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class="vector-toc-numb">2</span> <span>Contributions</span> </div> </a> <button aria-controls="toc-Contributions-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 Contributions subsection</span> </button> <ul id="toc-Contributions-sublist" class="vector-toc-list"> <li id="toc-Distribution_of_eigenvalues" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Distribution_of_eigenvalues"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Distribution of eigenvalues</span> </div> </a> <ul id="toc-Distribution_of_eigenvalues-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometric_foundations_of_manifolds_and_physics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geometric_foundations_of_manifolds_and_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Geometric foundations of manifolds and physics</span> </div> </a> <ul id="toc-Geometric_foundations_of_manifolds_and_physics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Topological_groups,_Lie_groups_and_representation_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Topological_groups,_Lie_groups_and_representation_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Topological groups, Lie groups and representation theory</span> </div> </a> <ul id="toc-Topological_groups,_Lie_groups_and_representation_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Harmonic_analysis_and_analytic_number_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Harmonic_analysis_and_analytic_number_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Harmonic analysis and analytic number theory</span> </div> </a> <ul id="toc-Harmonic_analysis_and_analytic_number_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Foundations_of_mathematics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Foundations_of_mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Foundations of mathematics</span> </div> </a> <ul id="toc-Foundations_of_mathematics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Weyl_equation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Weyl_equation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Weyl equation</span> </div> </a> <ul id="toc-Weyl_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Philosophy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Philosophy"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Philosophy</span> </div> </a> <ul id="toc-Philosophy-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Quotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Quotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Quotes</span> </div> </a> <ul id="toc-Quotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</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-Topics_named_after_Hermann_Weyl" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Topics_named_after_Hermann_Weyl"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Topics named after Hermann Weyl</span> </div> </a> <ul id="toc-Topics_named_after_Hermann_Weyl-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</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" title="Table of Contents" > <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">Hermann Weyl</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 60 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-60" 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">60 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D9%8A%D8%B1%D9%85%D8%A7%D9%86_%D9%81%D8%A7%D9%8A%D9%84" title="هيرمان فايل – Arabic" lang="ar" hreflang="ar" data-title="هيرمان فايل" 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/Hermann_Weyl" title="Hermann Weyl – Asturian" lang="ast" hreflang="ast" data-title="Hermann Weyl" 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/Herman_Veyl" title="Herman Veyl – Azerbaijani" lang="az" hreflang="az" data-title="Herman Veyl" 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/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%88%DB%8C%D9%84" title="هرمان ویل – South Azerbaijani" lang="azb" hreflang="azb" data-title="هرمان ویل" 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%B9%E0%A7%87%E0%A6%B0%E0%A7%8D%E0%A6%AE%E0%A6%BE%E0%A6%A8_%E0%A6%AD%E0%A6%BE%E0%A6%87%E0%A6%B2" title="হের্মান ভাইল – Bangla" lang="bn" hreflang="bn" data-title="হের্মান ভাইল" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B5%D0%B9%D0%BB%D1%8C" title="Герман Вейль – Belarusian" lang="be" hreflang="be" data-title="Герман Вейль" 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%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B0%D0%B9%D0%BB" title="Херман Вайл – Bulgarian" lang="bg" hreflang="bg" data-title="Херман Вайл" 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/Hermann_Weyl" title="Hermann Weyl – Bosnian" lang="bs" hreflang="bs" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Catalan" lang="ca" hreflang="ca" data-title="Hermann Weyl" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Czech" lang="cs" hreflang="cs" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Danish" lang="da" hreflang="da" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – German" lang="de" hreflang="de" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Estonian" lang="et" hreflang="et" data-title="Hermann Weyl" 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%A7%CE%AD%CF%81%CE%BC%CE%B1%CE%BD_%CE%92%CE%AC%CF%85%CE%BB" title="Χέρμαν Βάυλ – Greek" lang="el" hreflang="el" data-title="Χέρμαν Βάυλ" 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/Hermann_Weyl" title="Hermann Weyl – Spanish" lang="es" hreflang="es" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Esperanto" lang="eo" hreflang="eo" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Basque" lang="eu" hreflang="eu" data-title="Hermann Weyl" 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/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%88%D8%A7%DB%8C%D9%84" title="هرمان وایل – Persian" lang="fa" hreflang="fa" data-title="هرمان وایل" 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/Hermann_Weyl" title="Hermann Weyl – French" lang="fr" hreflang="fr" data-title="Hermann Weyl" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Irish" lang="ga" hreflang="ga" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Galician" lang="gl" hreflang="gl" data-title="Hermann Weyl" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%97%A4%EB%A5%B4%EB%A7%8C_%EB%B0%94%EC%9D%BC" title="헤르만 바일 – Korean" lang="ko" hreflang="ko" data-title="헤르만 바일" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D6%80%D5%B4%D5%A1%D5%B6_%D5%8E%D5%A5%D5%B5%D5%AC" title="Հերման Վեյլ – Armenian" lang="hy" hreflang="hy" data-title="Հերման Վեյլ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Indonesian" lang="id" hreflang="id" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Italian" lang="it" hreflang="it" data-title="Hermann Weyl" 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%94%D7%A8%D7%9E%D7%9F_%D7%95%D7%99%D7%99%D7%9C" title="הרמן וייל – Hebrew" lang="he" hreflang="he" data-title="הרמן וייל" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Haitian Creole" lang="ht" hreflang="ht" data-title="Hermann Weyl" 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-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Kurdish" lang="ku" hreflang="ku" data-title="Hermann Weyl" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B5%D0%B9%D0%BB" title="Герман Вейл – Kyrgyz" lang="ky" hreflang="ky" data-title="Герман Вейл" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Hermanis_Veils" title="Hermanis Veils – Latvian" lang="lv" hreflang="lv" data-title="Hermanis Veils" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Lithuanian" lang="lt" hreflang="lt" data-title="Hermann Weyl" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Hungarian" lang="hu" hreflang="hu" data-title="Hermann Weyl" 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%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B0%D1%98%D0%BB" title="Херман Вајл – Macedonian" lang="mk" hreflang="mk" data-title="Херман Вајл" 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/Hermann_Weyl" title="Hermann Weyl – Malagasy" lang="mg" hreflang="mg" data-title="Hermann Weyl" 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%B0%E1%83%94%E1%83%A0%E1%83%9B%E1%83%90%E1%83%9C_%E1%83%95%E1%83%90%E1%83%98%E1%83%9A%E1%83%98" title="ჰერმან ვაილი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ჰერმან ვაილი" 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%8A%D8%B1%D9%85%D8%A7%D9%86_%D9%81%D8%A7%D9%8A%D9%84" title="هيرمان فايل – Egyptian Arabic" lang="arz" hreflang="arz" data-title="هيرمان فايل" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9F%E1%80%AC%E1%80%99%E1%80%94%E1%80%BA_%E1%80%97%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%9C%E1%80%BA" title="ဟာမန် ဗိုင်းလ် – Burmese" lang="my" hreflang="my" data-title="ဟာမန် ဗိုင်းလ်" 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/Hermann_Weyl" title="Hermann Weyl – Dutch" lang="nl" hreflang="nl" data-title="Hermann Weyl" 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%83%98%E3%83%AB%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%AF%E3%82%A4%E3%83%AB" title="ヘルマン・ワイル – Japanese" lang="ja" hreflang="ja" data-title="ヘルマン・ワイル" 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/Claus_Hugo_Hermann_Weyl" title="Claus Hugo Hermann Weyl – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Claus Hugo Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Hermann Weyl" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Uzbek" lang="uz" hreflang="uz" data-title="Hermann Weyl" 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-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Piedmontese" lang="pms" hreflang="pms" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Polish" lang="pl" hreflang="pl" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Portuguese" lang="pt" hreflang="pt" data-title="Hermann Weyl" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B5%D0%B9%D0%BB%D1%8C,_%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD" title="Вейль, Герман – Russian" lang="ru" hreflang="ru" data-title="Вейль, Герман" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Sicilian" lang="scn" hreflang="scn" data-title="Hermann Weyl" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Simple English" lang="en-simple" hreflang="en-simple" data-title="Hermann Weyl" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hermann_Weyl" title="Hermann Weyl – Slovenian" lang="sl" hreflang="sl" data-title="Hermann Weyl" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B0%D1%98%D0%BB" title="Херман Вајл – Serbian" lang="sr" hreflang="sr" data-title="Херман Вајл" 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/Hermann_Weyl" title="Hermann Weyl – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Finnish" lang="fi" hreflang="fi" data-title="Hermann Weyl" 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/Hermann_Weyl" title="Hermann Weyl – Swedish" lang="sv" hreflang="sv" data-title="Hermann Weyl" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Hermann_Wayl" title="Hermann Wayl – Tatar" lang="tt" hreflang="tt" data-title="Hermann Wayl" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%92%D0%B5%D0%B9%D0%BB" title="Герман Вейл – Tajik" lang="tg" hreflang="tg" data-title="Герман Вейл" data-language-autonym="Тоҷикӣ" 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<div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">German mathematician (1885–1955)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Weyl" redirects here. For other persons, see <a href="/wiki/Weyl_(surname)" class="mw-redirect" title="Weyl (surname)">Weyl (surname)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) 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">Hermann Weyl</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Hermann_Weyl_ETH-Bib_Portr_00890.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hermann_Weyl_ETH-Bib_Portr_00890.jpg/220px-Hermann_Weyl_ETH-Bib_Portr_00890.jpg" decoding="async" width="220" height="228" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hermann_Weyl_ETH-Bib_Portr_00890.jpg/330px-Hermann_Weyl_ETH-Bib_Portr_00890.