">Faith and rationality</a></li> <li><a href="/wiki/Hard_and_soft_science" title="Hard and soft science">Hard and soft science</a></li> <li><a href="/wiki/History_and_philosophy_of_science" title="History and philosophy of science">History and philosophy of science</a></li> <li><a href="/wiki/Non-science" title="Non-science">Non-science</a> <ul><li><a href="/wiki/Pseudoscience" title="Pseudoscience">Pseudoscience</a></li></ul></li> <li><a href="/wiki/Normative_science" title="Normative science">Normative science</a></li> <li><a href="/wiki/Protoscience" title="Protoscience">Protoscience</a></li> <li><a href="/wiki/Questionable_cause" title="Questionable cause">Questionable cause</a></li> <li><a href="/wiki/Relationship_between_religion_and_science" title="Relationship between religion and science">Relationship between religion and science</a></li> <li><a href="/wiki/Rhetoric_of_science" title="Rhetoric of science">Rhetoric of science</a></li> <li><a href="/wiki/Science_studies" title="Science studies">Science studies</a></li> <li><a href="/wiki/Sociology_of_scientific_ignorance" title="Sociology of scientific ignorance">Sociology of scientific ignorance</a></li> <li><a href="/wiki/Sociology_of_scientific_knowledge" title="Sociology of scientific knowledge">Sociology of scientific knowledge</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_philosophers_of_science" title="List of philosophers of science">Philosophers of science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Precursors" scope="row" class="navbox-group" style="width:7.5em">Precursors</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Roger_Bacon" title="Roger Bacon">Roger Bacon</a></li> <li><a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a></li> <li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a></li> <li><a href="/wiki/David_Hume" title="David Hume">David Hume</a></li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Auguste_Comte" title="Auguste Comte">Auguste Comte</a></li> <li><a class="mw-selflink selflink">Henri Poincaré</a></li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Pierre Duhem</a></li> <li><a href="/wiki/Rudolf_Steiner" title="Rudolf Steiner">Rudolf Steiner</a></li> <li><a href="/wiki/Karl_Pearson" title="Karl Pearson">Karl Pearson</a></li> <li><a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a></li> <li><a href="/wiki/Wilhelm_Windelband" title="Wilhelm Windelband">Wilhelm Windelband</a></li> <li><a href="/wiki/Alfred_North_Whitehead" title="Alfred North Whitehead">Alfred North Whitehead</a></li> <li><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a></li> <li><a href="/wiki/Otto_Neurath" title="Otto Neurath">Otto Neurath</a></li> <li><a href="/wiki/C._D._Broad" title="C. D. Broad">C. D. Broad</a></li> <li><a href="/wiki/Michael_Polanyi" title="Michael Polanyi">Michael Polanyi</a></li> <li><a href="/wiki/Hans_Reichenbach" title="Hans Reichenbach">Hans Reichenbach</a></li> <li><a href="/wiki/Rudolf_Carnap" title="Rudolf Carnap">Rudolf Carnap</a></li> <li><a href="/wiki/Karl_Popper" title="Karl Popper">Karl Popper</a></li> <li><a href="/wiki/Carl_Gustav_Hempel" title="Carl Gustav Hempel">Carl Gustav Hempel</a></li> <li><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">W. V. O. Quine</a></li> <li><a href="/wiki/Thomas_Kuhn" title="Thomas Kuhn">Thomas Kuhn</a></li> <li><a href="/wiki/Imre_Lakatos" title="Imre Lakatos">Imre Lakatos</a></li> <li><a href="/wiki/Paul_Feyerabend" title="Paul Feyerabend">Paul Feyerabend</a></li> <li><a href="/wiki/Ian_Hacking" title="Ian Hacking">Ian Hacking</a></li> <li><a href="/wiki/Bas_van_Fraassen" title="Bas van Fraassen">Bas van Fraassen</a></li> <li><a href="/wiki/Larry_Laudan" title="Larry Laudan">Larry Laudan</a></li></ul></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <li><a href="/wiki/Category:Philosophy_of_science" title="Category:Philosophy of science">Category</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/36px-Socrates.png 2x" data-file-width="326" data-file-height="500" /></span></span> </span><a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_kalzium.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/28px-Nuvola_apps_kalzium.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/42px-Nuvola_apps_kalzium.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/56px-Nuvola_apps_kalzium.