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</ul> </li> <li id="toc-Singularity_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Singularity_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Singularity theory</span> </div> </a> <ul id="toc-Singularity_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fluid_dynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fluid_dynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Fluid dynamics</span> </div> </a> <ul id="toc-Fluid_dynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Real_algebraic_geometry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Real_algebraic_geometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Real algebraic geometry</span> </div> </a> <ul id="toc-Real_algebraic_geometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symplectic_geometry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Symplectic_geometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Symplectic geometry</span> </div> </a> <ul id="toc-Symplectic_geometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Topology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Topology"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Topology</span> </div> </a> <ul id="toc-Topology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theory_of_plane_curves" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Theory_of_plane_curves"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Theory of plane curves</span> </div> </a> <ul id="toc-Theory_of_plane_curves-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.9</span> <span>Other</span> </div> </a> <ul id="toc-Other-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Honours_and_awards" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Honours_and_awards"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Honours and awards</span> </div> </a> <button aria-controls="toc-Honours_and_awards-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 Honours and awards subsection</span> </button> <ul id="toc-Honours_and_awards-sublist" class="vector-toc-list"> <li id="toc-Fields_Medal_omission" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fields_Medal_omission"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Fields Medal omission</span> </div> </a> <ul id="toc-Fields_Medal_omission-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Selected_bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Selected_bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Selected bibliography</span> </div> </a> <button aria-controls="toc-Selected_bibliography-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Selected bibliography subsection</span> </button> <ul id="toc-Selected_bibliography-sublist" class="vector-toc-list"> <li id="toc-Collected_works" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Collected_works"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Collected works</span> </div> </a> <ul id="toc-Collected_works-sublist" class="vector-toc-list"> </ul> </li> </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">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </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">7</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">8</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">9</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">Vladimir Arnold</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" 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Available in 54 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-54" 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">54 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%81%D9%84%D8%A7%D8%AF%D9%8A%D9%85%D9%8A%D8%B1_%D8%A3%D8%B1%D9%86%D9%88%D9%84%D8%AF" title="فلاديمير أرنولد – Arabic" lang="ar" hreflang="ar" data-title="فلاديمير أرنولد" 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/Vlad%C3%ADmir_Arnold" title="Vladímir Arnold – Asturian" lang="ast" hreflang="ast" data-title="Vladímir Arnold" 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/Vladimir_Arnold" title="Vladimir Arnold – Azerbaijani" lang="az" hreflang="az" data-title="Vladimir Arnold" 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%88%D9%84%D8%A7%D8%AF%DB%8C%D9%85%DB%8C%D8%B1_%D8%A2%D8%B1%D9%86%D9%88%D9%84%D8%AF" title="ولادیمیر آرنولد – South Azerbaijani" lang="azb" hreflang="azb" data-title="ولادیمیر آرنولد" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%98%D0%B3%D0%BE%D1%80%D0%B5%D0%B2%D0%B8%D1%87" title="Арнольд Владимир Игоревич – Bashkir" lang="ba" hreflang="ba" data-title="Арнольд Владимир Игоревич" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A3%D0%BB%D0%B0%D0%B4%D0%B7%D1%96%D0%BC%D1%96%D1%80_%D0%86%D0%B3%D0%B0%D1%80%D0%B0%D0%B2%D1%96%D1%87_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4" title="Уладзімір Ігаравіч Арнольд – Belarusian" lang="be" hreflang="be" data-title="Уладзімір Ігаравіч Арнольд" 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%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D0%B4" title="Владимир Арнолд – Bulgarian" lang="bg" hreflang="bg" data-title="Владимир Арнолд" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Vlad%C3%ADmir_Arnold" title="Vladímir Arnold – Catalan" lang="ca" hreflang="ca" data-title="Vladímir Arnold" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%98%D0%B3%D0%BE%D1%80%D0%B5%D0%B2%D0%B8%D1%87" title="Арнольд Владимир Игоревич – Chuvash" lang="cv" hreflang="cv" data-title="Арнольд Владимир Игоревич" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Czech" lang="cs" hreflang="cs" data-title="Vladimir Arnold" 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/Vladimir_Arnold" title="Vladimir Arnold – Danish" lang="da" hreflang="da" data-title="Vladimir Arnold" 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/Wladimir_Igorewitsch_Arnold" title="Wladimir Igorewitsch Arnold – German" lang="de" hreflang="de" data-title="Wladimir Igorewitsch Arnold" 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/Vladimir_Arnold" title="Vladimir Arnold – Estonian" lang="et" hreflang="et" data-title="Vladimir Arnold" 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%92%CE%BB%CE%B1%CE%BD%CF%84%CE%AF%CE%BC%CE%B9%CF%81_%CE%91%CF%81%CE%BD%CF%8C%CE%BB%CE%BD%CF%84" title="Βλαντίμιρ Αρνόλντ – Greek" lang="el" hreflang="el" data-title="Βλαντίμιρ Αρνόλντ" 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/Vlad%C3%ADmir_Arnold" title="Vladímir Arnold – Spanish" lang="es" hreflang="es" data-title="Vladímir