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Hermann_Weyl_ETH-Bib_Portr_00890.jpg/440px-Hermann_Weyl_ETH-Bib_Portr_00890.jpg 2x" data-file-width="462" data-file-height="479" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="nickname">Hermann Klaus Hugo Weyl</div><br /><span style="display:none">(<span class="bday">1885-11-09</span>)</span>9 November 1885<br /><div style="display:inline" class="birthplace"><a href="/wiki/Elmshorn" title="Elmshorn">Elmshorn</a>, <a href="/wiki/German_Empire" title="German Empire">German Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">8 December 1955<span style="display:none">(1955-12-08)</span> (aged 70)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Z%C3%BCrich" class="mw-redirect" title="Zürich">Zürich</a>, <a href="/wiki/Switzerland" title="Switzerland">Switzerland</a></div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_Munich" class="mw-redirect" title="University of Munich">University of Munich</a><br /><a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/List_of_topics_named_after_Hermann_Weyl" class="mw-redirect" title="List of topics named after Hermann Weyl">List of topics named after Hermann Weyl</a><br /><a href="/wiki/Ontic_structural_realism" class="mw-redirect" title="Ontic structural realism">Ontic structural realism</a><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><br /><a href="/wiki/Wormhole" title="Wormhole">Wormhole</a></td></tr><tr><th scope="row" class="infobox-label">Spouses</th><td class="infobox-data">Friederike Bertha Helene Joseph (nickname "Hella") (1893–1948)<br />Ellen Bär (née Lohnstein) (1902–1988)</td></tr><tr><th scope="row" class="infobox-label">Children</th><td class="infobox-data"><a href="/wiki/Fritz_Joachim_Weyl" title="Fritz Joachim Weyl">Fritz Joachim Weyl</a> (1915–1977)<br />Michael Weyl (1917–2011)</td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><a href="/wiki/Fellow_of_the_Royal_Society" title="Fellow of the Royal Society">Fellow of the Royal Society</a><sup id="cite_ref-frs_1-0" class="reference"><a href="#cite_note-frs-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <br /><a href="/wiki/Lobachevsky_Prize" title="Lobachevsky Prize">Lobachevsky Prize</a> (1927)<br /> <a href="/wiki/Josiah_Willard_Gibbs_Lectureship" title="Josiah Willard Gibbs Lectureship">Gibbs Lecture</a> (1948)</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"><a href="/wiki/Pure_mathematics" title="Pure mathematics">Pure mathematics</a>, <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>, <a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">foundations of mathematics</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a><br /><a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a><br /><a href="/wiki/ETH_Z%C3%BCrich" class="mw-redirect" title="ETH Zürich">ETH Zürich</a></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://jscholarship.library.jhu.edu/bitstream/handle/1774.2/34190/31151014634046.pdf.">Singuläre Integralgleichungen mit besonder Berücksichtigung des Fourierschen Integraltheorems</a></i> <span style="font-size:97%;">(1908)</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/David_Hilbert" title="David Hilbert">David Hilbert</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</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><a href="/wiki/Alexander_Weinstein" title="Alexander Weinstein">Alexander Weinstein</a></li><li><a href="/wiki/Julius_Adams_Stratton" title="Julius Adams Stratton">Julius Adams Stratton</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Other notable students</th><td class="infobox-data"><a href="/wiki/Saunders_Mac_Lane" title="Saunders Mac Lane">Saunders Mac Lane</a></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:Hermann_Weyl_signature.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Hermann_Weyl_signature.svg/150px-Hermann_Weyl_signature.svg.png" decoding="async" width="150" height="38" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Hermann_Weyl_signature.svg/225px-Hermann_Weyl_signature.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Hermann_Weyl_signature.svg/300px-Hermann_Weyl_signature.svg.png 2x" data-file-width="240" data-file-height="61" /></a></span></td></tr></tbody></table> <p><b>Hermann Klaus Hugo Weyl</b>, <span class="nobold noexcerpt nowraplinks" style="font-size:85%;"><a href="/wiki/Foreign_Member_of_the_Royal_Society" class="mw-redirect" title="Foreign Member of the Royal Society">ForMemRS</a></span><sup id="cite_ref-frs_1-1" class="reference"><a href="#cite_note-frs-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> (<span class="rt-commentedText nowrap"><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="'v' in 'vie'">v</span><span title="/aɪ/: 'i' in 'tide'">aɪ</span><span title="'l' in 'lie'">l</span></span>/</a></span></span>;<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> <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">German:</span> <span class="IPA nowrap" lang="de-Latn-fonipa"><a href="/wiki/Help:IPA/Standard_German" title="Help:IPA/Standard German">[vaɪl]</a></span>; 9 November 1885 – 8 December 1955) was a German <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, <a href="/wiki/Theoretical_physicist" class="mw-redirect" title="Theoretical physicist">theoretical physicist</a>, <a href="/wiki/Logician" class="mw-redirect" title="Logician">logician</a> and <a href="/wiki/Philosopher" class="mw-redirect" title="Philosopher">philosopher</a>. Although much of his working life was spent in <a href="/wiki/Z%C3%BCrich" class="mw-redirect" title="Zürich">Zürich</a>, <a href="/wiki/Switzerland" title="Switzerland">Switzerland</a>, and then <a href="/wiki/Princeton,_New_Jersey" title="Princeton, New Jersey">Princeton, New Jersey</a>, he is associated with the <a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a> tradition of mathematics, represented by <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a>, <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a> and <a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Hermann Minkowski</a>. </p><p>His research has had major significance for <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a> as well as purely mathematical disciplines such as <a href="/wiki/Number_theory" title="Number theory">number theory</a>. He was one of the most influential mathematicians of the twentieth century, and an important member of the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> during its early years.<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><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> </p><p>Weyl contributed to an exceptionally<sup id="cite_ref-Dyson_7-0" class="reference"><a href="#cite_note-Dyson-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> wide range of fields, including works on <a href="/wiki/Space" title="Space">space</a>, <a href="/wiki/Time" title="Time">time</a>, <a href="/wiki/Matter" title="Matter">matter</a>, <a href="/wiki/Philosophy" title="Philosophy">philosophy</a>, <a href="/wiki/Logic" title="Logic">logic</a>, <a href="/wiki/Symmetry" title="Symmetry">symmetry</a> and the <a href="/wiki/History_of_mathematics" title="History of mathematics">history of mathematics</a>. He was one of the first to conceive of combining <a href="/wiki/General_relativity" title="General relativity">general relativity</a> with the laws of <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>. <a href="/wiki/Freeman_Dyson" title="Freeman Dyson">Freeman Dyson</a> wrote that Weyl alone bore comparison with the "last great universal mathematicians of the nineteenth century", <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> and <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a>.<sup id="cite_ref-Dyson_7-1" class="reference"><a href="#cite_note-Dyson-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Michael_Atiyah" title="Michael Atiyah">Michael Atiyah</a>, in particular, has commented that whenever he examined a mathematical topic, he found that Weyl had preceded him.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hermann Weyl was born in <a href="/wiki/Elmshorn" title="Elmshorn">Elmshorn</a>, a small town near <a href="/wiki/Hamburg" title="Hamburg">Hamburg</a>, in <a href="/wiki/Germany" title="Germany">Germany</a>, and attended the <a href="/wiki/Gymnasium_(school)" title="Gymnasium (school)">Gymnasium</a> <a href="/wiki/Christianeum" class="mw-redirect" title="Christianeum">Christianeum</a> in <a href="/wiki/Altona,_Hamburg" title="Altona, Hamburg">Altona</a>.<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> His father, Ludwig Weyl, was a banker; whereas his mother, Anna Weyl (née Dieck), came from a wealthy 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> </p><p>From 1904 to 1908, he studied mathematics and physics in both <a href="/wiki/G%C3%B6ttingen" title="Göttingen">Göttingen</a> and <a href="/wiki/Munich" title="Munich">Munich</a>. His doctorate was awarded at the <a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a> under the supervision of <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a>, whom he greatly admired. </p><p>In September 1913, in Göttingen, Weyl married <a href="/wiki/Helene_Weyl" title="Helene Weyl">Friederike Bertha Helene Joseph</a> (30 March 1893<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> – 5 September 1948<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>) who went by the name Helene (nickname "Hella"). Helene was a daughter of Dr. <a href="/w/index.php?title=Bruno_Joseph&action=edit&redlink=1" class="new" title="Bruno Joseph (page does not exist)">Bruno Joseph</a> (13 December 1861 – 10 June 1934), a physician who held the position of Sanitätsrat in <a href="/wiki/Ribnitz-Damgarten" title="Ribnitz-Damgarten">Ribnitz-Damgarten</a>, Germany. Helene was a philosopher (she was a disciple of phenomenologist <a href="/wiki/Edmund_Husserl" title="Edmund Husserl">Edmund Husserl</a>) and a translator of Spanish literature into German and English (especially the works of Spanish philosopher <a href="/wiki/Jos%C3%A9_Ortega_y_Gasset" title="José Ortega y Gasset">José Ortega y Gasset</a>).<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> It was through Helene's close connection with Husserl that Hermann became familiar with (and greatly influenced by) Husserl's thought. Hermann and Helene had two sons, <a href="/wiki/Fritz_Joachim_Weyl" title="Fritz Joachim Weyl">Fritz Joachim Weyl</a> (19 February 1915 – 20 July 1977) and <a href="/w/index.php?title=Michael_Weyl&action=edit&redlink=1" class="new" title="Michael Weyl (page does not exist)">Michael Weyl</a> (15 September 1917 – 19 March 2011),<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> both of whom were born in Zürich, Switzerland. Helene died in Princeton, New Jersey, on 5 September 1948. A memorial service in her honor was held in Princeton on 9 September 1948. Speakers at her memorial service included her son Fritz Joachim Weyl and mathematicians <a href="/wiki/Oswald_Veblen" title="Oswald Veblen">Oswald Veblen</a> and <a href="/wiki/Richard_Courant" title="Richard Courant">Richard Courant</a>.<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> In 1950. Hermann married sculptor <a href="/w/index.php?title=Ellen_B%C3%A4r&action=edit&redlink=1" class="new" title="Ellen Bär (page does not exist)">Ellen Bär</a> (née Lohnstein) (17 April 1902 – 14 July 1988),<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> who was the widow of professor <a href="/wiki/Richard_Josef_B%C3%A4r" class="mw-redirect" title="Richard Josef Bär">Richard Josef Bär</a> (11 September 1892 – 15 December 1940)<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> of Zürich. </p><p>After taking a teaching post for a few years, Weyl left Göttingen in 1913 for Zürich to take the chair of mathematics<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> at the <a href="/wiki/ETH_Z%C3%BCrich" class="mw-redirect" title="ETH Zürich">ETH Zürich</a>, where he was a colleague of <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, who was working out the details of the theory of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>. Einstein had a lasting influence on Weyl, who became fascinated by mathematical physics. In 1921, Weyl met <a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Erwin Schrödinger</a>, a theoretical physicist who at the time was a professor at the <a href="/wiki/University_of_Z%C3%BCrich" class="mw-redirect" title="University of Zürich">University of Zürich</a>. They were to become close friends over time. Weyl had some sort of childless love affair with Schrödinger's wife Annemarie (Anny) Schrödinger (née Bertel), while at the same time Anny was helping raise an illegitimate daughter of Erwin's named Ruth Georgie Erica March, who was born in 1934 in <a href="/wiki/Oxford" title="Oxford">Oxford</a>, England.