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Science" title="Portal:Science">Science portal</a></li> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Chaos_theory" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Chaos_theory" title="Template:Chaos theory"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Chaos_theory" title="Template talk:Chaos theory"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Chaos_theory" title="Special:EditPage/Template:Chaos theory"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Chaos_theory" style="font-size:114%;margin:0 4em"><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Core" scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Core</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Attractor" title="Attractor">Attractor</a></li> <li><a href="/wiki/Bifurcation_theory" title="Bifurcation theory">Bifurcation</a></li> <li><a href="/wiki/Fractal" title="Fractal">Fractal</a></li> <li><a href="/wiki/Limit_set" title="Limit set">Limit set</a></li> <li><a href="/wiki/Lyapunov_exponent" title="Lyapunov exponent">Lyapunov exponent</a></li> <li><a href="/wiki/Orbit_(dynamics)" title="Orbit (dynamics)">Orbit</a></li> <li><a href="/wiki/Periodic_point" title="Periodic point">Periodic point</a></li> <li><a href="/wiki/Phase_space" title="Phase space">Phase space</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anosov_diffeomorphism" title="Anosov diffeomorphism">Anosov diffeomorphism</a></li> <li><a href="/wiki/Arnold_tongue" title="Arnold tongue">Arnold tongue</a></li> <li><a href="/wiki/Axiom_A" title="Axiom A">axiom A dynamical system</a></li> <li><a href="/wiki/Bifurcation_diagram" title="Bifurcation diagram">Bifurcation diagram</a></li> <li><a href="/wiki/Box-counting_dimension" class="mw-redirect" title="Box-counting dimension">Box-counting dimension</a></li> <li><a href="/wiki/Correlation_dimension" title="Correlation dimension">Correlation dimension</a></li> <li><a href="/wiki/Conservative_system" title="Conservative system">Conservative system</a></li> <li><a href="/wiki/Ergodicity" title="Ergodicity">Ergodicity</a></li> <li><a href="/wiki/False_nearest_neighbors" class="mw-redirect" title="False nearest neighbors">False nearest neighbors</a></li> <li><a href="/wiki/Hausdorff_dimension" title="Hausdorff dimension">Hausdorff dimension</a></li> <li><a href="/wiki/Invariant_measure" title="Invariant measure">Invariant measure</a></li> <li><a href="/wiki/Lyapunov_stability" title="Lyapunov stability">Lyapunov stability</a></li> <li><a href="/wiki/Measure-preserving_dynamical_system" title="Measure-preserving dynamical system">Measure-preserving dynamical system</a></li> <li><a href="/wiki/Mixing_(mathematics)" title="Mixing (mathematics)">Mixing</a></li> <li><a href="/wiki/Poincar%C3%A9_section" class="mw-redirect" title="Poincaré section">Poincaré section</a></li> <li><a href="/wiki/Recurrence_plot" title="Recurrence plot">Recurrence plot</a></li> <li><a href="/wiki/SRB_measure" class="mw-redirect" title="SRB measure">SRB measure</a></li> <li><a href="/wiki/Stable_manifold" title="Stable manifold">Stable manifold</a></li> <li><a href="/wiki/Topological_conjugacy" title="Topological conjugacy">Topological conjugacy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Theorems</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ergodic_theory#Ergodic_theorems" title="Ergodic theory">Ergodic theorem</a></li> <li><a href="/wiki/Liouville%27s_theorem_(Hamiltonian)" title="Liouville's theorem (Hamiltonian)">Liouville's theorem</a></li> <li><a href="/wiki/Krylov%E2%80%93Bogolyubov_theorem" title="Krylov–Bogolyubov theorem">Krylov–Bogolyubov theorem</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Bendixson_theorem" title="Poincaré–Bendixson theorem">Poincaré–Bendixson theorem</a></li> <li><a href="/wiki/Poincar%C3%A9_recurrence_theorem" title="Poincaré recurrence theorem">Poincaré recurrence theorem</a></li> <li><a href="/wiki/Stable_manifold_theorem" title="Stable manifold theorem">Stable manifold theorem</a></li> <li><a href="/wiki/Takens%27s_theorem" title="Takens's theorem">Takens's theorem</a></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:C%C3%B4ne_textileII.png" class="mw-file-description" title="Conus textile shell"><img alt="Conus textile shell" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/100px-C%C3%B4ne_textileII.png" decoding="async" width="100" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/150px-C%C3%B4ne_textileII.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/200px-C%C3%B4ne_textileII.png 2x" data-file-width="2344" data-file-height="4211" /></a></span> <p><br /> </p> <span typeof="mw:File"><a href="/wiki/File:Circle_map_poincare_recurrence.jpeg" class="mw-file-description" title="Circle map with black Arnold tongues"><img alt="Circle map with black Arnold tongues" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/100px-Circle_map_poincare_recurrence.jpeg" decoding="async" width="100" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/150px-Circle_map_poincare_recurrence.