Arnold" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Basque" lang="eu" hreflang="eu" data-title="Vladimir Arnold" 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%88%D9%84%D8%A7%D8%AF%DB%8C%D9%85%DB%8C%D8%B1_%D8%A2%D8%B1%D9%86%D9%88%D9%84%D8%AF" title="ولادیمیر آرنولد – Persian" lang="fa" hreflang="fa" data-title="ولادیمیر آرنولد" 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/Vladimir_Arnold" title="Vladimir Arnold – French" lang="fr" hreflang="fr" data-title="Vladimir Arnold" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Western Frisian" lang="fy" hreflang="fy" data-title="Vladimir Arnold" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Galician" lang="gl" hreflang="gl" data-title="Vladimir Arnold" 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/%EB%B8%94%EB%9D%BC%EB%94%94%EB%AF%B8%EB%A5%B4_%EC%95%84%EB%A5%B4%EB%86%80%ED%8A%B8" title="블라디미르 아르놀트 – Korean" lang="ko" hreflang="ko" data-title="블라디미르 아르놀트" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Croatian" lang="hr" hreflang="hr" data-title="Vladimir Arnold" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Indonesian" lang="id" hreflang="id" data-title="Vladimir Arnold" 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/Vladimir_Igorevi%C4%8D_Arnol%27d" title="Vladimir Igorevič Arnol'd – Italian" lang="it" hreflang="it" data-title="Vladimir Igorevič Arnol'd" 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%95%D7%9C%D7%93%D7%99%D7%9E%D7%99%D7%A8_%D7%90%D7%A8%D7%A0%D7%95%D7%9C%D7%93" title="ולדימיר ארנולד – Hebrew" lang="he" hreflang="he" data-title="ולדימיר ארנולד" 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/Vladimir_Arnold" title="Vladimir Arnold – Haitian Creole" lang="ht" hreflang="ht" data-title="Vladimir Arnold" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Vladimirus_Arnold" title="Vladimirus Arnold – Latin" lang="la" hreflang="la" data-title="Vladimirus Arnold" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Vladimirs_Arnolds" title="Vladimirs Arnolds – Latvian" lang="lv" hreflang="lv" data-title="Vladimirs Arnolds" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Malagasy" lang="mg" hreflang="mg" data-title="Vladimir Arnold" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%81%D9%84%D8%A7%D8%AF%D9%8A%D9%85%D9%8A%D8%B1_%D8%A7%D8%B1%D9%86%D9%88%D9%84%D8%AF" title="فلاديمير ارنولد – Egyptian Arabic" lang="arz" hreflang="arz" data-title="فلاديمير ارنولد" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Mirandese" lang="mwl" hreflang="mwl" data-title="Vladimir Arnold" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Dutch" lang="nl" hreflang="nl" data-title="Vladimir Arnold" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A6%E3%83%A9%E3%82%B8%E3%83%BC%E3%83%9F%E3%83%AB%E3%83%BB%E3%82%A2%E3%83%BC%E3%83%8E%E3%83%AB%E3%83%89" title="ウラジーミル・アーノルド – Japanese" lang="ja" hreflang="ja" data-title="ウラジーミル・アーノルド" 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/Vladimir_Arnold" title="Vladimir Arnold – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Vladimir Arnold" 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Occitan" lang="oc" hreflang="oc" data-title="Vladimir Arnold" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Uzbek" lang="uz" hreflang="uz" data-title="Vladimir Arnold" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/W%C5%82adimir_Arnold" title="Władimir Arnold – Polish" lang="pl" hreflang="pl" data-title="Władimir Arnold" 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/Vladimir_Arnold" title="Vladimir Arnold – Portuguese" lang="pt" hreflang="pt" data-title="Vladimir Arnold" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Romanian" lang="ro" hreflang="ro" data-title="Vladimir Arnold" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4,_%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%98%D0%B3%D0%BE%D1%80%D0%B5%D0%B2%D0%B8%D1%87" title="Арнольд, Владимир Игоревич – Russian" lang="ru" hreflang="ru" data-title="Арнольд, Владимир Игоревич" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Simple English" lang="en-simple" hreflang="en-simple" data-title="Vladimir Arnold" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Vladimir_Igorevi%C4%8D_Arno%C4%BEd" title="Vladimir Igorevič Arnoľd – Slovak" lang="sk" hreflang="sk" data-title="Vladimir Igorevič Arnoľd" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Vladimir_Igorjevi%C4%8D_Arnold" title="Vladimir Igorjevič Arnold – Slovenian" lang="sl" hreflang="sl" data-title="Vladimir Igorjevič Arnold" 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/Vladimir_Arnold" title="Vladimir Arnold – Serbian" lang="sr" hreflang="sr" data-title="Vladimir Arnold" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Finnish" lang="fi" hreflang="fi" data-title="Vladimir Arnold" 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/Vladimir_Arnold" title="Vladimir Arnold – Swedish" lang="sv" hreflang="sv" data-title="Vladimir Arnold" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%BF%E0%AE%B3%E0%AE%BE%E0%AE%A4%E0%AE%BF%E0%AE%AE%E0%AE%BF%E0%AE%B0%E0%AF%8D_%E0%AE%86%E0%AE%B0%E0%AF%8D%E0%AE%A9%E0%AF%8B%E0%AE%B2%E0%AF%8D%E0%AE%9F%E0%AF%81" title="விளாதிமிர் ஆர்னோல்டு – Tamil" lang="ta" hreflang="ta" data-title="விளாதிமிர் ஆர்னோல்டு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4" title="Владимир Арнольд – Tatar" lang="tt" hreflang="tt" data-title="Владимир Арнольд" 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-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Turkish" lang="tr" hreflang="tr" data-title="Vladimir Arnold" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%92%D0%BE%D0%BB%D0%BE%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%86%D0%B3%D0%BE%D1%80%D0%BE%D0%B2%D0%B8%D1%87" title="Арнольд Володимир Ігорович – Ukrainian" lang="uk" hreflang="uk" data-title="Арнольд Володимир Ігорович" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Vladimir_Igorevich_Arnold" title="Vladimir Igorevich Arnold – Vietnamese" lang="vi" hreflang="vi" data-title="Vladimir Igorevich Arnold" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Vladimir_Arnold" title="Vladimir Arnold – Waray" lang="war" hreflang="war" data-title="Vladimir Arnold" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%BC%97%E6%8B%89%E5%9F%BA%E7%B1%B3%E7%88%BE%C2%B7%E9%98%BF%E8%AB%BE%E7%88%BE%E5%BE%B7" title="弗拉基米爾·阿諾爾德 – Cantonese" lang="yue" hreflang="yue" data-title="弗拉基米爾·阿諾爾德" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh 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print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">In this name that follows <a href="/wiki/Eastern_Slavic_naming_customs" title="Eastern Slavic naming customs">Eastern Slavic naming customs</a>, the <a href="/wiki/Patronymic" title="Patronymic">patronymic</a> is <i> Igorevich</i> and the <a href="/wiki/Surname" title="Surname">family name</a> is <i> Arnold</i>.