<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><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Weyl was a Plenary Speaker of the <a href="/wiki/International_Congress_of_Mathematicians" title="International Congress of Mathematicians">International Congress of Mathematicians</a> (ICM) in 1928 at <a href="/wiki/Bologna" title="Bologna">Bologna</a><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> and an Invited Speaker of the ICM in 1936 at <a href="/wiki/Oslo" title="Oslo">Oslo</a>. He was elected a fellow of the <a href="/wiki/American_Physical_Society" title="American Physical Society">American Physical Society</a> in 1928,<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> a member of the <a href="/wiki/American_Academy_of_Arts_and_Sciences" title="American Academy of Arts and Sciences">American Academy of Arts and Sciences</a> in 1929,<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> a member of the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a> in 1935,<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> and a member of the <a href="/wiki/National_Academy_of_Sciences" title="National Academy of Sciences">National Academy of Sciences</a> in 1940.<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> For the academic year 1928–1929, he was a visiting professor at <a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a>,<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> where he wrote a paper, "On a problem in the theory of groups arising in the foundations of infinitesimal geometry," with <a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Howard P. Robertson</a>.<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> </p><p>Weyl left Zürich in 1930 to become Hilbert's successor at Göttingen, leaving when the <a href="/wiki/Nazi_Germany" title="Nazi Germany">Nazis</a> assumed power in 1933, particularly as his wife was <a href="/wiki/Jews" title="Jews">Jewish</a>. He had been offered one of the first faculty positions at the new <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> in <a href="/wiki/Princeton,_New_Jersey" title="Princeton, New Jersey">Princeton, New Jersey</a>, but had declined because he did not desire to leave his homeland. As the political situation in Germany grew worse, he changed his mind and accepted when offered the position again. He remained there until his retirement in 1951. Together with his second wife Ellen, he spent his time in Princeton and Zürich, and died from a heart attack on 8 December 1955, while living in Zürich. </p><p>Weyl was cremated in Zürich on 12 December 1955.<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> His ashes remained in private hands<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources"><span title="The material near this tag may rely on an unreliable source. (March 2019)">unreliable source?</span></a></i>]</sup> until 1999, at which time they were interred in an outdoor columbarium vault in the <a href="/wiki/Princeton_Cemetery" title="Princeton Cemetery">Princeton Cemetery</a>.<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> The remains of Hermann's son Michael Weyl (1917–2011) are interred right next to Hermann's ashes in the same columbarium vault. </p><p>Weyl was a <a href="/wiki/Pantheist" class="mw-redirect" title="Pantheist">pantheist</a>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Contributions">Contributions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=2" title="Edit section: Contributions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Hermann_Weyl" title="Special:EditPage/Hermann Weyl">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">February 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Hermann_Weyl,_Ernst_Peschl.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Hermann_Weyl%2C_Ernst_Peschl.jpg/220px-Hermann_Weyl%2C_Ernst_Peschl.jpg" decoding="async" width="220" height="309" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/90/Hermann_Weyl%2C_Ernst_Peschl.jpg 1.5x" data-file-width="285" data-file-height="400" /></a><figcaption>Hermann Weyl (left) with <a href="/wiki/Ernst_Peschl" title="Ernst Peschl">Ernst Peschl</a></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Distribution_of_eigenvalues">Distribution of eigenvalues</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=3" title="Edit section: Distribution of eigenvalues"><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/Weyl_law" title="Weyl law">Weyl law</a> and <a href="/wiki/Weyl_law#Weyl_conjecture" title="Weyl law">Weyl law § Weyl conjecture</a></div> <p>In 1911 Weyl published <i>Über die asymptotische Verteilung der Eigenwerte</i> (<i>On the asymptotic distribution of eigenvalues</i>) in which he proved that the <a href="/wiki/Eigenvalues_and_eigenvectors" title="Eigenvalues and eigenvectors">eigenvalues</a> of the <a href="/wiki/Laplacian" class="mw-redirect" title="Laplacian">Laplacian</a> in a compact domain are distributed according to the so-called <a href="/wiki/Weyl_law" title="Weyl law">Weyl law</a>. In 1912 he suggested a new proof, based on variational principles. Weyl returned to this topic several times, considered elasticity system and formulated the <a href="/wiki/Weyl_law#Weyl_conjecture" title="Weyl law">Weyl conjecture</a>. These works started an important domain—<a href="/wiki/Asymptote" title="Asymptote">asymptotic</a> distribution of eigenvalues—of modern analysis. </p> <div class="mw-heading mw-heading3"><h3 id="Geometric_foundations_of_manifolds_and_physics">Geometric foundations of manifolds and physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=4" title="Edit section: Geometric foundations of manifolds and physics"><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/Weyl_transformation" title="Weyl transformation">Weyl transformation</a> and <a href="/wiki/Weyl_tensor" title="Weyl tensor">Weyl tensor</a></div> <p>In 1913, Weyl published <i>Die Idee der Riemannschen Fläche</i> (<i>The Concept of a Riemann Surface</i>), which gave a unified treatment of <a href="/wiki/Riemann_surface" title="Riemann surface">Riemann surfaces</a>. In it Weyl utilized <a href="/wiki/Point_set_topology" class="mw-redirect" title="Point set topology">point set topology</a>, in order to make Riemann surface theory more rigorous, a model followed in later work on <a href="/wiki/Manifold" title="Manifold">manifolds</a>. He absorbed <a href="/wiki/Luitzen_Egbertus_Jan_Brouwer" class="mw-redirect" title="Luitzen Egbertus Jan Brouwer">L. E. J. Brouwer's</a> early work in topology for this purpose. </p><p>Weyl, as a major figure in the Göttingen school, was fully apprised of Einstein's work from its early days. He tracked the development of <a href="/wiki/General_relativity" title="General relativity">relativity</a> physics in his <i>Raum, Zeit, Materie</i> (<i>Space, Time, Matter</i>) from 1918, reaching a 4th edition in 1922. In 1918, he introduced the notion of <a href="/wiki/Gauge_(mathematics)" class="mw-redirect" title="Gauge (mathematics)">gauge</a>, and gave the first example of what is now known as a <a href="/wiki/Gauge_theory" title="Gauge theory">gauge theory</a>. Weyl's gauge theory was an unsuccessful attempt to model the <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic field</a> and the <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a> as geometrical properties of <a href="/wiki/Spacetime" title="Spacetime">spacetime</a>. The Weyl tensor in <a href="/wiki/Riemannian_geometry" title="Riemannian geometry">Riemannian geometry</a> is of major importance in understanding the nature of <a href="/wiki/Conformal_geometry" title="Conformal geometry">conformal geometry</a>. </p><p>His overall approach in physics was based on the <a href="/wiki/Phenomenology_(philosophy)" title="Phenomenology (philosophy)">phenomenological</a> philosophy of <a href="/wiki/Edmund_Husserl" title="Edmund Husserl">Edmund Husserl</a>, specifically Husserl's 1913 <i>Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. Erstes Buch: Allgemeine Einführung in die reine Phänomenologie </i> (Ideas of a Pure Phenomenology and Phenomenological Philosophy. First Book: General Introduction). Husserl had reacted strongly to <a href="/wiki/Gottlob_Frege" title="Gottlob Frege">Gottlob Frege</a>'s criticism of his first work on the philosophy of arithmetic and was investigating the sense of mathematical and other structures, which Frege had distinguished from empirical reference.<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. (January 2016)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Topological_groups,_Lie_groups_and_representation_theory"><span id="Topological_groups.2C_Lie_groups_and_representation_theory"></span>Topological groups, Lie groups and representation theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=5" title="Edit section: Topological groups, Lie groups and representation theory"><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/Peter%E2%80%93Weyl_theorem" title="Peter–Weyl theorem">Peter–Weyl theorem</a>, <a href="/wiki/Weyl_group" title="Weyl group">Weyl group</a>, <a href="/wiki/Weyl_spinor" class="mw-redirect" title="Weyl spinor">Weyl spinor</a>, and <a href="/wiki/Weyl_algebra" title="Weyl algebra">Weyl algebra</a></div> <p>From 1923 to 1938, Weyl developed the theory of <a href="/wiki/Compact_group" title="Compact group">compact groups</a>, in terms of <a href="/wiki/Representation_theory" title="Representation theory">matrix representations</a>. In the <a href="/wiki/Compact_Lie_group" class="mw-redirect" title="Compact Lie group">compact Lie group</a> case he proved a fundamental <a href="/wiki/Weyl%27s_character_formula" class="mw-redirect" title="Weyl's character formula">character formula</a>. </p><p>These results are foundational in understanding the symmetry structure of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, which he put on a group-theoretic basis. This included <a href="/wiki/Spinor" title="Spinor">spinors</a>. Together with the <a href="/wiki/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">mathematical formulation of quantum mechanics</a>, in large measure due to <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a>, this gave the treatment familiar since about 1930. Non-compact groups and their representations, particularly the <a href="/wiki/Heisenberg_group" title="Heisenberg group">Heisenberg group</a>, were also streamlined in that specific context, in his 1927 <a href="/wiki/Weyl_quantization" class="mw-redirect" title="Weyl quantization">Weyl quantization</a>, the best extant bridge between classical and quantum physics to date. From this time, and certainly much helped by Weyl's expositions, <a href="/wiki/Lie_group" title="Lie group">Lie groups</a> and <a href="/wiki/Lie_algebra" title="Lie algebra">Lie algebras</a> became a mainstream part both of <a href="/wiki/Pure_mathematics" title="Pure mathematics">pure mathematics</a> and <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>. </p><p>His book <i><a href="/wiki/The_Classical_Groups" title="The Classical Groups">The Classical Groups</a></i> reconsidered <a href="/wiki/Invariant_theory" title="Invariant theory">invariant theory</a>. It covered <a href="/wiki/Symmetric_group" title="Symmetric group">symmetric groups</a>, <a href="/wiki/General_linear_group" title="General linear group">general linear groups</a>, <a href="/wiki/Orthogonal_group" title="Orthogonal group">orthogonal groups</a>, and <a href="/wiki/Symplectic_group" title="Symplectic group">symplectic groups</a> and results on their <a href="/wiki/Invariant_(mathematics)" title="Invariant (mathematics)">invariants</a> and <a href="/wiki/Group_representation" title="Group representation">representations</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Harmonic_analysis_and_analytic_number_theory">Harmonic analysis and analytic number theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=6" title="Edit