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/200px-Circle_map_poincare_recurrence.jpeg 2x" data-file-width="450" data-file-height="900" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theoretical<br />branches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bifurcation_theory" title="Bifurcation theory">Bifurcation theory</a></li> <li><a href="/wiki/Control_of_chaos" title="Control of chaos">Control of chaos</a></li> <li><a href="/wiki/Dynamical_system" title="Dynamical system">Dynamical system</a></li> <li><a href="/wiki/Ergodic_theory" title="Ergodic theory">Ergodic theory</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Stability_theory" title="Stability theory">Stability theory</a></li> <li><a href="/wiki/Synchronization_of_chaos" title="Synchronization of chaos">Synchronization of chaos</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chaotic<br />maps (<a href="/wiki/List_of_chaotic_maps" title="List of chaotic maps">list</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Discrete</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arnold%27s_cat_map" title="Arnold's cat map">Arnold's cat map</a></li> <li><a href="/wiki/Baker%27s_map" title="Baker's map">Baker's map</a></li> <li><a href="/wiki/Complex_quadratic_polynomial" title="Complex quadratic polynomial">Complex quadratic map</a></li> <li><a href="/wiki/Coupled_map_lattice" title="Coupled map lattice">Coupled map lattice</a></li> <li><a href="/wiki/Duffing_map" title="Duffing map">Duffing map</a></li> <li><a href="/wiki/Dyadic_transformation" title="Dyadic transformation">Dyadic transformation</a></li> <li><a href="/wiki/Dynamical_billiards" title="Dynamical billiards">Dynamical billiards</a> <ul><li><a href="/wiki/Outer_billiards" title="Outer billiards">outer</a></li></ul></li> <li><a href="/wiki/Exponential_map_(discrete_dynamical_systems)" title="Exponential map (discrete dynamical systems)">Exponential map</a></li> <li><a href="/wiki/Gauss_iterated_map" title="Gauss iterated map">Gauss map</a></li> <li><a href="/wiki/Gingerbreadman_map" title="Gingerbreadman map">Gingerbreadman map</a></li> <li><a href="/wiki/H%C3%A9non_map" title="Hénon map">Hénon map</a></li> <li><a href="/wiki/Horseshoe_map" title="Horseshoe map">Horseshoe map</a></li> <li><a href="/wiki/Ikeda_map" title="Ikeda map">Ikeda map</a></li> <li><a href="/wiki/Interval_exchange_transformation" title="Interval exchange transformation">Interval exchange map</a></li> <li><a href="/wiki/Irrational_rotation" title="Irrational rotation">Irrational rotation</a></li> <li><a href="/wiki/Kaplan%E2%80%93Yorke_map" title="Kaplan–Yorke map">Kaplan–Yorke map</a></li> <li><a href="/wiki/Langton%27s_ant" title="Langton's ant">Langton's ant</a></li> <li><a href="/wiki/Logistic_map" title="Logistic map">Logistic map</a></li> <li><a href="/wiki/Standard_map" title="Standard map">Standard map</a></li> <li><a href="/wiki/Tent_map" title="Tent map">Tent map</a></li> <li><a href="/wiki/Tinkerbell_map" title="Tinkerbell map">Tinkerbell map</a></li> <li><a href="/wiki/Zaslavskii_map" title="Zaslavskii map">Zaslavskii map</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Continuous</div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Double_scroll_attractor" class="mw-redirect" title="Double scroll attractor">Double scroll attractor</a></li> <li><a href="/wiki/Duffing_equation" title="Duffing equation">Duffing equation</a></li> <li><a href="/wiki/Lorenz_system" title="Lorenz system">Lorenz system</a></li> <li><a href="/wiki/Lotka%E2%80%93Volterra_equations" title="Lotka–Volterra equations">Lotka–Volterra equations</a></li> <li><a href="/wiki/Mackey%E2%80%93Glass_equations" title="Mackey–Glass equations">Mackey–Glass equations</a></li> <li><a href="/wiki/Rabinovich%E2%80%93Fabrikant_equations" title="Rabinovich–Fabrikant equations">Rabinovich–Fabrikant equations</a></li> <li><a href="/wiki/R%C3%B6ssler_attractor" title="Rössler attractor">Rössler attractor</a></li> <li><a href="/wiki/Three-body_problem" title="Three-body problem">Three-body problem</a></li> <li><a href="/wiki/Van_der_Pol_oscillator" title="Van der Pol oscillator">Van der Pol oscillator</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physical<br />systems</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chua%27s_circuit" title="Chua's circuit">Chua's circuit</a></li> <li><a href="/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection" title="Rayleigh–Bénard