</div> <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">Vladimir Arnold</div></th></tr><tr><td colspan="2" class="infobox-subheader" style="font-size:125%;"><div class="nickname" lang="ru"><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style><span class="nobold">Владимир Арнольд</span></div></td></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Vladimir_Arnold-1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Vladimir_Arnold-1.jpg/200px-Vladimir_Arnold-1.jpg" decoding="async" width="200" height="292" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Vladimir_Arnold-1.jpg/300px-Vladimir_Arnold-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Vladimir_Arnold-1.jpg/400px-Vladimir_Arnold-1.jpg 2x" data-file-width="1815" data-file-height="2646" /></a></span><div class="infobox-caption">Arnold in 2008</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1937-06-12</span>)</span>12 June 1937<br /><div style="display:inline" class="birthplace"><a href="/wiki/Odesa" title="Odesa">Odesa</a>, <a href="/wiki/Ukrainian_SSR" class="mw-redirect" title="Ukrainian SSR">Ukrainian SSR</a>, Soviet Union</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">3 June 2010<span style="display:none">(2010-06-03)</span> (aged 72)<br /><div style="display:inline" class="deathplace">Paris, France</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li 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class="hlist"><ul><li>Soviet</li><li>Russian</li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/Moscow_State_University" title="Moscow State University">Moscow State University</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/ADE_classification" title="ADE classification">ADE classification</a><br /><a href="/wiki/Arnold%27s_cat_map" title="Arnold's cat map">Arnold's cat map</a><br /><a href="/wiki/Arnold_conjecture" title="Arnold conjecture">Arnold conjecture</a><br /><a href="/wiki/Arnold_diffusion" title="Arnold diffusion">Arnold diffusion</a><br /><a href="/wiki/Arnold_invariants" title="Arnold invariants">Arnold invariants</a><br /><i><a href="/wiki/Arnold%27s_Problems" title="Arnold's Problems">Arnold's Problems</a></i><br /><a href="/wiki/Arnold%27s_rouble_problem" class="mw-redirect" title="Arnold's rouble problem">Arnold's rouble problem</a><br /><a href="/wiki/Arnold%27s_spectral_sequence" title="Arnold's spectral sequence">Arnold's spectral sequence</a><br /><a href="/wiki/Arnold_tongue" title="Arnold tongue">Arnold tongue</a><br /><a href="/wiki/Arnold%E2%80%93Beltrami%E2%80%93Childress_flow" title="Arnold–Beltrami–Childress flow">ABC flow</a><br /><a href="/wiki/Arnold%E2%80%93Givental_conjecture" class="mw-redirect" title="Arnold–Givental conjecture">Arnold–Givental conjecture</a><br /><a href="/wiki/G%C3%B6mb%C3%B6c" title="Gömböc">Gömböc</a><br /><a href="/wiki/Gudkov%27s_conjecture" title="Gudkov's conjecture">Gudkov's conjecture</a><br /><a href="/wiki/Hilbert%E2%80%93Arnold_problem" title="Hilbert–Arnold problem">Hilbert–Arnold problem</a><br /><a href="/wiki/Hilbert%27s_thirteenth_problem" title="Hilbert's thirteenth problem">Hilbert's thirteenth problem</a><br /><a href="/wiki/Kolmogorov%E2%80%93Arnold%E2%80%93Moser_theorem" title="Kolmogorov–Arnold–Moser theorem">KAM theorem</a><br /><a href="/wiki/Kolmogorov%E2%80%93Arnold_representation_theorem" title="Kolmogorov–Arnold representation theorem">Kolmogorov–Arnold theorem</a><br /><a href="/wiki/Liouville%E2%80%93Arnold_theorem" title="Liouville–Arnold theorem">Liouville–Arnold theorem</a><br /><a href="/wiki/Topological_Galois_theory" title="Topological Galois theory">Topological Galois theory</a><br /><i><a href="/wiki/Mathematical_Methods_of_Classical_Mechanics" title="Mathematical Methods of Classical Mechanics">Mathematical Methods of Classical Mechanics</a></i></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><a href="/wiki/Shaw_Prize" title="Shaw Prize">Shaw Prize</a> (2008) <br /> <a href="/wiki/State_Prize_of_the_Russian_Federation" title="State Prize of the Russian Federation">State Prize of the Russian Federation</a> (2007) <br /> <a href="/wiki/Wolf_Prize_in_Mathematics" title="Wolf Prize in Mathematics">Wolf Prize</a> (2001) <br /> <a href="/wiki/Dannie_Heineman_Prize_for_Mathematical_Physics" title="Dannie Heineman Prize for Mathematical Physics">Dannie Heineman Prize for Mathematical Physics</a> (2001) <br /> <a href="/wiki/Harvey_Prize" title="Harvey Prize">Harvey Prize</a> (1994) <br /> <a href="/wiki/Lobachevsky_Prize#Russian_Academy_of_Sciences" title="Lobachevsky Prize">RAS Lobachevsky Prize</a> (1992) <br /> <a href="/wiki/Crafoord_Prize" title="Crafoord Prize">Crafoord Prize</a> (1982) <br /> <a href="/wiki/Lenin_Prize" title="Lenin Prize">Lenin Prize</a> (1965)</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">Mathematics</td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/Paris_Dauphine_University" title="Paris Dauphine University">Paris Dauphine University</a><br /><a href="/wiki/Steklov_Institute_of_Mathematics" title="Steklov Institute of Mathematics">Steklov Institute of Mathematics</a><br /><a href="/wiki/Independent_University_of_Moscow" title="Independent University of Moscow">Independent University of Moscow</a><br /><a href="/wiki/Moscow_State_University" title="Moscow State University">Moscow State University</a></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/Andrey_Kolmogorov" title="Andrey Kolmogorov">Andrey Kolmogorov</a></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/Rifkat_Bogdanov" title="Rifkat Bogdanov">Rifkat Bogdanov</a></li> <li><a href="/wiki/Alexander_Givental" title="Alexander Givental">Alexander Givental</a></li> <li><a href="/wiki/Victor_Goryunov" title="Victor Goryunov">Victor Goryunov</a></li> <li><a href="/wiki/Sabir_Gusein-Zade" title="Sabir Gusein-Zade">Sabir Gusein-Zade</a></li> <li><a href="/wiki/Emil_Horozov" title="Emil Horozov">Emil Horozov</a></li> <li><a href="/wiki/Yulij_Ilyashenko" title="Yulij Ilyashenko">Yulij Ilyashenko</a></li> <li><a href="/wiki/Boris_Khesin" title="Boris Khesin">Boris Khesin</a><sup id="cite_ref-rsbm_1-0" class="reference"><a href="#cite_note-rsbm-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Askold_Khovanskii" title="Askold Khovanskii">Askold Khovanskii</a></li> <li><a href="/wiki/Nikolay_Nekhoroshev" title="Nikolay