section: Harmonic analysis and analytic number theory"><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/Weyl%27s_criterion" class="mw-redirect" title="Weyl's criterion">Weyl's criterion</a></div> <p>Weyl also showed how to use <a href="/wiki/Exponential_sum" title="Exponential sum">exponential sums</a> in <a href="/wiki/Diophantine_approximation" title="Diophantine approximation">diophantine approximation</a>, with his criterion for <a href="/wiki/Equidistributed_mod_1" class="mw-redirect" title="Equidistributed mod 1">uniform distribution mod 1</a>, which was a fundamental step in <a href="/wiki/Analytic_number_theory" title="Analytic number theory">analytic number theory</a>. This work applied to the <a href="/wiki/Riemann_zeta_function" title="Riemann zeta function">Riemann zeta function</a>, as well as <a href="/wiki/Additive_number_theory" title="Additive number theory">additive number theory</a>. It was developed by many others. </p> <div class="mw-heading mw-heading3"><h3 id="Foundations_of_mathematics">Foundations of mathematics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=7" title="Edit section: Foundations of mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <i>The Continuum</i> Weyl developed the logic of <a href="/wiki/Impredicativity" title="Impredicativity">predicative analysis</a> using the lower levels of <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a>'s <a href="/wiki/Ramified_theory_of_types" class="mw-redirect" title="Ramified theory of types">ramified theory of types</a>. He was able to develop most of classical <a href="/wiki/Infinitesimal_calculus" class="mw-redirect" title="Infinitesimal calculus">calculus</a>, while using neither the <a href="/wiki/Axiom_of_choice" title="Axiom of choice">axiom of choice</a> nor <a href="/wiki/Proof_by_contradiction" title="Proof by contradiction">proof by contradiction</a>, and avoiding <a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a>'s <a href="/wiki/Infinite_set" title="Infinite set">infinite sets</a>. Weyl appealed<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (August 2021)">clarification needed</span></a></i>]</sup> in this period to the radical <a href="/wiki/Constructivism_(mathematics)" class="mw-redirect" title="Constructivism (mathematics)">constructivism</a> of the German romantic, subjective idealist <a href="/wiki/Fichte" class="mw-redirect" title="Fichte">Fichte</a>. </p><p>Shortly after publishing <i>The Continuum</i> Weyl briefly shifted his position wholly to the <a href="/wiki/Intuitionism" title="Intuitionism">intuitionism</a> of Brouwer. In <i>The Continuum</i>, the constructible points exist as discrete entities. Weyl wanted a <a href="/wiki/Continuum_(set_theory)" title="Continuum (set theory)">continuum</a> that was not an aggregate of points. He wrote a controversial article proclaiming, for himself and <a href="/wiki/L._E._J._Brouwer" title="L. E. J. Brouwer">L. E. J. Brouwer</a>, a "revolution."<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> This article was far more influential in propagating intuitionistic views than the original works of Brouwer himself. </p><p><a href="/wiki/George_P%C3%B3lya" title="George Pólya">George Pólya</a> and Weyl, during a mathematicians' gathering in Zürich (9 February 1918), made a bet concerning the future direction of mathematics. Weyl predicted that in the subsequent 20 years, mathematicians would come to realize the total vagueness of notions such as <a href="/wiki/Real_number" title="Real number">real numbers</a>, <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">sets</a>, and <a href="/wiki/Countable" class="mw-redirect" title="Countable">countability</a>, and moreover, that asking about the <a href="/wiki/Truth" title="Truth">truth</a> or falsity of the <a href="/wiki/Completeness_of_the_real_numbers" title="Completeness of the real numbers">least upper bound property</a> of the real numbers was as meaningful as asking about truth of the basic assertions of <a href="/wiki/Georg_Wilhelm_Friedrich_Hegel" title="Georg Wilhelm Friedrich Hegel">Hegel</a> on the philosophy of nature.<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> Any answer to such a question would be unverifiable, unrelated to experience, and therefore senseless. </p><p>However, within a few years Weyl decided that Brouwer's intuitionism did put too great restrictions on mathematics, as critics had always said. The "Crisis" article had disturbed Weyl's <a href="/wiki/Formalism_(mathematics)" class="mw-redirect" title="Formalism (mathematics)">formalist</a> teacher Hilbert, but later in the 1920s Weyl partially reconciled his position with that of Hilbert. </p><p>After about 1928 Weyl had apparently decided that mathematical intuitionism was not compatible with his enthusiasm for the <a href="/wiki/Phenomenology_(philosophy)" title="Phenomenology (philosophy)">phenomenological</a> philosophy of <a href="/wiki/Husserl" class="mw-redirect" title="Husserl">Husserl</a>, as he had apparently earlier thought. In the last decades of his life Weyl emphasized mathematics as "symbolic construction" and moved to a position closer not only to Hilbert but to that of <a href="/wiki/Ernst_Cassirer" title="Ernst Cassirer">Ernst Cassirer</a>. Weyl however rarely refers to Cassirer, and wrote only brief articles and passages articulating this position. </p><p>By 1949, Weyl was thoroughly disillusioned with the ultimate value of intuitionism, and wrote: "Mathematics with Brouwer gains its highest intuitive clarity. He succeeds in developing the beginnings of analysis in a natural manner, all the time preserving the contact with intuition much more closely than had been done before. It cannot be denied, however, that in advancing to higher and more general theories the inapplicability of the simple laws of <a href="/wiki/Classical_logic" title="Classical logic">classical logic</a> eventually results in an almost unbearable awkwardness. And the mathematician watches with pain the greater part of his towering edifice which he believed to be built of concrete blocks dissolve into mist before his eyes." As John L Bell puts it: "It seems to me a great pity that Weyl did not live to see the emergence in the 1970s of smooth infinitesimal analysis, a mathematical framework within which his vision of a true continuum, not “synthesized” from discrete elements, is realized. Although the underlying logic of smooth infinitesimal analysis is intuitionistic — the <a href="/wiki/Law_of_excluded_middle" title="Law of excluded middle">law of excluded middle</a> not being generally affirmable — mathematics developed within avoids the “unbearable awkwardness” to which Weyl refers above." </p> <div class="mw-heading mw-heading3"><h3 id="Weyl_equation">Weyl equation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=8" title="Edit section: Weyl equation"><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 article: <a href="/wiki/Weyl_equation" title="Weyl equation">Weyl equation</a></div> <p>In 1929, Weyl proposed an equation, known as the <a href="/wiki/Weyl_equation" title="Weyl equation">Weyl equation</a>, for use in a replacement to the <a href="/wiki/Dirac_equation" title="Dirac equation">Dirac equation</a>. This equation describes massless <a href="/wiki/Fermion" title="Fermion">fermions</a>. A normal Dirac fermion could be split into two Weyl fermions or formed from two Weyl fermions. <a href="/wiki/Neutrino" title="Neutrino">Neutrinos</a> were once thought to be Weyl fermions, but they are now known to have mass. Weyl fermions are sought after for electronics applications. <a href="/wiki/Quasiparticle" title="Quasiparticle">Quasiparticles</a> that behave as Weyl fermions were discovered in 2015, in a form of crystals known as <a href="/wiki/Weyl_semimetal" title="Weyl semimetal">Weyl semimetals</a>, a type of topological material.<sup id="cite_ref-I3Espectrum-2015-07-16_33-0" class="reference"><a href="#cite_note-I3Espectrum-2015-07-16-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ScienceDaily-2015-07-16_34-0" class="reference"><a href="#cite_note-ScienceDaily-2015-07-16-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10.1126/science.aaa9297_35-0" class="reference"><a href="#cite_note-10.1126/science.aaa9297-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Philosophy">Philosophy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=9" title="Edit section: Philosophy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Weyl had been interested in philosophy since his youth, when he read <a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Immanuel Kant</a>'s "Critique of Pure Reason" with space and time as a priori concepts of knowledge (even if he later disliked Kant's too close ties to Euclidean geometry). From 1912 onwards he was strongly influenced by Edmund Husserl and his phenomenology, which was also reflected in some passages in his book “Space, Time, Matter”. In 1927 his contribution Philosophy of Mathematics and Natural Sciences to the Handbook of Philosophy was published by Oldenbourg Verlag, which was later published separately and revised as a book. In an attempt to reconstruct the origins of Hermann Weyl's philosophy and to integrate them into the main currents of philosophy, Norman Sieroka<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> pointed to intensive, long-term discussions between Weyl and his Zurich philosopher colleague Fritz Medicus, a specialist on Johann Gottlieb Fichte. Fichte's Wissenschaftslehre and philosophy, according to which "being" results from the interaction of the "absolute ego" with its material neighbourhood (Umgebung), is also of great influence on Weyl and is reflected in Weyl's use of the neighbourhood concept of topology (continuum) and in Weyl's conception of the general theory of relativity, alongside the influences of Edmund Husserl's phenomenology known directly from Weyl's writings. According to Sieroka, Weyl also finds influences from Gottfried Wilhelm Leibniz's theory of matter (the theory of monads, etc.) and German idealism (Fichte's dialectic) in Weyl's philosophical interpretation of the physical concept of matter in the context of quantum theory and general relativity and with regard to interaction of a symbol with its surroundings in a mathematical theory structure also in Weyl's philosophy of mathematics (debate between formalism and intuitionism under the influence of Brouwer). He understands the intra-mathematical debate about intuitionism and formalism along the lines of a debate between Husserlian phenomenology and Fichtean constructivism. In the 1920s, before the development of quantum mechanics and inspired by the statistical nature of quantum theory, which was becoming increasingly clear at the time, Weyl turned away from the field-theoretical description of matter towards a theory of active (agens) matter, which was achieved by including the spatial environment in the field theoretical description expressed. He had previously described the general theory of relativity and his own extensions of it, which led to the origin of today's concept of gauge field theories, using differential geometric methods. Under the influence of quantum theory, he turned away from this “geometric field theory”. According to Sieroka, Fichte and <a href="/wiki/Ernst_Cassirer" title="Ernst Cassirer">Ernst Cassirer</a> were also an important influence in Weyl's late philosophy (science as a “symbolic construction”). Weyl's involvement with <a href="/wiki/Martin_Heidegger" title="Martin Heidegger">Martin Heidegger</a> was less well known. Although Weyl did not agree with Heidegger's opinion about death, his conception of neighbourhood (Umgebung) was influenced by Heidegger's Existentialism. </p> <div class="mw-heading mw-heading2"><h2 id="Quotes">Quotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=10" title="Edit section: Quotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>The question for the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization.</li></ul> <dl><dd>—<i>Gesammelte Abhandlungen</i>—as quoted in <i>Year book – The American Philosophical Society</i>, 1943, p. 392</dd></dl> <ul><li>In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.