convection">Convection</a></li> <li><a href="/wiki/Double_pendulum" title="Double pendulum">Double pendulum</a></li> <li><a href="/wiki/Elastic_pendulum" title="Elastic pendulum">Elastic pendulum</a></li> <li><a href="/wiki/Fermi%E2%80%93Pasta%E2%80%93Ulam%E2%80%93Tsingou_problem" title="Fermi–Pasta–Ulam–Tsingou problem">FPUT problem</a></li> <li><a href="/wiki/H%C3%A9non%E2%80%93Heiles_system" title="Hénon–Heiles system">Hénon–Heiles system</a></li> <li><a href="/wiki/Kicked_rotator" title="Kicked rotator">Kicked rotator</a></li> <li><a href="/wiki/Multiscroll_attractor" title="Multiscroll attractor">Multiscroll attractor</a></li> <li><a href="/wiki/Population_dynamics" title="Population dynamics">Population dynamics</a></li> <li><a href="/wiki/Swinging_Atwood%27s_machine" title="Swinging Atwood's machine">Swinging Atwood's machine</a></li> <li><a href="/wiki/Tilt-A-Whirl" title="Tilt-A-Whirl">Tilt-A-Whirl</a></li> <li><a href="/wiki/Weather_forecasting" title="Weather forecasting">Weather</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chaos<br />theorists</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Michael_Berry_(physicist)" title="Michael Berry (physicist)">Michael Berry</a></li> <li><a href="/wiki/Rufus_Bowen" title="Rufus Bowen">Rufus Bowen</a></li> <li><a href="/wiki/Mary_Cartwright" title="Mary Cartwright">Mary Cartwright</a></li> <li><a href="/wiki/Chen_Guanrong" title="Chen Guanrong">Chen Guanrong</a></li> <li><a href="/wiki/Leon_O._Chua" title="Leon O. Chua">Leon O. Chua</a></li> <li><a href="/wiki/Mitchell_Feigenbaum" title="Mitchell Feigenbaum">Mitchell Feigenbaum</a></li> <li><a href="/wiki/Peter_Grassberger" title="Peter Grassberger">Peter Grassberger</a></li> <li><a href="/wiki/Celso_Grebogi" title="Celso Grebogi">Celso Grebogi</a></li> <li><a href="/wiki/Martin_Gutzwiller" title="Martin Gutzwiller">Martin Gutzwiller</a></li> <li><a href="/wiki/Brosl_Hasslacher" title="Brosl Hasslacher">Brosl Hasslacher</a></li> <li><a href="/wiki/Michel_H%C3%A9non" title="Michel Hénon">Michel Hénon</a></li> <li><a href="/wiki/Svetlana_Jitomirskaya" title="Svetlana Jitomirskaya">Svetlana Jitomirskaya</a></li> <li><a href="/wiki/Bryna_Kra" title="Bryna Kra">Bryna Kra</a></li> <li><a href="/wiki/Edward_Norton_Lorenz" title="Edward Norton Lorenz">Edward Norton Lorenz</a></li> <li><a href="/wiki/Aleksandr_Lyapunov" title="Aleksandr Lyapunov">Aleksandr Lyapunov</a></li> <li><a href="/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot">Benoît Mandelbrot</a></li> <li><a href="/wiki/Hee_Oh" title="Hee Oh">Hee Oh</a></li> <li><a href="/wiki/Edward_Ott" title="Edward Ott">Edward Ott</a></li> <li><a class="mw-selflink selflink">Henri Poincaré</a></li> <li><a href="/wiki/Itamar_Procaccia" title="Itamar Procaccia">Itamar Procaccia</a></li> <li><a href="/wiki/Mary_Rees" title="Mary Rees">Mary Rees</a></li> <li><a href="/wiki/Otto_R%C3%B6ssler" title="Otto Rössler">Otto Rössler</a></li> <li><a href="/wiki/David_Ruelle" title="David Ruelle">David Ruelle</a></li> <li><a href="/wiki/Caroline_Series" title="Caroline Series">Caroline Series</a></li> <li><a href="/wiki/Yakov_Sinai" title="Yakov Sinai">Yakov Sinai</a></li> <li><a href="/wiki/Oleksandr_Mykolayovych_Sharkovsky" class="mw-redirect" title="Oleksandr Mykolayovych Sharkovsky">Oleksandr Mykolayovych Sharkovsky</a></li> <li><a href="/wiki/Nina_Snaith" title="Nina Snaith">Nina Snaith</a></li> <li><a href="/wiki/Floris_Takens" title="Floris Takens">Floris Takens</a></li> <li><a href="/wiki/Audrey_Terras" title="Audrey Terras">Audrey Terras</a></li> <li><a href="/wiki/Mary_Tsingou" title="Mary Tsingou">Mary Tsingou</a></li> <li><a href="/wiki/Marcelo_Viana" title="Marcelo Viana">Marcelo Viana</a></li> <li><a href="/wiki/Amie_Wilkinson" title="Amie Wilkinson">Amie Wilkinson</a></li> <li><a href="/wiki/James_A._Yorke" title="James A. Yorke">James A. Yorke</a></li> <li><a href="/wiki/Lai-Sang_Young" title="Lai-Sang Young">Lai-Sang Young</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related<br />articles</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Butterfly_effect" title="Butterfly effect">Butterfly effect</a></li> <li><a href="/wiki/Complexity" title="Complexity">Complexity</a></li> <li><a href="/wiki/Edge_of_chaos" title="Edge of chaos">Edge of chaos</a></li> <li><a href="/wiki/Predictability" title="Predictability">Predictability</a></li> <li><a href="/wiki/Santa_Fe_Institute" title="Santa Fe Institute">Santa Fe