Nekhoroshev">Nikolay Nekhoroshev</a></li> <li><a href="/wiki/Boris_Shapiro_(mathematician)" class="mw-redirect" title="Boris Shapiro (mathematician)">Boris Shapiro</a></li> <li><a href="/wiki/Alexander_Varchenko" title="Alexander Varchenko">Alexander Varchenko</a></li> <li><a href="/wiki/Victor_Anatolyevich_Vassiliev" class="mw-redirect" title="Victor Anatolyevich Vassiliev">Victor Vassiliev</a></li> <li><a href="/wiki/Vladimir_Zakalyukin" title="Vladimir Zakalyukin">Vladimir Zakalyukin</a><sup id="cite_ref-mathgene_2-0" class="reference"><a href="#cite_note-mathgene-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li></ul> </div></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Vladimir Igorevich Arnold</b> (or <b>Arnol'd</b>; Russian: <span lang="ru">Влади́мир И́горевич Арно́льд</span>, <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">IPA:</span> <span class="IPA nowrap" lang="ru-Latn-fonipa"><a href="/wiki/Help:IPA/Russian" title="Help:IPA/Russian">[vlɐˈdʲimʲɪr<span class="wrap"> </span>ˈiɡərʲɪvʲɪtɕ<span class="wrap"> </span>ɐrˈnolʲt]</a></span>; 12 June 1937 – 3 June 2010)<sup id="cite_ref-rsbm_1-1" class="reference"><a href="#cite_note-rsbm-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><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><sup id="cite_ref-obituary_4-0" class="reference"><a href="#cite_note-obituary-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> was a Soviet and Russian mathematician. He is best known for the <a href="/wiki/Kolmogorov%E2%80%93Arnold%E2%80%93Moser_theorem" title="Kolmogorov–Arnold–Moser theorem">Kolmogorov–Arnold–Moser theorem</a> regarding the <a href="/wiki/Stability_theory" title="Stability theory">stability</a> of <a href="/wiki/Integrable_system" title="Integrable system">integrable systems</a>, and contributed to several areas, including geometrical theory of <a href="/wiki/Dynamical_systems_theory" title="Dynamical systems theory">dynamical systems</a>, <a href="/wiki/Algebra" title="Algebra">algebra</a>, <a href="/wiki/Catastrophe_theory" title="Catastrophe theory">catastrophe theory</a>, <a href="/wiki/Topology" title="Topology">topology</a>, <a href="/wiki/Real_algebraic_geometry" title="Real algebraic geometry">real algebraic geometry</a>, <a href="/wiki/Symplectic_geometry" title="Symplectic geometry">symplectic geometry</a>, <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a>, <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a>, <a href="/wiki/Differential_geometry" title="Differential geometry">differential-geometric</a> approach to <a href="/wiki/Hydrodynamics" class="mw-redirect" title="Hydrodynamics">hydrodynamics</a>, <a href="/wiki/Geometric_analysis" title="Geometric analysis">geometric analysis</a> and <a href="/wiki/Singularity_theory" title="Singularity theory">singularity theory</a>, including posing the <a href="/wiki/ADE_classification" title="ADE classification">ADE classification</a> problem. </p><p>His first main result was the solution of <a href="/wiki/Hilbert%27s_thirteenth_problem" title="Hilbert's thirteenth problem">Hilbert's thirteenth problem</a> in 1957 at the age of 19. He co-founded three new <a href="/wiki/Areas_of_mathematics" class="mw-redirect" title="Areas of mathematics">branches of mathematics</a>: <a href="/wiki/Topological_Galois_theory" title="Topological Galois theory">topological Galois theory</a> (with his student <a href="/wiki/Askold_Khovanskii" title="Askold Khovanskii">Askold Khovanskii</a>), <a href="/wiki/Symplectic_topology" class="mw-redirect" title="Symplectic topology">symplectic topology</a> and <a href="/wiki/Kolmogorov%E2%80%93Arnold%E2%80%93Moser_theorem#KAM_theory" title="Kolmogorov–Arnold–Moser theorem">KAM theory</a>. </p><p>Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as <i><a href="/wiki/Mathematical_Methods_of_Classical_Mechanics" title="Mathematical Methods of Classical Mechanics">Mathematical Methods of Classical Mechanics</a></i>) and popular mathematics books, he influenced many mathematicians and physicists.<sup id="cite_ref-MacTutor_5-0" class="reference"><a href="#cite_note-MacTutor-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> Many of his books were translated into English. His views on education were particularly opposed to those of <a href="/wiki/Nicolas_Bourbaki" title="Nicolas Bourbaki">Bourbaki</a>. </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=Vladimir_Arnold&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%B2_1963_%D0%B3.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%B2_1963_%D0%B3.jpg/300px-%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%B2_1963_%D0%B3.jpg" decoding="async" width="300" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%B2_1963_%D0%B3.jpg/450px-%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%B2_1963_%D0%B3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%B2_1963_%D0%B3.jpg/600px-%D0%92%D0%BB%D0%B0%D0%B4%D0%B8%D0%BC%D0%B8%D1%80_%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4_%D0%B2_1963_%D0%B3.jpg 2x" data-file-width="776" data-file-height="519" /></a><figcaption>Arnold in 1963.</figcaption></figure> <p>Vladimir Igorevich Arnold was born on 12 June 1937 in <a href="/wiki/Odesa" title="Odesa">Odesa</a>, <a href="/wiki/Soviet_Union" title="Soviet Union">Soviet Union</a> (now Odesa, <a href="/wiki/Ukraine" title="Ukraine">Ukraine</a>). His father was Igor Vladimirovich Arnold (1900–1948), a mathematician. His mother was Nina Alexandrovna Arnold (1909–1986, <i><a href="/wiki/Name_at_birth" class="mw-redirect" title="Name at birth">née</a></i> Isakovich), a Jewish art historian.<sup id="cite_ref-obituary_4-1" class="reference"><a href="#cite_note-obituary-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> While a school student, Arnold once asked his father on the reason why the multiplication of two negative numbers yielded a positive number, and his father provided an answer involving the <a href="/wiki/Field_(mathematics)#Classic_definition" title="Field (mathematics)">field properties</a> of <a href="/wiki/Real_number" title="Real number">real numbers</a> and the preservation of the <a href="/wiki/Distributive_property" title="Distributive property">distributive property</a>. Arnold was deeply disappointed with this answer, and developed an aversion to the <a href="/wiki/Axiomatic_method" class="mw-redirect" title="Axiomatic method">axiomatic method</a> that lasted through his life.