</li></ul> <dl><dd>—<a href="#CITEREFWeyl1939b">Weyl (1939b</a>, p. 500)</dd></dl> <ul><li>Whenever you have to do with a structure-endowed entity S try to determine its group of automorphisms, the group of those element-wise transformations which leave all structural relations undisturbed. You can expect to gain a deep insight into the constitution of S in this way.</li></ul> <dl><dd>—<i>Symmetry</i>, Princeton Univ. Press, p. 144; 1952</dd></dl> <ul><li>Beyond the knowledge gained from the individual sciences, there remains the task of <b>comprehending</b>. In spite of the fact that the views of philosophy sway from one system to another, we cannot dispense with it unless we are to convert knowledge into a meaningless chaos.</li></ul> <dl><dd>—<i>Space-Time-Matter</i> — 4th edition (1922), English translation, Dover (1952) p. 10; Weyl’s boldfaced highlight.</dd></dl> <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=Hermann_Weyl&action=edit&section=11" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>1911. <i><a rel="nofollow" class="external text" href="http://gdz.sub.uni-goettingen.de/en/dms/load/img/?PID=GDZPPN002502526">Über die asymptotische Verteilung der Eigenwerte</a></i>, Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 110–117 (1911).</li> <li>1913. <i>Die Idee der Riemannschen Flāche</i>,<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> 2d 1955. <i>The Concept of a Riemann Surface</i>. Addison–Wesley.</li> <li>1918. <i>Das Kontinuum</i>, trans. 1987 <i>The Continuum : A Critical Examination of the Foundation of Analysis</i>. <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><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-67982-9" title="Special:BookSources/0-486-67982-9">0-486-67982-9</a></li> <li>1918. <i><a rel="nofollow" class="external text" href="https://archive.org/details/raumzeitmateriev00weyl">Raum, Zeit, Materie</a></i>. 5 edns. to 1922 ed. with notes by Jūrgen Ehlers, 1980. trans. 4th edn. Henry Brose, 1922 <i><a rel="nofollow" class="external text" href="https://archive.org/details/spacetimematter00weyluoft">Space Time Matter</a></i>, Methuen, rept. 1952 Dover. <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/0-486-60267-2" title="Special:BookSources/0-486-60267-2">0-486-60267-2</a>.</li> <li>1923. <i>Mathematische Analyse des Raumproblems</i>.</li> <li>1924. <i>Was ist Materie?</i></li> <li>1925. (publ. 1988 ed. K. Chandrasekharan) <i>Riemann's Geometrische Idee</i>.</li> <li>1927. Philosophie der Mathematik und Naturwissenschaft, 2d edn. 1949. <i>Philosophy of Mathematics and Natural Science</i>, Princeton 0689702078. With new introduction by <a href="/wiki/Frank_Wilczek" title="Frank Wilczek">Frank Wilczek</a>, Princeton University Press, 2009, <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/978-0-691-14120-6" title="Special:BookSources/978-0-691-14120-6">978-0-691-14120-6</a>.</li> <li>1928. <i><a href="/wiki/Gruppentheorie_und_Quantenmechanik" title="Gruppentheorie und Quantenmechanik">Gruppentheorie und Quantenmechanik</a></i>. transl. by H. P. Robertson, <i><a rel="nofollow" class="external text" href="https://books.google.com/books?isbn=0486602699">The Theory of Groups and Quantum Mechanics</a></i>, 1931, rept. 1950 Dover. <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/0-486-60269-9" title="Special:BookSources/0-486-60269-9">0-486-60269-9</a></li> <li><figure typeof="mw:File/Thumb"><a href="/wiki/File:Weyl-2.jpg" class="mw-file-description"><img alt="The Theory of Groups and Quantum Mechanics (translated from the second, revised German edition by Howard P. Robertson" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Weyl-2.jpg/150px-Weyl-2.jpg" decoding="async" width="150" height="234" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Weyl-2.jpg/225px-Weyl-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Weyl-2.jpg/300px-Weyl-2.jpg 2x" data-file-width="3114" data-file-height="4863" /></a><figcaption>The Theory of Groups and Quantum Mechanics (translated from the second, revised German edition by <a href="/wiki/Howard_P._Robertson" title="Howard P. Robertson">Howard P. Robertson</a>)</figcaption></figure>1929. "Elektron und Gravitation I", <i>Zeitschrift Physik</i>, 56, pp 330–352. – introduction of the <a href="/wiki/Cartan_connection_applications" class="mw-redirect" title="Cartan connection applications">vierbein</a> into <a href="/wiki/General_relativity" title="General relativity">GR</a></li> <li>1931: <i><a rel="nofollow" class="external text" href="https://libserv.aip.org/ipac20/ipac.jsp?session=167NT8P289225.1867993&profile=rev-nbl&source=~!horizon&view=subscriptionsummary&uri=full=3100006~!44625~!2&ri=5&aspect=power&menu=search&ipp=20&spp=20&staffonly=&term=%22The+Theory+of+Groups+and+Quantum+Mechanics%22&index=.GW&uindex=&aspect=power&menu=search&ri=5">The Theory of Groups and Quantum Mechanics</a></i>," London, : Methuen & Co., [1931]</li> <li>1933. <i>The Open World</i> Yale, rept. 1989 Oxbow 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/0-918024-70-6" title="Special:BookSources/0-918024-70-6">0-918024-70-6</a></li> <li>1934. <i>Mind and Nature</i> U. of Pennsylvania Press.</li> <li>1934. "On generalized Riemann matrices," <i>Ann. Math. 35</i>: 400–415.</li> <li>1935. <i>Elementary Theory of Invariants</i>.</li> <li>1935. <i>The structure and representation of continuous groups: Lectures at Princeton university during 1933–34</i>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeyl1939" class="citation cs2"><a class="mw-selflink selflink">Weyl, Hermann</a> (1939), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=2twDDAAAQBAJ&q=The+Classical+Groups%3A+Their+Invariants+and+Representations"><i>The Classical Groups. Their Invariants and Representations</i></a>, <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-05756-9" title="Special:BookSources/978-0-691-05756-9"><bdi>978-0-691-05756-9</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0000255">0000255</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Classical+Groups.+Their+Invariants+and+Representations&rft.pub=Princeton+University+Press&rft.date=1939&rft.isbn=978-0-691-05756-9&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0000255%23id-name%3DMR&rft.aulast=Weyl&rft.aufirst=Hermann&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D2twDDAAAQBAJ%26q%3DThe%2BClassical%2BGroups%253A%2BTheir%2BInvariants%2Band%2BRepresentations&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeyl1939b" class="citation cs2"><a class="mw-selflink selflink">Weyl, Hermann</a> (1939b), "Invariants", <i><a href="/wiki/Duke_Mathematical_Journal" title="Duke Mathematical Journal">Duke Mathematical Journal</a></i>, <b>5</b> (3): <span class="nowrap">489–</span>502, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1215%2FS0012-7094-39-00540-5">10.1215/S0012-7094-39-00540-5</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/0012-7094">0012-7094</a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0000030">0000030</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Duke+Mathematical+Journal&rft.atitle=Invariants&rft.volume=5&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E489-%3C%2Fspan%3E502&rft.date=1939&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0000030%23id-name%3DMR&rft.issn=0012-7094&rft_id=info%3Adoi%2F10.1215%2FS0012-7094-39-00540-5&rft.aulast=Weyl&rft.aufirst=Hermann&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></li> <li>1940. <i>Algebraic Theory of Numbers</i> rept. 1998 Princeton U. 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/0-691-05917-9" title="Special:BookSources/0-691-05917-9">0-691-05917-9</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeyl1950" class="citation cs2">Weyl, Hermann (1950), <a rel="nofollow" class="external text" href="https://projecteuclid.org/download/pdf_1/euclid.bams/1183514553">"Ramifications, old and new, of the eigenvalue problem"</a>, <i>Bull. Amer. Math. Soc.</i>, <b>56</b> (2): <span class="nowrap">115–</span>139, <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/10.1090%2FS0002-9904-1950-09369-0">10.1090/S0002-9904-1950-09369-0</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Ramifications%2C+old+and+new%2C+of+the+eigenvalue+problem&rft.volume=56&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E115-%3C%2Fspan%3E139&rft.date=1950&rft_id=info%3Adoi%2F10.1090%2FS0002-9904-1950-09369-0&rft.aulast=Weyl&rft.aufirst=Hermann&rft_id=https%3A%2F%2Fprojecteuclid.org%2Fdownload%2Fpdf_1%2Feuclid.bams%2F1183514553&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span> (text of 1948 <a href="/wiki/Josiah_Willard_Gibbs_Lectureship" title="Josiah Willard Gibbs Lectureship">Josiah Wilard Gibbs Lecture</a>)</li> <li>1952. <i>Symmetry</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/0-691-02374-3" title="Special:BookSources/0-691-02374-3">0-691-02374-3</a></li> <li>1968. in K. Chandrasekharan <i>ed</i>, <i>Gesammelte Abhandlungen</i>. Vol IV. Springer.</li></ul> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Weyl,_Hermann_%E2%80%93_Raum,_Zeit,_Materie,_1922_%E2%80%93_BEIC_3898041.jpg" class="mw-file-description" title="Temps, espace, matière (French, 1922)"><img alt="Temps, espace, matière (French, 1922)" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Weyl%2C_Hermann_%E2%80%93_Raum%2C_Zeit%2C_Materie%2C_1922_%E2%80%93_BEIC_3898041.jpg/79px-Weyl%2C_Hermann_%E2%80%93_Raum%2C_Zeit%2C_Materie%2C_1922_%E2%80%93_BEIC_3898041.jpg" decoding="async" width="79" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Weyl%2C_Hermann_%E2%80%93_Raum%2C_Zeit%2C_Materie%2C_1922_%E2%80%93_BEIC_3898041.jpg/119px-Weyl%2C_Hermann_%E2%80%93_Raum%2C_Zeit%2C_Materie%2C_1922_%E2%80%93_BEIC_3898041.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Weyl%2C_Hermann_%E2%80%93_Raum%2C_Zeit%2C_Materie%2C_1922_%E2%80%93_BEIC_3898041.jpg/158px-Weyl%2C_Hermann_%E2%80%93_Raum%2C_Zeit%2C_Materie%2C_1922_%E2%80%93_BEIC_3898041.jpg 2x" data-file-width="854" data-file-height="1293" /></a></span></div> <div class="gallerytext"><i>Temps, espace, matière</i> (French, 1922)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Weyl-17.jpg" class="mw-file-description" title="Space, Time, Matter (English, 1922: translated from German from Henry L. Brose)"><img alt="Space, Time, Matter (English, 1922: translated from German from Henry L. Brose)" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Weyl-17.jpg/69px-Weyl-17.jpg" decoding="async" width="69" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Weyl-17.jpg/104px-Weyl-17.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Weyl-17.jpg/139px-Weyl-17.jpg 2x" data-file-width="2967" data-file-height="5108" /></a></span></div> <div class="gallerytext"><i>Space, Time, Matter</i> (English, 1922: translated from German from <a href="/wiki/Henry_Brose" title="Henry Brose">Henry L. Brose</a>)</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Weyl-9.jpg" class="mw-file-description" title="Raum - Zeit - Materie (German, 1918)"><img alt="Raum - Zeit - Materie (German, 1918)" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Weyl-9.jpg/78px-Weyl-9.jpg" decoding="async" width="78" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Weyl-9.jpg/117px-Weyl-9.