Institute</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Relativity" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Relativity" title="Template:Relativity"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Relativity" title="Template talk:Relativity"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Relativity" title="Special:EditPage/Template:Relativity"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Relativity" style="font-size:114%;margin:0 4em"><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Relativity</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Special_relativity" title="Special relativity">Special<br />relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Principle_of_relativity" title="Principle of relativity">Principle of relativity</a> (<a href="/wiki/Galilean_invariance" title="Galilean invariance">Galilean relativity</a></li> <li><a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformation</a>)</li> <li><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></li> <li><a href="/wiki/Doubly_special_relativity" title="Doubly special relativity">Doubly special relativity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Fundamental<br />concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Frame_of_reference" title="Frame of reference">Frame of reference</a></li> <li><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light</a></li> <li><a href="/wiki/Hyperbolic_orthogonality" title="Hyperbolic orthogonality">Hyperbolic orthogonality</a></li> <li><a href="/wiki/Rapidity" title="Rapidity">Rapidity</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a></li> <li><a href="/wiki/Proper_length" title="Proper length">Proper length</a></li> <li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Proper_acceleration" title="Proper acceleration">Proper acceleration</a></li> <li><a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity">Relativistic mass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Formulation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></li> <li><a href="/wiki/List_of_textbooks_on_relativity" title="List of textbooks on relativity">Textbooks</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence (E=mc<sup>2</sup>)</a></li> <li><a href="/wiki/Length_contraction" title="Length contraction">Length contraction</a></li> <li><a href="/wiki/Relativity_of_simultaneity" title="Relativity of simultaneity">Relativity of simultaneity</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li> <li><a href="/wiki/Thomas_precession" title="Thomas precession">Thomas precession</a></li> <li><a href="/wiki/Ladder_paradox" title="Ladder paradox">Ladder paradox</a></li> <li><a href="/wiki/Twin_paradox" title="Twin paradox">Twin paradox</a></li> <li><a href="/wiki/Terrell_rotation" title="Terrell rotation">Terrell rotation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;"><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Light_cone" title="Light cone">Light cone</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Minkowski diagram</a></li> <li><a href="/wiki/Biquaternion" title="Biquaternion">Biquaternions</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/General_relativity" title="General relativity">General<br />relativity</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Background</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_general_relativity" title="Introduction to general relativity">Introduction</a></li> <li><a href="/wiki/Mathematics_of_general_relativity" title="Mathematics of general relativity">Mathematical formulation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Fundamental<br />concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Equivalence_principle" title="Equivalence principle">Equivalence principle</a></li> <li><a href="/wiki/Riemannian_geometry" title="Riemannian geometry">Riemannian geometry</a></li> <li><a href="/wiki/Penrose_diagram" title="Penrose diagram">Penrose diagram</a></li> <li><a href="/wiki/Geodesics_in_general_relativity" title="Geodesics in general relativity">Geodesics</a></li> <li><a href="/wiki/Mach%27s_principle" title="Mach's principle">Mach's principle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Formulation</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ADM_formalism" title="ADM formalism">ADM formalism</a></li> <li><a href="/wiki/BSSN_formalism" title="BSSN formalism">BSSN formalism</a></li> <li><a href="/wiki/Einstein_field_equations" title="Einstein field equations">Einstein field equations</a></li> <li><a href="/wiki/Linearized_gravity" title="Linearized gravity">Linearized gravity</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">Post-Newtonian formalism</a></li> <li><a