<sup id="cite_ref-Arnold2007_7-0" class="reference"><a href="#cite_note-Arnold2007-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> When Arnold was thirteen, his uncle Nikolai B. Zhitkov,<sup id="cite_ref-earlylife_8-0" class="reference"><a href="#cite_note-earlylife-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> who was an engineer, told him about <a href="/wiki/Calculus" title="Calculus">calculus</a> and how it could be used to understand some physical phenomena. This contributed to sparking his interest for mathematics, and he started to study by himself the mathematical books his father had left to him, which included some works of <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> and <a href="/wiki/Charles_Hermite" title="Charles Hermite">Charles Hermite</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> </p><p>Arnold entered <a href="/wiki/Moscow_State_University" title="Moscow State University">Moscow State University</a> in 1954.<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> Among his teachers there were <a href="/wiki/Andrey_Kolmogorov" title="Andrey Kolmogorov">A. N. Kolmogorov</a>, <a href="/wiki/Israel_Gelfand" title="Israel Gelfand">I. M. Gelfand</a>, <a href="/wiki/Lev_Pontryagin" title="Lev Pontryagin">L. S. Pontriagin</a> and <a href="/wiki/Pavel_Alexandrov" title="Pavel Alexandrov">Pavel Alexandrov</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> While a student of Andrey Kolmogorov at <a href="/wiki/Moscow_State_University" title="Moscow State University">Moscow State University</a> and still a teenager, Arnold showed in 1957 that any <a href="/wiki/Continuous_function" title="Continuous function">continuous function</a> of several variables can be constructed with a finite number of two-variable functions, thereby solving <a href="/wiki/Hilbert%27s_thirteenth_problem" title="Hilbert's thirteenth problem">Hilbert's thirteenth problem</a>.<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> This is the <a href="/wiki/Kolmogorov%E2%80%93Arnold_representation_theorem" title="Kolmogorov–Arnold representation theorem">Kolmogorov–Arnold representation theorem</a>. </p><p>Arnold obtained his PhD in 1961, with Kolmogorov as advisor.<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> </p><p>After graduating from Moscow State University in 1959, he worked there until 1986 (a professor since 1965), and then at <a href="/wiki/Steklov_Mathematical_Institute" class="mw-redirect" title="Steklov Mathematical Institute">Steklov Mathematical Institute</a>. </p><p>He became an academician of the <a href="/wiki/Academy_of_Sciences_of_the_Soviet_Union" title="Academy of Sciences of the Soviet Union">Academy of Sciences of the Soviet Union</a> (<a href="/wiki/Russian_Academy_of_Science" class="mw-redirect" title="Russian Academy of Science">Russian Academy of Science</a> since 1991) in 1990.<sup id="cite_ref-GRE_14-0" class="reference"><a href="#cite_note-GRE-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Arnold can be said to have initiated the theory of <a href="/wiki/Symplectic_topology" class="mw-redirect" title="Symplectic topology">symplectic topology</a> as a distinct discipline. The <a href="/wiki/Arnold_conjecture" title="Arnold conjecture">Arnold conjecture</a> on the number of fixed points of <a href="/wiki/Symplectomorphism" title="Symplectomorphism">Hamiltonian symplectomorphisms</a> and <a href="/w/index.php?title=Lagrangian_intersection&action=edit&redlink=1" class="new" title="Lagrangian intersection (page does not exist)">Lagrangian intersections</a> was also a motivation in the development of <a href="/wiki/Floer_homology" title="Floer homology">Floer homology</a>. </p><p>In 1999 he suffered a serious bicycle accident in Paris, resulting in <a href="/wiki/Traumatic_brain_injury" title="Traumatic brain injury">traumatic brain injury</a>. He regained consciousness after a few weeks but had <a href="/wiki/Amnesia" title="Amnesia">amnesia</a> and for some time could not even recognize his own wife at the hospital.<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> He went on to make a good recovery.<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> </p><p>Arnold worked at the Steklov Mathematical Institute in Moscow and at <a href="/wiki/Paris_Dauphine_University" title="Paris Dauphine University">Paris Dauphine University</a> up until his death. His PhD students include <a href="/wiki/Rifkat_Bogdanov" title="Rifkat Bogdanov">Rifkat Bogdanov</a>, <a href="/wiki/Alexander_Givental" title="Alexander Givental">Alexander Givental</a>, <a href="/wiki/Victor_Goryunov" title="Victor Goryunov">Victor Goryunov</a>, <a href="/wiki/Sabir_Gusein-Zade" title="Sabir Gusein-Zade">Sabir Gusein-Zade</a>, <a href="/wiki/Emil_Horozov" title="Emil Horozov">Emil Horozov</a>, <a href="/wiki/Yulij_Ilyashenko" title="Yulij Ilyashenko">Yulij Ilyashenko</a>, <a href="/wiki/Boris_Khesin" title="Boris Khesin">Boris Khesin</a>, <a href="/wiki/Askold_Khovanskii" title="Askold Khovanskii">Askold Khovanskii</a>, <a href="/wiki/Nikolay_Nekhoroshev" title="Nikolay Nekhoroshev">Nikolay Nekhoroshev</a>, <a href="/wiki/Boris_Shapiro_(mathematician)" class="mw-redirect" title="Boris Shapiro (mathematician)">Boris Shapiro</a>, <a href="/wiki/Alexander_Varchenko" title="Alexander Varchenko">Alexander Varchenko</a>, <a href="/wiki/Victor_Anatolyevich_Vassiliev" class="mw-redirect" title="Victor Anatolyevich Vassiliev">Victor Vassiliev</a> and <a href="/wiki/Vladimir_Zakalyukin" title="Vladimir Zakalyukin">Vladimir Zakalyukin</a>.<sup id="cite_ref-mathgene_2-1" class="reference"><a href="#cite_note-mathgene-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>To his students and colleagues Arnold was known also for his sense of humour. For example, once at his seminar in Moscow, at the beginning of the school year, when he usually was formulating new problems, he said: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>There is a general principle that a stupid man can ask such questions to which one hundred wise men would not be able to answer. In accordance with this principle I shall formulate some problems.<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></p></blockquote> <div class="mw-heading mw-heading3"><h3 id="Death">Death</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=2" title="Edit section: Death"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Arnold died of <a href="/wiki/Acute_pancreatitis" title="Acute pancreatitis">acute pancreatitis</a><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> on 3 June 2010 in Paris, nine days before his 73rd birthday.