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Weyl-9.jpg/156px-Weyl-9.jpg 2x" data-file-width="3480" data-file-height="5341" /></a></span></div> <div class="gallerytext"><i>Raum - Zeit - Materie</i> (German, 1918)</div> </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=Hermann_Weyl&action=edit&section=12" 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="Topics_named_after_Hermann_Weyl">Topics named after Hermann Weyl</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Weyl&action=edit&section=13" title="Edit section: Topics named after Hermann Weyl"><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 article: <a href="/wiki/List_of_things_named_after_Hermann_Weyl" title="List of things named after Hermann Weyl">List of things named after Hermann Weyl</a></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: 25em;"> <ul><li><a href="/wiki/Majorana%E2%80%93Weyl_spinor" class="mw-redirect" title="Majorana–Weyl spinor">Majorana–Weyl spinor</a></li> <li><a href="/wiki/Peter%E2%80%93Weyl_theorem" title="Peter–Weyl theorem">Peter–Weyl theorem</a></li> <li><a href="/wiki/Schur%E2%80%93Weyl_duality" title="Schur–Weyl duality">Schur–Weyl duality</a></li> <li><a href="/wiki/Weyl_algebra" title="Weyl algebra">Weyl algebra</a></li> <li><a href="/wiki/Weyl_basis" class="mw-redirect" title="Weyl basis">Weyl basis</a> of the <a href="/wiki/Gamma_matrices" title="Gamma matrices">gamma matrices</a></li> <li><a href="/wiki/Weyl_chamber" class="mw-redirect" title="Weyl chamber">Weyl chamber</a></li> <li><a href="/wiki/Weyl_character_formula" title="Weyl character formula">Weyl character formula</a></li> <li><a href="/wiki/Weyl_equation" title="Weyl equation">Weyl equation</a>, a <a href="/wiki/Relativistic_wave_equation" class="mw-redirect" title="Relativistic wave equation">relativistic wave equation</a></li> <li><a href="/wiki/Weyl_expansion" title="Weyl expansion">Weyl expansion</a></li> <li><a href="/wiki/Weyl_fermion" class="mw-redirect" title="Weyl fermion">Weyl fermion</a></li> <li><a href="/wiki/Weyl_gauge" class="mw-redirect" title="Weyl gauge">Weyl gauge</a></li> <li><a href="/wiki/Conformal_gravity" title="Conformal gravity">Weyl gravity</a></li> <li><a href="/wiki/Weyl_notation" class="mw-redirect" title="Weyl notation">Weyl notation</a></li> <li><a href="/wiki/Weyl_quantization" class="mw-redirect" title="Weyl quantization">Weyl quantization</a></li> <li><a href="/wiki/Weyl_spinor" class="mw-redirect" title="Weyl spinor">Weyl spinor</a></li> <li><a href="/wiki/Weyl_sum" class="mw-redirect" title="Weyl sum">Weyl sum</a>, a type of <a href="/wiki/Exponential_sum" title="Exponential sum">exponential sum</a></li> <li><a href="/wiki/Weyl_symmetry" class="mw-redirect" title="Weyl symmetry">Weyl symmetry</a>: see Weyl transformation</li> <li><a href="/wiki/Weyl_tensor" title="Weyl tensor">Weyl tensor</a></li> <li><a href="/wiki/Weyl_transform" class="mw-redirect" title="Weyl transform">Weyl transform</a></li> <li><a href="/wiki/Weyl_transformation" title="Weyl transformation">Weyl transformation</a></li> <li><a href="/wiki/Weyl%E2%80%93Schouten_theorem" title="Weyl–Schouten theorem">Weyl–Schouten theorem</a></li> <li><a href="/wiki/Weyl%27s_criterion" class="mw-redirect" title="Weyl's criterion">Weyl's criterion</a></li> <li><a href="/wiki/Weyl_sum" class="mw-redirect" title="Weyl sum">Weyl's lemma</a> on <a href="/wiki/Hypoellipticity" class="mw-redirect" title="Hypoellipticity">hypoellipticity</a></li> <li><a href="/wiki/Weyl%27s_lemma_(Laplace_equation)" title="Weyl's lemma (Laplace equation)">Weyl's lemma</a> on the "very weak" form of the <a href="/wiki/Laplace_equation" class="mw-redirect" title="Laplace equation">Laplace equation</a></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=Hermann_Weyl&action=edit&section=14" title="Edit section: References"><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 reflist-columns references-column-width" style="column-width: 35em;"> <ol class="references"> <li id="cite_note-frs-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-frs_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-frs_1-1"><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="CITEREFNewman1957" class="citation journal cs1"><a href="/wiki/Max_Newman" title="Max Newman">Newman, M. H. A.</a> (1957). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsbm.1957.0021">"Hermann Weyl. 1885-1955"</a>. <i><a href="/wiki/Biographical_Memoirs_of_Fellows_of_the_Royal_Society" title="Biographical Memoirs of Fellows of the Royal Society">Biographical Memoirs of Fellows of the Royal Society</a></i>. <b>3</b>: <span class="nowrap">305–</span>328. <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/10.1098%2Frsbm.1957.0021">10.1098/rsbm.1957.0021</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Biographical+Memoirs+of+Fellows+of+the+Royal+Society&rft.atitle=Hermann+Weyl.+1885-1955&rft.volume=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E305-%3C%2Fspan%3E328&rft.date=1957&rft_id=info%3Adoi%2F10.1098%2Frsbm.1957.0021&rft.aulast=Newman&rft.aufirst=M.+H.+A.&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frsbm.1957.0021&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeyl1944" class="citation journal cs1"><a class="mw-selflink selflink">Weyl, H.</a> (1944). "David Hilbert. 1862-1943". <i><a href="/wiki/Obituary_Notices_of_Fellows_of_the_Royal_Society" class="mw-redirect" title="Obituary Notices of Fellows of the Royal Society">Obituary Notices of Fellows of the Royal Society</a></i>. <b>4</b> (13): <span class="nowrap">547–</span>553. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsbm.1944.0006">10.1098/rsbm.1944.0006</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:161435959">161435959</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Obituary+Notices+of+Fellows+of+the+Royal+Society&rft.atitle=David+Hilbert.+1862-1943&rft.volume=4&rft.issue=13&rft.pages=%3Cspan+class%3D%22nowrap%22%3E547-%3C%2Fspan%3E553&rft.date=1944&rft_id=info%3Adoi%2F10.1098%2Frsbm.1944.0006&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A161435959%23id-name%3DS2CID&rft.aulast=Weyl&rft.aufirst=H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</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> <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" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://www.dictionary.com/browse/Weyl">"Weyl"</a>. <i><a href="/wiki/Dictionary.com" title="Dictionary.com">Dictionary.com Unabridged</a></i> (Online). n.d.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Weyl&rft.btitle=Dictionary.com+Unabridged&rft_id=https%3A%2F%2Fwww.dictionary.com%2Fbrowse%2FWeyl&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" 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="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" class="mw-redirect" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Weyl.html">"Hermann Weyl"</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=Hermann+Weyl&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%2FWeyl.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" 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"><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=7373">Hermann Weyl</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></span> </li> <li id="cite_note-Dyson-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Dyson_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Dyson_7-1"><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="CITEREFFreeman_Dyson1956" class="citation journal cs1"><a href="/wiki/Freeman_Dyson" title="Freeman Dyson">Freeman Dyson</a> (10 March 1956). <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F177457a0">"Prof. Hermann Weyl, For.Mem.R.S."</a> <i>Nature</i>. <b>177</b> (4506): <span class="nowrap">457–</span>458. <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/1956Natur.177..457D">1956Natur.177..457D</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/10.1038%2F177457a0">10.1038/177457a0</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:216075495">216075495</a>. <q>He alone could stand comparison with the last great universal mathematicians of the nineteenth century, Hilbert and Poincaré. ... Now he is dead, the contact is broken, and our hopes of comprehending the physical universe by a direct use of creative mathematical imagination are for the time being ended.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Prof.+Hermann+Weyl%2C+For.Mem.R.S.&rft.volume=177&rft.issue=4506&rft.pages=%3Cspan+class%3D%22nowrap%22%3E457-%3C%2Fspan%3E458&rft.date=1956-03-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A216075495%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F177457a0&rft_id=info%3Abibcode%2F1956Natur.177..457D&rft.au=Freeman+Dyson&rft_id=https%3A%2F%2Fdoi.org%2F10.1038%252F177457a0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAtiyah1984" class="citation journal cs1"><a href="/wiki/Michael_Atiyah" title="Michael Atiyah">Atiyah, Michael</a> (1984). <a rel="nofollow" class="external text" href="https://link.springer.com/article/10.1007/BF03024202">"An Interview With Michael Atiyah"</a>. <i><a href="/wiki/The_Mathematical_Intelligencer" title="The Mathematical Intelligencer">The Mathematical Intelligencer</a></i>. <b>6</b> (1): 19. <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%2FBF03024202">10.1007/BF03024202</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:140298726">140298726</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=An+Interview+With+Michael+Atiyah&rft.volume=6&rft.issue=1&rft.pages=19&rft.date=1984&rft_id=info%3Adoi%2F10.1007%2FBF03024202&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A140298726%23id-name%3DS2CID&rft.aulast=Atiyah&rft.aufirst=Michael&rft_id=https%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2FBF03024202&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" 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="CITEREFElsner2008" class="citation journal cs1">Elsner, Bernd (2008). "Die Abiturarbeit Hermann Weyls". <i>Christianeum</i>. <b>63</b> (1): <span class="nowrap">3–</span>15.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Christianeum&rft.atitle=Die+Abiturarbeit+Hermann+Weyls&rft.volume=63&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3-%3C%2Fspan%3E15&rft.date=2008&rft.aulast=Elsner&rft.aufirst=Bernd&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJames2002" class="citation book cs1">James, Ioan (2002). <i>Remarkable Mathematicians</i>. Cambridge University Press. p. 345. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-52094-2" title="Special:BookSources/978-0-521-52094-2"><bdi>978-0-521-52094-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Remarkable+Mathematicians&rft.pages=345&rft.pub=Cambridge+University+Press&rft.date=2002&rft.isbn=978-0-521-52094-2&rft.aulast=James&rft.aufirst=Ioan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></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"><a rel="nofollow" class="external text" href="http://www.matrikel.uzh.ch/active/static/28236.htm">Universität Zũrich Matrikeledition</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="https://archive.org/details/hermannweylf001">[1]</a> Hermann Weyl Collection (AR 3344) (Sys #000195637), Leo Baeck Institute, Center for Jewish History, 15 West 16th Street, New York, NY 10011. The collection includes a typewritten document titled "Hellas letzte Krankheit" ("Hella's Last Illness"); the last sentence on page 2 of the document states: "Hella starb am 5. September [1948], mittags 12 Uhr." ("Hella died at 12:00 Noon on September 5 [1948]"). Helene's funeral arrangements were handled by the M. A. Mather Funeral Home (now named the Mather-Hodge Funeral Home), located at 40 Vandeventer Avenue, Princeton, New Jersey. Helene Weyl was cremated on 6 September 1948, at the Ewing Cemetery & Crematory, 78 Scotch Road, Trenton (Mercer County), New Jersey.</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">For additional information on Helene Weyl, including a bibliography of her translations, published works, and manuscripts, see the following link: <a rel="nofollow" class="external text" href="http://digital.cjh.org/R/JVSF47K3SQLELY84UGG7YPFA37DG678XF613V1EL1lAVK8UXA2-03415?func=dbin-jump-full&object_id=418384&local_base=GEN01&pds_handle=GUEST">"In Memoriam Helene Weyl"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200205130420/http://digital.cjh.org/R/JVSF47K3SQLELY84UGG7YPFA37DG678XF613V1EL1lAVK8UXA2-03415?func=dbin-jump-full&object_id=418384&local_base=GEN01&pds_handle=GUEST">Archived</a> 5 February 2020 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> by Hermann Weyl. This document, which is one of the items in the Hermann Weyl Collection at the Leo Baeck Institute in New York City, was written by Hermann Weyl at the end of June 1948, about nine weeks before Helene died on 5 September 1948, in <a href="/wiki/Princeton,_New_Jersey" title="Princeton, New Jersey">Princeton, New Jersey</a>. The first sentence in this document reads as follows: "Eine Skizze, nicht so sehr von Hellas, als von unserem gemeinsamen Leben, niedergeschrieben Ende Juni 1948." ("A sketch, not so much of Hella's life as of our common life, written at the end of June 1948.")