href="/wiki/Raychaudhuri_equation" title="Raychaudhuri equation">Raychaudhuri equation</a></li> <li><a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation" title="Hamilton–Jacobi–Einstein equation">Hamilton–Jacobi–Einstein equation</a></li> <li><a href="/wiki/Ernst_equation" title="Ernst equation">Ernst equation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_hole" title="Black hole">Black hole</a></li> <li><a href="/wiki/Event_horizon" title="Event horizon">Event horizon</a></li> <li><a href="/wiki/Gravitational_singularity" title="Gravitational singularity">Singularity</a></li> <li><a href="/wiki/Two-body_problem_in_general_relativity" title="Two-body problem in general relativity">Two-body problem</a></li></ul> <ul><li><a href="/wiki/Gravitational_wave" title="Gravitational wave">Gravitational waves</a>: <a href="/wiki/Gravitational-wave_astronomy" title="Gravitational-wave astronomy">astronomy</a></li> <li><a href="/wiki/Gravitational-wave_observatory" title="Gravitational-wave observatory">detectors</a> (<a href="/wiki/LIGO" title="LIGO">LIGO</a> and <a href="/wiki/LIGO_Scientific_Collaboration" title="LIGO Scientific Collaboration">collaboration</a></li> <li><a href="/wiki/Virgo_interferometer" title="Virgo interferometer">Virgo</a></li> <li><a href="/wiki/LISA_Pathfinder" title="LISA Pathfinder">LISA Pathfinder</a></li> <li><a href="/wiki/GEO600" title="GEO600">GEO</a>)</li> <li><a href="/wiki/Hulse%E2%80%93Taylor_binary" class="mw-redirect" title="Hulse–Taylor binary">Hulse–Taylor binary</a></li></ul> <ul><li><a href="/wiki/Tests_of_general_relativity" title="Tests of general relativity">Other tests</a>: <a href="/wiki/Apsidal_precession" title="Apsidal precession">precession</a> of Mercury</li> <li><a href="/wiki/Gravitational_lens" title="Gravitational lens">lensing</a> (together with <a href="/wiki/Einstein_cross" class="mw-redirect" title="Einstein cross">Einstein cross</a> and <a href="/wiki/Einstein_rings" class="mw-redirect" title="Einstein rings">Einstein rings</a>)</li> <li><a href="/wiki/Gravitational_redshift" title="Gravitational redshift">redshift</a></li> <li><a href="/wiki/Shapiro_time_delay" title="Shapiro time delay">Shapiro delay</a></li> <li><a href="/wiki/Frame-dragging" title="Frame-dragging">frame-dragging</a> / <a href="/wiki/Geodetic_effect" title="Geodetic effect">geodetic effect</a> (<a href="/wiki/Lense%E2%80%93Thirring_precession" title="Lense–Thirring precession">Lense–Thirring precession</a>)</li> <li><a href="/wiki/Pulsar_timing_array" title="Pulsar timing array">pulsar timing arrays</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;">Advanced<br />theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Brans%E2%80%93Dicke_theory" title="Brans–Dicke theory">Brans–Dicke theory</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein</a></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em;text-align:center;"><a href="/wiki/Exact_solutions_in_general_relativity" title="Exact solutions in general relativity">Solutions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Cosmological: <a href="/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" title="Friedmann–Lemaître–Robertson–Walker metric">Friedmann–Lemaître–Robertson–Walker</a> (<a href="/wiki/Friedmann_equations" title="Friedmann equations">Friedmann equations</a>)</li> <li><a href="/wiki/Lema%C3%AEtre%E2%80%93Tolman_metric" title="Lemaître–Tolman metric">Lemaître–Tolman</a></li> <li><a href="/wiki/Kasner_metric" title="Kasner metric">Kasner</a></li> <li><a href="/wiki/BKL_singularity" title="BKL singularity">BKL singularity</a></li> <li><a href="/wiki/G%C3%B6del_metric" title="Gödel metric">Gödel</a></li> <li><a href="/wiki/Milne_model" title="Milne model">Milne</a></li></ul> <ul><li>Spherical: <a href="/wiki/Schwarzschild_metric" title="Schwarzschild metric">Schwarzschild</a> (<a href="/wiki/Interior_Schwarzschild_metric" title="Interior Schwarzschild metric">interior</a></li> <li><a href="/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation" title="Tolman–Oppenheimer–Volkoff equation">Tolman–Oppenheimer–Volkoff equation</a>)</li> <li><a href="/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric" title="Reissner–Nordström metric">Reissner–Nordström</a></li></ul> <ul><li>Axisymmetric: <a href="/wiki/Kerr_metric" title="Kerr metric">Kerr</a> (<a href="/wiki/Kerr%E2%80%93Newman_metric" title="Kerr–Newman metric">Kerr–Newman</a>)</li> <li><a href="/wiki/Weyl%E2%88%92Lewis%E2%88%92Papapetrou_coordinates" class="mw-redirect" title="Weyl−Lewis−Papapetrou coordinates">Weyl−Lewis−Papapetrou</a></li> <li><a href="/wiki/Taub%E2%80%93NUT_space" title="Taub–NUT