<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> He was buried on 15 June in Moscow, at the <a href="/wiki/Novodevichy_Convent" title="Novodevichy Convent">Novodevichy Monastery</a>.<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>In a telegram to Arnold's family, <a href="/wiki/Russian_President" class="mw-redirect" title="Russian President">Russian President</a> <a href="/wiki/Dmitry_Medvedev" title="Dmitry Medvedev">Dmitry Medvedev</a> stated: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>The death of Vladimir Arnold, one of the greatest mathematicians of our time, is an irretrievable loss for world science. It is difficult to overestimate the contribution made by academician Arnold to modern mathematics and the prestige of Russian science. </p><p>Teaching had a special place in Vladimir Arnold's life and he had great influence as an enlightened mentor who taught several generations of talented scientists. </p><p> The memory of Vladimir Arnold will forever remain in the hearts of his colleagues, friends and students, as well as everyone who knew and admired this brilliant man.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Popular_mathematical_writings">Popular mathematical writings</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=3" title="Edit section: Popular mathematical writings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Arnold is well known for his lucid writing style, combining mathematical rigour with physical intuition, and an easy conversational style of teaching and education. His writings present a fresh, often <a href="/wiki/Geometric" class="mw-redirect" title="Geometric">geometric</a> approach to traditional mathematical topics like <a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">ordinary differential equations</a>, and his many textbooks have proved influential in the development of new areas of mathematics. The standard criticism about Arnold's pedagogy is that his books "are beautiful treatments of their subjects that are appreciated by experts, but too many details are omitted for students to learn the mathematics required to prove the statements that he so effortlessly justifies." His defense was that his books are meant to teach the subject to "those who truly wish to understand it" (Chicone, 2007).<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the <a href="/wiki/Nicolas_Bourbaki" title="Nicolas Bourbaki">Bourbaki</a> school in France—initially had a negative impact on French <a href="/wiki/Mathematical_education" class="mw-redirect" title="Mathematical education">mathematical education</a>, and then later on that of other countries as well.<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><sup id="cite_ref-interview1_24-0" class="reference"><a href="#cite_note-interview1-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> He was very concerned about what he saw as the divorce of mathematics from the <a href="/wiki/Natural_science" title="Natural science">natural sciences</a> in the 20th century.<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> Arnold was very interested in the <a href="/wiki/History_of_mathematics" title="History of mathematics">history of mathematics</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> In an interview,<sup id="cite_ref-interview1_24-1" class="reference"><a href="#cite_note-interview1-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> he said he had learned much of what he knew about mathematics through the study of <a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a>'s book <i>Development of Mathematics in the 19th Century</i> —a book he often recommended to his students.<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> He studied the classics, most notably the works of <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a>, <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> and <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a>,<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> and many times he reported to have found in their works ideas that had not been explored yet.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_work">Mathematical work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=4" title="Edit section: Mathematical work"><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">See also: <a href="/wiki/Stability_of_the_Solar_System" title="Stability of the Solar System">Stability of the Solar System</a></div> <p>Arnold worked on <a href="/wiki/Dynamical_systems_theory" title="Dynamical systems theory">dynamical systems theory</a>, <a href="/wiki/Catastrophe_theory" title="Catastrophe theory">catastrophe theory</a>, <a href="/wiki/Topology" title="Topology">topology</a>, <a href="/wiki/Algebraic_geometry" title="Algebraic geometry">algebraic geometry</a>, <a href="/wiki/Symplectic_geometry" title="Symplectic geometry">symplectic geometry</a>, <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a>, <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a>, <a href="/wiki/Hydrodynamics" class="mw-redirect" title="Hydrodynamics">hydrodynamics</a> and <a href="/wiki/Singularity_theory" title="Singularity theory">singularity theory</a>.<sup id="cite_ref-MacTutor_5-1" class="reference"><a href="#cite_note-MacTutor-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Mich%C3%A8le_Audin" title="Michèle Audin">Michèle Audin</a> described him as "a geometer in the widest possible sense of the word" and said that "he was very fast to make connections between different fields".<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-heading3"><h3 id="Hilbert's_thirteenth_problem"><span id="Hilbert.27s_thirteenth_problem"></span>Hilbert's thirteenth problem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=5" title="Edit section: Hilbert's thirteenth problem"><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">See also: <a href="/wiki/Kolmogorov%E2%80%93Arnold_representation_theorem" title="Kolmogorov–Arnold representation theorem">Kolmogorov–Arnold representation theorem</a></div> <p>The problem is the following question: can every continuous function of three variables be expressed as a <a href="/wiki/Function_composition" title="Function composition">composition</a> of finitely many continuous functions of two variables? The affirmative answer to this general question was given in 1957 by Vladimir Arnold, then only nineteen years old and a student of <a href="/wiki/Andrey_Kolmogorov" title="Andrey Kolmogorov">Andrey Kolmogorov</a>. Kolmogorov had shown in the previous year that any function of several variables can be constructed with a finite number of three-variable functions. Arnold then expanded on this work to show that only two-variable functions were in fact required, thus answering the Hilbert's question when posed for the class of continuous functions.