</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"><a rel="nofollow" class="external text" href="https://www.washingtonpost.com/local/obituaries/michael-weyl-foreign-service-officer/2011/04/04/AFRUXBlC_story.html">WashingtonPost.com</a></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"><i>In Memoriam Helene Weyl</i> (1948) by Fritz Joachim Weyl. See: (i) <a rel="nofollow" class="external free" href="http://www.worldcat.org/oclc/724142550">http://www.worldcat.org/oclc/724142550</a> and (ii) <a rel="nofollow" class="external free" href="http://d-nb.info/993224164">http://d-nb.info/993224164</a></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"><a rel="nofollow" class="external text" href="http://www.artist-finder.com/stuff/database/info_popup.php?menu=artist&info=80111">artist-finder.com</a></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"><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/20151222134906/http://www.tribalpages.com/tribe/familytree?uid=jeffreymarx&surname=Baer">"Ellen Lohnstein and Richard Josef Bär were married on September 14, 1922 in Zürich, Switzerland"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.tribalpages.com/tribe/familytree?uid=jeffreymarx&surname=Baer">the original</a> on 22 December 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">18 December</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=Ellen+Lohnstein+and+Richard+Josef+B%C3%A4r+were+married+on+September+14%2C+1922+in+Z%C3%BCrich%2C+Switzerland.&rft_id=http%3A%2F%2Fwww.tribalpages.com%2Ftribe%2Ffamilytree%3Fuid%3Djeffreymarx%26surname%3DBaer&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></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">Weyl went to ETH Zürich in 1913 to fill the professorial chair vacated by the retirement of <a href="/wiki/Carl_Friedrich_Geiser" title="Carl Friedrich Geiser">Carl Friedrich Geiser</a>.</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMoore1989" class="citation book cs1">Moore, Walter (1989). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=m-YF1g1KWLoC&pg=PA175"><i>Schrödinger: Life and Thought</i></a>. Cambridge University Press. pp. <span class="nowrap">175–</span>176. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-43767-9" title="Special:BookSources/0-521-43767-9"><bdi>0-521-43767-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Schr%C3%B6dinger%3A+Life+and+Thought&rft.pages=%3Cspan+class%3D%22nowrap%22%3E175-%3C%2Fspan%3E176&rft.pub=Cambridge+University+Press&rft.date=1989&rft.isbn=0-521-43767-9&rft.aulast=Moore&rft.aufirst=Walter&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dm-YF1g1KWLoC%26pg%3DPA175&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external autonumber" href="https://familysearch.org/pal:/MM9.1.1/QVQC-RNQH">[2]</a> Ruth Georgie Erica March was born on 30 May 1934 in Oxford, England, but—according to the records presented here—it appears that her birth wasn't "registered" with the British authorities until the 3rd registration quarter (the July–August–September quarter) of the year 1934. Ruth's actual, biological father was Erwin Schrödinger (1887–1961), and her mother was Hildegunde March (née Holzhammer) (born 1900), wife of Austrian physicist <a href="/wiki/Arthur_March" title="Arthur March">Arthur March</a> (23 February 1891 – 17 April 1957). Hildegunde's friends often called her "Hilde" or "Hilda" rather than Hildegunde. Arthur March was Erwin Schrödinger's assistant at the time of Ruth's birth. The reason Ruth's surname is March (instead of Schrödinger) is because Arthur had agreed to be named as Ruth's father on her birth certificate, even though he wasn't her biological father. Ruth married the engineer Arnulf Braunizer in May 1956, and they have lived in Alpbach, Austria for many years. Ruth has been very active as the sole administrator of the intellectual (and other) property of her father Erwin's estate, which she manages from Alpbach.</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1 cs1-prop-long-vol"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=vzMKd3IlqswC&pg=PA189">"<i>Kontinuierliche Gruppen und ihre Darstellung durch lineare Transformationen</i> von H. Weyl"</a>. <i>Atti del Congresso internazionale dei Matematici, Bologna, 1928</i>. Vol. Tomo I. Bologna: N. Zanichelli. 1929. pp. <span class="nowrap">233–</span>246. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783540043881" title="Special:BookSources/9783540043881"><bdi>9783540043881</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Kontinuierliche+Gruppen+und+ihre+Darstellung+durch+lineare+Transformationen+von+H.+Weyl&rft.btitle=Atti+del+Congresso+internazionale+dei+Matematici%2C+Bologna%2C+1928&rft.place=Bologna&rft.pages=%3Cspan+class%3D%22nowrap%22%3E233-%3C%2Fspan%3E246&rft.pub=N.+Zanichelli&rft.date=1929&rft.isbn=9783540043881&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DvzMKd3IlqswC%26pg%3DPA189&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></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://www.aps.org/programs/honors/fellowships/archive-all.cfm?initial=&year=1928&unit_id=&institution=Princeton+University">"APS Fellow Archive"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=APS+Fellow+Archive&rft_id=https%3A%2F%2Fwww.aps.org%2Fprograms%2Fhonors%2Ffellowships%2Farchive-all.cfm%3Finitial%3D%26year%3D1928%26unit_id%3D%26institution%3DPrinceton%2BUniversity&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</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://www.amacad.org/person/hermann-weyl">"Hermann Weyl"</a>. <i>American Academy of Arts & Sciences</i>. 9 February 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">5 June</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=American+Academy+of+Arts+%26+Sciences&rft.atitle=Hermann+Weyl&rft.date=2023-02-09&rft_id=https%3A%2F%2Fwww.amacad.org%2Fperson%2Fhermann-weyl&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</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://search.amphilsoc.org/memhist/search?creator=Hermann+Weyl&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced">"APS Member History"</a>. <i>search.amphilsoc.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">5 June</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=search.amphilsoc.org&rft.atitle=APS+Member+History&rft_id=https%3A%2F%2Fsearch.amphilsoc.org%2Fmemhist%2Fsearch%3Fcreator%3DHermann%2BWeyl%26title%3D%26subject%3D%26subdiv%3D%26mem%3D%26year%3D%26year-max%3D%26dead%3D%26keyword%3D%26smode%3Dadvanced&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.nasonline.org/member-directory/deceased-members/20000916.html">"Hermann Weyl"</a>. <i>National Academy of Sciences</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=National+Academy+of+Sciences&rft.atitle=Hermann+Weyl&rft_id=http%3A%2F%2Fwww.nasonline.org%2Fmember-directory%2Fdeceased-members%2F20000916.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" 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="CITEREFShenstone,_Allen_G.1961" class="citation journal cs1"><a href="/wiki/Allen_Shenstone" title="Allen Shenstone">Shenstone, Allen G.</a> (24 February 1961). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=8hJbAAAAYAAJ&pg=PA363">"Princeton & Physics"</a>. <i>Princeton Alumni Weekly</i>. <b>61</b>: 7–8 of article on pp. 6–13 & p. 20.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Princeton+Alumni+Weekly&rft.atitle=Princeton+%26+Physics&rft.volume=61&rft.pages=7-8+of+article+on+pp.+6-13+%26+p.+20&rft.date=1961-02-24&rft.au=Shenstone%2C+Allen+G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D8hJbAAAAYAAJ%26pg%3DPA363&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" 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="CITEREFRobertson,_H._P.Weyl,_H.1929" class="citation journal cs1">Robertson, H. P.; Weyl, H. (1929). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9904-1929-04801-8">"On a problem in the theory of groups arising in the foundations of infinitesimal geometry"</a>. <i>Bull. Amer. Math. Soc</i>. <b>35</b> (5): <span class="nowrap">686–</span>690. <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/10.1090%2FS0002-9904-1929-04801-8">10.1090/S0002-9904-1929-04801-8</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=On+a+problem+in+the+theory+of+groups+arising+in+the+foundations+of+infinitesimal+geometry&rft.volume=35&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E686-%3C%2Fspan%3E690&rft.date=1929&rft_id=info%3Adoi%2F10.1090%2FS0002-9904-1929-04801-8&rft.au=Robertson%2C+H.+P.&rft.au=Weyl%2C+H.&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252FS0002-9904-1929-04801-8&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></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"><i>137: Jung, Pauli, and the Pursuit of a Scientific Obsession</i> (New York and London: W. W. Norton & Company, 2009), by Arthur I. Miller (p. 228).</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">Hermann Weyl's cremains (ashes) are interred in an outdoor <a href="/wiki/Columbarium" title="Columbarium">columbarium</a> vault in the <a href="/wiki/Princeton_Cemetery" title="Princeton Cemetery">Princeton Cemetery</a> at this location: Section 3, Block 04, Lot C1, Grave B15.</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHermann_WeylPeter_Pesic2009" class="citation book cs1">Hermann Weyl; Peter Pesic (20 April 2009). Peter Pesic (ed.). <i>Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics</i>. Princeton University Press. p. 12. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780691135458" title="Special:BookSources/9780691135458"><bdi>9780691135458</bdi></a>. <q>To use the apt phrase of his son Michael, 'The Open World' (1932) contains "Hermann's dialogues with God" because here the mathematician confronts his ultimate concerns. These do not fall into the traditional religious traditions but are much closer in spirit to Spinoza's rational analysis of what he called "God or nature," so important for Einstein as well. ...In the end, Weyl concludes that this God "cannot and will not be comprehended" by the human mind, even though "mind is freedom within the limitations of existence; it is open toward t///he infinite." Nevertheless, "neither can God penetrate into man by revelation, nor man penetrate to him by mystical perception."<span class="cs1-kern-right"></span></q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mind+and+Nature%3A+Selected+Writings+on+Philosophy%2C+Mathematics%2C+and+Physics&rft.pages=12&rft.pub=Princeton+University+Press&rft.date=2009-04-20&rft.isbn=9780691135458&rft.au=Hermann+Weyl&rft.au=Peter+Pesic&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></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"><a rel="nofollow" class="external text" href="https://gdz.sub.uni-goettingen.de/id/PPN266833020_0010">"Über die neue Grundlagenkrise der Mathematik" </a>(About the new foundational crisis of mathematics), H. Weyl, Springer Mathematische Zeitschrift 1921 Vol. 10, p.45 (22 pages)</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">Gurevich, Yuri. <a rel="nofollow" class="external text" href="http://research.microsoft.com/~gurevich/Opera/123.pdf">"Platonism, Constructivism and Computer Proofs vs Proofs by Hand"</a>, <i>Bulletin of the European Association of Theoretical Computer Science</i>, 1995. This paper describes a letter discovered by Gurevich in 1995 that documents the bet. It is said that when the friendly bet ended, the individuals gathered cited Pólya as the victor (with <a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Kurt Gödel</a> not in concurrence).</span> </li> <li id="cite_note-I3Espectrum-2015-07-16-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-I3Espectrum-2015-07-16_33-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCharles_Q._Choi2015" class="citation news cs1">Charles Q. Choi (16 July 2015). <a rel="nofollow" class="external text" href="https://spectrum.ieee.org/exotic-particles-could-lead-to-faster-electronics">"Weyl Fermions Found, a Quasiparticle That Acts Like a Massless Electron"</a>. <i>IEEE Spectrum</i>. IEEE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Spectrum&rft.atitle=Weyl+Fermions+Found%2C+a+Quasiparticle+That+Acts+Like+a+Massless+Electron&rft.date=2015-07-16&rft.au=Charles+Q.+Choi&rft_id=https%3A%2F%2Fspectrum.ieee.org%2Fexotic-particles-could-lead-to-faster-electronics&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-ScienceDaily-2015-07-16-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-ScienceDaily-2015-07-16_34-0">^</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://www.sciencedaily.com/releases/2015/07/150716160325.htm">"After 85-year search, massless particle with promise for next-generation electronics found"</a>. <i>Science Daily</i>. 