space">Taub–NUT</a></li> <li><a href="/wiki/Van_Stockum_dust" title="Van Stockum dust">van Stockum dust</a></li> <li><a href="/wiki/Relativistic_disk" title="Relativistic disk">discs</a></li></ul> <ul><li>Others: <a href="/wiki/Pp-wave_spacetime" title="Pp-wave spacetime">pp-wave</a></li> <li><a href="/wiki/Ozsv%C3%A1th%E2%80%93Sch%C3%BCcking_metric" title="Ozsváth–Schücking metric">Ozsváth–Schücking</a></li> <li><a href="/wiki/Alcubierre_drive" title="Alcubierre drive">Alcubierre</a></li></ul> <ul><li>In computational physics: <a href="/wiki/Numerical_relativity" title="Numerical relativity">Numerical relativity</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Scientists</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Poincaré</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Karl_Schwarzschild" title="Karl Schwarzschild">Schwarzschild</a></li> <li><a href="/wiki/Willem_de_Sitter" title="Willem de Sitter">de Sitter</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Arthur_Eddington" title="Arthur Eddington">Eddington</a></li> <li><a href="/wiki/Alexander_Friedmann" title="Alexander Friedmann">Friedmann</a></li> <li><a href="/wiki/Georges_Lema%C3%AEtre" title="Georges Lemaître">Lemaître</a></li> <li><a href="/wiki/Edward_Arthur_Milne" title="Edward Arthur Milne">Milne</a></li> <li><a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Robertson</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Chandrasekhar</a></li> <li><a href="/wiki/Fritz_Zwicky" title="Fritz Zwicky">Zwicky</a></li> <li><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">Wheeler</a></li> <li><a href="/wiki/Yvonne_Choquet-Bruhat" title="Yvonne Choquet-Bruhat">Choquet-Bruhat</a></li> <li><a href="/wiki/Roy_Kerr" title="Roy Kerr">Kerr</a></li> <li><a href="/wiki/Yakov_Zeldovich" title="Yakov Zeldovich">Zel'dovich</a></li> <li><a href="/wiki/Igor_Dmitriyevich_Novikov" title="Igor Dmitriyevich Novikov">Novikov</a></li> <li><a href="/wiki/J%C3%BCrgen_Ehlers" title="Jürgen Ehlers">Ehlers</a></li> <li><a href="/wiki/Robert_Geroch" title="Robert Geroch">Geroch</a></li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Penrose</a></li> <li><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Hawking</a></li> <li><a href="/wiki/Joseph_Hooton_Taylor_Jr." title="Joseph Hooton Taylor Jr.">Taylor</a></li> <li><a href="/wiki/Russell_Alan_Hulse" title="Russell Alan Hulse">Hulse</a></li> <li><a href="/wiki/Hermann_Bondi" title="Hermann Bondi">Bondi</a></li> <li><a href="/wiki/Charles_W._Misner" title="Charles W. Misner">Misner</a></li> <li><a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Yau</a></li> <li><a href="/wiki/Kip_Thorne" title="Kip Thorne">Thorne</a></li> <li><a href="/wiki/Rainer_Weiss" title="Rainer Weiss">Weiss</a></li> <li><a href="/wiki/List_of_contributors_to_general_relativity" title="List of contributors to general relativity"><i>others</i></a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" 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class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA00112718?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=34227">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.scopus.com/authid/detail.uri?authorId=17336815800">Scopus</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:poincare.henri">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/140565">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/948520">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd118595407.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118595407">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/027943585">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6dz09rs">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Henri_Poincaré&oldid=1259895070">https://en.wikipedia.org/w/index.php?title=Henri_Poincaré&oldid=1259895070</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:1854_births" title="Category:1854 births">1854 births</a></li><li><a href="/wiki/Category:1912_deaths" title="Category:1912 deaths">1912 deaths</a></li><li><a href="/wiki/Category:Henri_Poincar%C3%A9" title="Category:Henri Poincaré">Henri 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= 1,\n [\"CITEREFGargani_Julien2012\"] = 1,\n [\"CITEREFGiannetto,_E.1998\"] = 1,\n [\"CITEREFGiedymin,_J.1982\"] = 1,\n [\"CITEREFGinouxGerini2013\"] = 1,\n [\"CITEREFGoldberg,_S.1967\"] = 1,\n [\"CITEREFGoldberg,_S.1970\"] = 1,\n [\"CITEREFGray2013\"] = 1,\n [\"CITEREFHadamard,_Jacques1922\"] = 1,\n [\"CITEREFHentschel1990\"] = 1,\n [\"CITEREFHolton,_G.1988\"] = 1,\n [\"CITEREFHsuHsu2006\"] = 