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Dynamical_systems">Dynamical systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=6" title="Edit section: Dynamical systems"><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">See also: <a href="/wiki/Arnold_diffusion" title="Arnold diffusion">Arnold diffusion</a>, <a href="/wiki/Arnold_tongue" title="Arnold tongue">Arnold tongue</a>, <a href="/wiki/Liouville%E2%80%93Arnold_theorem" title="Liouville–Arnold theorem">Liouville–Arnold theorem</a>, and <a href="/wiki/Hilbert%E2%80%93Arnold_problem" title="Hilbert–Arnold problem">Hilbert–Arnold problem</a></div> <p><a href="/wiki/J%C3%BCrgen_Moser" title="Jürgen Moser">Moser</a> and Arnold expanded the ideas of <a href="/wiki/Andrey_Kolmogorov" title="Andrey Kolmogorov">Kolmogorov</a> (who was inspired by questions of <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a>) and gave rise to what is now known as <a href="/wiki/Kolmogorov%E2%80%93Arnold%E2%80%93Moser_theorem" title="Kolmogorov–Arnold–Moser theorem">Kolmogorov–Arnold–Moser theorem</a> (or "KAM theory"), which concerns the persistence of some quasi-periodic motions (nearly integrable <a href="/wiki/Hamiltonian_system" title="Hamiltonian system">Hamiltonian systems</a>) when they are perturbed. KAM theory shows that, despite the perturbations, such systems can be stable over an infinite period of time, and specifies what the conditions for this are.<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> </p><p>In 1964, Arnold introduced the <a href="/w/index.php?title=Arnold_web&action=edit&redlink=1" class="new" title="Arnold web (page does not exist)">Arnold web</a>, the first example of a stochastic web.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Singularity_theory">Singularity theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=7" title="Edit section: Singularity theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1965, Arnold attended <a href="/wiki/Ren%C3%A9_Thom" title="René Thom">René Thom</a>'s seminar on <a href="/wiki/Catastrophe_theory" title="Catastrophe theory">catastrophe theory</a>. He later said of it: "I am deeply indebted to Thom, whose singularity seminar at the <a href="/wiki/Institut_des_Hautes_%C3%89tudes_Scientifiques" title="Institut des Hautes Études Scientifiques">Institut des Hautes Etudes Scientifiques</a>, which I frequented throughout the year 1965, profoundly changed my mathematical universe."<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> After this event, <a href="/wiki/Singularity_theory" title="Singularity theory">singularity theory</a> became one of the major interests of Arnold and his students.<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> Among his most famous results in this area is his classification of simple singularities, contained in his paper "Normal forms of functions near degenerate critical points, the Weyl groups of A<sub>k</sub>,D<sub>k</sub>,E<sub>k</sub> and Lagrangian singularities".<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><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> </p> <div class="mw-heading mw-heading3"><h3 id="Fluid_dynamics">Fluid dynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=8" title="Edit section: Fluid dynamics"><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">See also: <a href="/wiki/Arnold%E2%80%93Beltrami%E2%80%93Childress_flow" title="Arnold–Beltrami–Childress flow">Arnold–Beltrami–Childress flow</a> and <a href="/wiki/Beltrami_vector_field#Beltrami_fields_and_complexity_in_fluid_mechanics" title="Beltrami vector field">Beltrami vector field § Beltrami fields and complexity in fluid mechanics</a></div> <p>In 1966, Arnold published "<span title="French-language text"><i lang="fr">Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits</i></span>", in which he presented a common geometric interpretation for both the <a href="/wiki/Euler%27s_equations_(rigid_body_dynamics)" title="Euler's equations (rigid body dynamics)">Euler's equations for rotating rigid bodies</a> and the <a href="/wiki/Euler_equations_(fluid_dynamics)" title="Euler equations (fluid dynamics)">Euler's equations of fluid dynamics</a>, this effectively linked topics previously thought to be unrelated, and enabled mathematical solutions to many questions related to fluid flows and their turbulence.<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><sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Real_algebraic_geometry">Real algebraic geometry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=9" title="Edit section: Real algebraic geometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the year 1971, Arnold published "On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms",<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> which gave new life to <a href="/wiki/Real_algebraic_geometry" title="Real algebraic geometry">real algebraic geometry</a>. In it, he made major advances in the direction of a solution to <a href="/wiki/Gudkov%27s_conjecture" title="Gudkov's conjecture">Gudkov's conjecture</a>, by finding a connection between it and <a href="/wiki/Low-dimensional_topology#Four_dimensions" title="Low-dimensional topology">four-dimensional topology</a>.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Conjecture" title="Conjecture">conjecture</a> was to be later fully solved by <a href="/wiki/Vladimir_Abramovich_Rokhlin" title="Vladimir Abramovich Rokhlin">V. A. Rokhlin</a> building on Arnold's work.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Symplectic_geometry">Symplectic geometry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=10" title="Edit section: Symplectic geometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Arnold_conjecture" title="Arnold conjecture">Arnold conjecture</a>, linking the number of fixed points of Hamiltonian <a href="/wiki/Symplectomorphism" title="Symplectomorphism">symplectomorphisms</a> and the topology of the subjacent <a href="/wiki/Manifold" title="Manifold">manifolds</a>, was the motivating source of many of the pioneer studies in symplectic topology.