16 July 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Science+Daily&rft.atitle=After+85-year+search%2C+massless+particle+with+promise+for+next-generation+electronics+found&rft.date=2015-07-16&rft_id=https%3A%2F%2Fwww.sciencedaily.com%2Freleases%2F2015%2F07%2F150716160325.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-10.1126/science.aaa9297-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-10.1126/science.aaa9297_35-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSu-Yang_XuIlya_BelopolskiNasser_AlidoustMadhab_Neupane2015" class="citation journal cs1">Su-Yang Xu; Ilya Belopolski; Nasser Alidoust; Madhab Neupane; Guang Bian; Chenglong Zhang; Raman Sankar; Guoqing Chang; Zhujun Yuan; Chi-Cheng Lee; Shin-Ming Huang; Hao Zheng; Jie Ma; Daniel S. Sanchez; BaoKai Wang; Arun Bansil; Fangcheng Chou; Pavel P. Shibayev; Hsin Lin; Shuang Jia; <a href="/wiki/M._Zahid_Hasan" title="M. Zahid Hasan">M. Zahid Hasan</a> (2015). "Discovery of a Weyl Fermion semimetal and topological Fermi arcs". <i>Science</i>. <b>349</b> (6248): <span class="nowrap">613–</span>617. <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/1502.03807">1502.03807</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/2015Sci...349..613X">2015Sci...349..613X</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.aaa9297">10.1126/science.aaa9297</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/26184916">26184916</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:206636457">206636457</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=Discovery+of+a+Weyl+Fermion+semimetal+and+topological+Fermi+arcs&rft.volume=349&rft.issue=6248&rft.pages=%3Cspan+class%3D%22nowrap%22%3E613-%3C%2Fspan%3E617&rft.date=2015&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A206636457%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2015Sci...349..613X&rft_id=info%3Aarxiv%2F1502.03807&rft_id=info%3Apmid%2F26184916&rft_id=info%3Adoi%2F10.1126%2Fscience.aaa9297&rft.au=Su-Yang+Xu&rft.au=Ilya+Belopolski&rft.au=Nasser+Alidoust&rft.au=Madhab+Neupane&rft.au=Guang+Bian&rft.au=Chenglong+Zhang&rft.au=Raman+Sankar&rft.au=Guoqing+Chang&rft.au=Zhujun+Yuan&rft.au=Chi-Cheng+Lee&rft.au=Shin-Ming+Huang&rft.au=Hao+Zheng&rft.au=Jie+Ma&rft.au=Daniel+S.+Sanchez&rft.au=BaoKai+Wang&rft.au=Arun+Bansil&rft.au=Fangcheng+Chou&rft.au=Pavel+P.+Shibayev&rft.au=Hsin+Lin&rft.au=Shuang+Jia&rft.au=M.+Zahid+Hasan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text">Sieroka, Umgebungen. Symbolischer Konstruktivismus im Anschluss an Hermann Weyl und Fritz Medicus. Chronos, Zürich 2010, <a rel="nofollow" class="external text" href="https://www.chronos-verlag.ch/node/20562">Verlagsseite zum Buch</a></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text">Rezension von Sierokas Buch <i>Umgebungen</i> von <a href="/w/index.php?title=Thomas_Ryckman&action=edit&redlink=1" class="new" title="Thomas Ryckman (page does not exist)">Thomas Ryckman</a> in Hopos, Band 3, 2013, S. 164–168</span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text">Sieroka: <i>Weyl’s “agens theory” of matter and the Zurich Fichte</i>, Studies in History and Philosophy of Science, Part A, Band 38, 2007, S. 84–107.</span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMoulton,_F._R.1914" class="citation journal cs1"><a href="/wiki/Forest_Ray_Moulton" title="Forest Ray Moulton">Moulton, F. R.</a> (1914). <a rel="nofollow" class="external text" href="https://www.ams.org/journals/bull/1914-20-07/S0002-9904-1914-02505-4/S0002-9904-1914-02505-4.pdf">"Review: <i>Die Idee der Riemannschen Fläche</i> by Hermann Weyl"</a> <span class="cs1-format">(PDF)</span>. <i>Bull. Amer. Math. Soc</i>. <b>20</b> (7): <span class="nowrap">384–</span>387. <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/10.1090%2Fs0002-9904-1914-02505-4">10.1090/s0002-9904-1914-02505-4</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Review%3A+Die+Idee+der+Riemannschen+Fl%C3%A4che+by+Hermann+Weyl&rft.volume=20&rft.issue=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E384-%3C%2Fspan%3E387&rft.date=1914&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1914-02505-4&rft.au=Moulton%2C+F.+R.&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fbull%2F1914-20-07%2FS0002-9904-1914-02505-4%2FS0002-9904-1914-02505-4.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJacobson,_N.1940" class="citation journal cs1"><a href="/wiki/Nathan_Jacobson" title="Nathan Jacobson">Jacobson, N.</a> (1940). <a rel="nofollow" class="external text" href="https://www.ams.org/journals/bull/1940-46-07/S0002-9904-1940-07236-2/S0002-9904-1940-07236-2.pdf">"Review: <i>The Classical Groups</i> by Hermann Weyl"</a> <span class="cs1-format">(PDF)</span>. <i>Bull. Amer. Math. Soc</i>. <b>46</b> (7): <span class="nowrap">592–</span>595. <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/10.1090%2Fs0002-9904-1940-07236-2">10.1090/s0002-9904-1940-07236-2</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Review%3A+The+Classical+Groups+by+Hermann+Weyl&rft.volume=46&rft.issue=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E592-%3C%2Fspan%3E595&rft.date=1940&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1940-07236-2&rft.au=Jacobson%2C+N.&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fbull%2F1940-46-07%2FS0002-9904-1940-07236-2%2FS0002-9904-1940-07236-2.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></span> </li> </ol></div> <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=Hermann_Weyl&action=edit&section=15" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>ed. K. Chandrasekharan, <i>Hermann Weyl, 1885–1985, Centenary lectures delivered by C. N. Yang, R. Penrose, A. Borel, at the ETH Zürich</i> Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo – 1986, published for the Eidgenössische Technische Hochschule, Zürich.</li> <li>Deppert, Wolfgang et al., eds., <i>Exact Sciences and their Philosophical Foundations. Vorträge des Internationalen Hermann-Weyl-Kongresses, Kiel 1985</i>, Bern; New York; Paris: Peter Lang 1988,</li> <li><a href="/wiki/Ivor_Grattan-Guinness" title="Ivor Grattan-Guinness">Ivor Grattan-Guinness</a>, 2000. <i>The Search for Mathematical Roots 1870-1940</i>. Princeton Uni. Press.</li> <li>Thomas Hawkins, <i>Emergence of the Theory of Lie Groups</i>, New York: Springer, 2000.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKilmister1980" class="citation cs2">Kilmister, C. W. (October 1980), "Zeno, Aristotle, Weyl and Shuard: two-and-a-half millennia of worries over number", <i>The Mathematical Gazette</i>, <b>64</b> (429), The Mathematical Gazette, Vol. 64, No. 429: <span class="nowrap">149–</span>158, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F3615116">10.2307/3615116</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/3615116">3615116</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:125725659">125725659</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+Gazette&rft.atitle=Zeno%2C+Aristotle%2C+Weyl+and+Shuard%3A+two-and-a-half+millennia+of+worries+over+number&rft.volume=64&rft.issue=429&rft.pages=%3Cspan+class%3D%22nowrap%22%3E149-%3C%2Fspan%3E158&rft.date=1980-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A125725659%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F3615116%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F3615116&rft.aulast=Kilmister&rft.aufirst=C.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></li> <li>In connection with the Weyl–Pólya bet, a copy of the original letter together with some background can be found in: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPólya1972" class="citation journal cs1">Pólya, G. (1972). "Eine Erinnerung an Hermann Weyl". <i>Mathematische Zeitschrift</i>. <b>126</b> (3): <span class="nowrap">296–</span>298. <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%2FBF01110732">10.1007/BF01110732</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:118945480">118945480</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Zeitschrift&rft.atitle=Eine+Erinnerung+an+Hermann+Weyl&rft.volume=126&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E296-%3C%2Fspan%3E298&rft.date=1972&rft_id=info%3Adoi%2F10.1007%2FBF01110732&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118945480%23id-name%3DS2CID&rft.aulast=P%C3%B3lya&rft.aufirst=G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></li> <li>Erhard Scholz; Robert Coleman; Herbert Korte; Hubert Goenner; Skuli Sigurdsson; Norbert Straumann eds. <i>Hermann Weyl's Raum – Zeit – Materie and a General Introduction to his Scientific Work</i> (Oberwolfach Seminars) (<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/3-7643-6476-9" title="Special:BookSources/3-7643-6476-9">3-7643-6476-9</a>) Springer-Verlag New York, New York, N.Y.</li> <li>Skuli Sigurdsson. "Physics, Life, and Contingency: Born, Schrödinger, and Weyl in Exile." In Mitchell G. Ash, and Alfons Söllner, eds., <i>Forced Migration and Scientific Change: Emigré German-Speaking Scientists and Scholars after 1933</i> (Washington, D.C.: German Historical Institute and New York: Cambridge University Press, 1996), pp. 48–70.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeyl2012" class="citation cs2">Weyl, Hermann (2012), Peter Pesic (ed.), <i>Levels of Infinity / Selected Writings on Mathematics and Philosophy</i>, Dover, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-48903-2" title="Special:BookSources/978-0-486-48903-2"><bdi>978-0-486-48903-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Levels+of+Infinity+%2F+Selected+Writings+on+Mathematics+and+Philosophy&rft.pub=Dover&rft.date=2012&rft.isbn=978-0-486-48903-2&rft.aulast=Weyl&rft.aufirst=Hermann&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Weyl" class="Z3988"></span></li> <li><a href="/wiki/David_Clary" title="David Clary">Clary, David C.</a> (2012), <a rel="nofollow" class="external text" href="https://doi.org/10.1142/12661"><i>Schrödinger in Oxford</i></a>, World Scientific Publishing, <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/9789811251009" title="Special:BookSources/9789811251009">9789811251009</a>.</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=Hermann_Weyl&action=edit&section=16" 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 #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output 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href="https://commons.wikimedia.org/wiki/Category:Hermann_Weyl" class="extiw" title="commons:Category:Hermann Weyl">Hermann Weyl</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.nap.edu/readingroom/books/biomems/hweyl.html">National Academy of Sciences biography</a></li> <li><a href="/wiki/John_Lane_Bell" title="John Lane Bell">Bell, John L.</a> <i><a rel="nofollow" class="external text" href="http://publish.uwo.ca/~jbell/Hermann%20Weyl.pdf">Hermann Weyl on intuition and the continuum</a></i></li> <li>Feferman, Solomon. <a rel="nofollow" class="external text" href="http://math.stanford.edu/~feferman/papers/DasKontinuum.pdf">"Significance of Hermann Weyl's das Kontinuum"</a></li> <li>Straub, William O. <a rel="nofollow" class="external text" href="http://www.weylmann.com">Hermann Weyl Website</a></li> <li><a rel="nofollow" class="external text" href="https://www.gutenberg.org/ebooks/author/41982">Works by Hermann Weyl</a> at <a 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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> <li><a href="/wiki/Ellis_wormhole" title="Ellis wormhole">Ellis</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 href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">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 class="mw-selflink selflink">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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href="https://zbmath.org/authors/?q=ai:weyl.hermann">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/182220">MathSciNet</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.leopoldina.org/mitgliederverzeichnis/mitglieder/member/Member/show/hermann-weyl/">Leopoldina</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/1010959">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/118816624.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" 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