1,\n [\"CITEREFIrons2001\"] = 1,\n [\"CITEREFJean_Mawhin2005\"] = 1,\n [\"CITEREFKatzir,_S.2005\"] = 1,\n [\"CITEREFKeswani,_G.H.,_Kilmister,_C.W.1983\"] = 1,\n [\"CITEREFKeswani,_G.H.1965\"] = 2,\n [\"CITEREFKeswani,_G.H.1966\"] = 1,\n [\"CITEREFKolmogorovYushkevich1998\"] = 1,\n [\"CITEREFKragh,_H.1999\"] = 1,\n [\"CITEREFLangevin,_P.1913\"] = 1,\n [\"CITEREFLeveugle,_J.2004\"] = 1,\n [\"CITEREFLogunov,_A.A.2004\"] = 1,\n [\"CITEREFLorentz1895\"] = 1,\n [\"CITEREFMacrossan,_M._N.1986\"] = 1,\n [\"CITEREFMazliak2014\"] = 1,\n [\"CITEREFMcCormmach1967\"] = 1,\n [\"CITEREFMiller,_A.I.1973\"] = 1,\n [\"CITEREFMiller,_A.I.1981\"] = 1,\n [\"CITEREFMiller,_A.I.1996\"] = 1,\n [\"CITEREFMinkowski1908\"] = 1,\n [\"CITEREFMoultonJeffries1945\"] = 1,\n [\"CITEREFNastasi2013\"] = 1,\n [\"CITEREFPoincaré,_H.1881\"] = 1,\n [\"CITEREFPoincaré,_H.1892\"] = 1,\n [\"CITEREFPoincaré,_H.1900\"] = 1,\n [\"CITEREFPoincaré,_H.1906\"] = 1,\n [\"CITEREFPoincaré,_H.2007\"] = 2,\n [\"CITEREFPoincaré,_Henri1902–1908\"] = 1,\n [\"CITEREFPoincaré,_Henri1908–1913\"] = 1,\n [\"CITEREFPoincaré,_Henri1913\"] = 1,\n [\"CITEREFPoincaré1898\"] = 1,\n [\"CITEREFPoincaré1900\"] = 1,\n [\"CITEREFPoincaré1905\"] = 1,\n [\"CITEREFPoincaré1914\"] = 1,\n [\"CITEREFPoincaré2007\"] = 1,\n [\"CITEREFPoincaré2017\"] = 2,\n [\"CITEREFPopp,_B.D.2020\"] = 1,\n [\"CITEREFPrentis1995\"] = 1,\n [\"CITEREFReynolds,_W._F.1993\"] = 1,\n [\"CITEREFRollet2012\"] = 1,\n [\"CITEREFSass1979\"] = 1,\n [\"CITEREFSatzer,_William_J.2011\"] = 1,\n [\"CITEREFSchwartz,_H._M.1971\"] = 1,\n [\"CITEREFSchwartz,_H._M.1972\"] = 2,\n [\"CITEREFScribner,_C.1964\"] = 1,\n [\"CITEREFStillwell2010\"] = 1,\n [\"CITEREFToulouse,_E.2013\"] = 1,\n [\"CITEREFTudor,_T.2018\"] = 1,\n [\"CITEREFWalter,_S.2005\"] = 1,\n [\"CITEREFWalter,_S.2007\"] = 1,\n [\"CITEREFWalter2007\"] = 1,\n [\"CITEREFWhittaker,_E.T.1953\"] = 1,\n [\"CITEREFZahar,_E.2001\"] = 1,\n}\ntemplate_list = table#1 {\n [\"Authority control\"] = 1,\n [\"Birth date\"] = 1,\n [\"Blockquote\"] = 5,\n [\"Center\"] = 2,\n [\"Chaos theory\"] = 1,\n [\"Citation\"] = 57,\n [\"Citation needed\"] = 1,\n [\"Cite book\"] = 29,\n [\"Cite journal\"] = 13,\n [\"Cite thesis\"] = 1,\n [\"Cite web\"] = 8,\n [\"Colend\"] = 3,\n [\"Cols\"] = 3,\n [\"Commons category\"] = 1,\n [\"DEFAULTSORT:Poincare, Henri\"] = 1,\n [\"Dead link\"] = 1,\n [\"Death date and age\"] = 1,\n [\"Flatlist\"] = 1,\n [\"For\"] = 1,\n [\"Full citation needed\"] = 1,\n [\"Further\"] = 2,\n [\"Gutenberg author\"] = 1,\n [\"IPA\"] = 1,\n [\"IPAc-en\"] = 2,\n [\"Ill\"] = 2,\n [\"Infobox scientist\"] = 1,\n [\"Internet Archive author\"] = 1,\n [\"Isbn\"] = 5,\n [\"Librivox author\"] = 1,\n [\"MacTutor Biography\"] = 1,\n [\"Main\"] = 1,\n [\"MathGenealogy\"] = 1,\n [\"More citations needed\"] = 1,\n [\"Nowrap\"] = 2,\n [\"OED\"] = 1,\n [\"Philosophy of science\"] = 1,\n [\"Plainlist\"] = 6,\n [\"PlanetMath attribution\"] = 1,\n [\"Reflist\"] = 1,\n [\"Relativity\"] = 1,\n [\"S-aft\"] = 1,\n [\"S-bef\"] = 1,\n [\"S-culture\"] = 1,\n [\"S-end\"] = 1,\n [\"S-start\"] = 1,\n [\"S-ttl\"] = 1,\n [\"Sfn\"] = 1,\n [\"Short description\"] = 1,\n [\"Snd\"] = 1,\n [\"Special relativity sidebar\"] = 1,\n [\"Use dmy dates\"] = 1,\n [\"Webarchive\"] = 3,\n [\"Wikiquote\"] = 1,\n [\"Wikisource author\"] = 1,\n}\narticle_whitelist = table#1 {\n}\ntable#1 {\n}\ntable#1 {\n}\n","limitreport-profile":[["?","260","23.6"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::callParserFunction","100","9.1"],["recursiveClone \u003CmwInit.lua:45\u003E","100","9.1"],["dataWrapper \u003Cmw.lua:672\u003E","100","9.1"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::getExpandedArgument","60","5.5"],["type","60","5.5"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::gsub","60","5.5"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::match","40","3.6"],["date","40","3.6"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::getEntityStatements","40","3.6"],["[others]","240","21.8"]]},"cachereport":{"origin":"mw-web.codfw.main-6df7948d6c-lbwrs","timestamp":"20241127201658","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Henri Poincar\u00e9","url":"https:\/\/en.wikipedia.org\/wiki\/Henri_Poincar%C3%A9","sameAs":"http:\/\/www.wikidata.org\/entity\/Q81082","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q81082","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2002-04-11T19:49:52Z","dateModified":"2024-11-27T17:47:02Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/f\/f4\/PSM_V82_D416_Henri_Poincare.png","headline":"French mathematician, physicist and engineer (1854\u20131912)"}</script> </body> </html>