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Topology">Topology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=11" title="Edit section: Topology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to <a href="/wiki/Victor_Vassiliev" class="mw-redirect" title="Victor Vassiliev">Victor Vassiliev</a>, Arnold "worked comparatively little on topology for topology's sake." And he was rather motivated by problems on other areas of mathematics where topology could be of use. His contributions include the invention of a topological form of the <a href="/wiki/Abel%E2%80%93Ruffini_theorem" title="Abel–Ruffini theorem">Abel–Ruffini theorem</a> and the initial development of some of the consequent ideas, a work which resulted in the creation of the field of <a href="/wiki/Topological_Galois_theory" title="Topological Galois theory">topological Galois theory</a> in the 1960s.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Theory_of_plane_curves">Theory of plane curves</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=12" title="Edit section: Theory of plane curves"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to <a href="/wiki/Marcel_Berger" title="Marcel Berger">Marcel Berger</a>, Arnold revolutionized <a href="/wiki/Plane_curve" title="Plane curve">plane curves</a> theory.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> He developed the theory of smooth closed plane curves in the 1990s.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> Among his contributions are the introduction of the three <a href="/wiki/Arnold_invariants" title="Arnold invariants">Arnold invariants</a> of plane curves: <i>J</i><sup>+</sup>, <i>J</i><sup>−</sup> and <i>St</i>.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other">Other</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=13" title="Edit section: Other"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Arnold conjectured the existence of the <a href="/wiki/G%C3%B6mb%C3%B6c" title="Gömböc">gömböc</a>, a body with just one stable and one unstable <a href="/wiki/Mechanical_equilibrium" title="Mechanical equilibrium">point of equilibrium</a> when resting on a flat surface.<sup id="cite_ref-wolfram_55-0" class="reference"><a href="#cite_note-wolfram-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p><p>Arnold generalized the results of <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>, <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Pierre-Simon Laplace</a>, and <a href="/wiki/James_Ivory_(mathematician)" title="James Ivory (mathematician)">James Ivory</a> on the <a href="/wiki/Shell_theorem" title="Shell theorem">shell theorem</a>, showing it to be applicable to algebraic hypersurfaces.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Honours_and_awards">Honours and awards</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=14" title="Edit section: Honours and awards"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Dmitry_Medvedev_12_June_2008-10.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Dmitry_Medvedev_12_June_2008-10.jpg/300px-Dmitry_Medvedev_12_June_2008-10.jpg" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Dmitry_Medvedev_12_June_2008-10.jpg/450px-Dmitry_Medvedev_12_June_2008-10.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/3/3a/Dmitry_Medvedev_12_June_2008-10.jpg 2x" data-file-width="500" data-file-height="334" /></a><figcaption>Arnold (left) and Russia's president <a href="/wiki/Dmitry_Medvedev" title="Dmitry Medvedev">Dmitry Medvedev</a></figcaption></figure> <ul><li><a href="/wiki/Lenin_Prize" title="Lenin Prize">Lenin Prize</a> (1965, with <a href="/wiki/Andrey_Kolmogorov" title="Andrey Kolmogorov">Andrey Kolmogorov</a>),<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> "for work on <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a>."</li> <li><a href="/wiki/Crafoord_Prize" title="Crafoord Prize">Crafoord Prize</a> (1982, with <a href="/wiki/Louis_Nirenberg" title="Louis Nirenberg">Louis Nirenberg</a>),<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> "for their outstanding achievements in the theory of non-linear differential equations."<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup></li> <li>Elected member of the United States <a href="/wiki/National_Academy_of_Sciences" title="National Academy of Sciences">National Academy of Sciences</a> in 1983.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup></li> <li>Foreign Honorary 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> (1987)<sup id="cite_ref-AAAS_62-0" class="reference"><a href="#cite_note-AAAS-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup></li> <li>Elected a <a href="/wiki/Foreign_Member_of_the_Royal_Society" class="mw-redirect" title="Foreign Member of the Royal Society">Foreign Member of the Royal Society</a> (ForMemRS) of London in 1988.<sup id="cite_ref-rsbm_1-2" class="reference"><a href="#cite_note-rsbm-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li> <li>Elected member of the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a> in 1990.<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Lobachevsky_Prize#Russian_Academy_of_Sciences" title="Lobachevsky Prize">Lobachevsky Prize of the Russian Academy of Sciences</a> (1992)<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Harvey_Prize" title="Harvey Prize">Harvey Prize</a> (1994), "In recognition of his basic contribution to the stability theory of Dynamical Systems, his pioneering work on singularity theory and seminal contributions to analysis and geometry."<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Dannie_Heineman_Prize_for_Mathematical_Physics" title="Dannie Heineman Prize for Mathematical Physics">Dannie Heineman Prize for Mathematical Physics</a> (2001), "for his fundamental contributions to our understanding of dynamics and of singularities of maps with profound consequences for <a href="/wiki/Mechanics" title="Mechanics">mechanics</a>, <a href="/wiki/Astrophysics" title="Astrophysics">astrophysics</a>, <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a>, <a href="/wiki/Hydrodynamics" class="mw-redirect" title="Hydrodynamics">hydrodynamics</a> and <a href="/wiki/Optics" title="Optics">optics</a>."<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Wolf_Prize_in_Mathematics" title="Wolf Prize in Mathematics">Wolf Prize in Mathematics</a> (2001), "for his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory."<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/State_Prize_of_the_Russian_Federation" title="State Prize of the Russian Federation">State Prize of the Russian Federation</a> (2007),<sup id="cite_ref-Kommersant_68-0" class="reference"><a href="#cite_note-Kommersant-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> "for outstanding success in mathematics."</li> <li><a href="/wiki/Shaw_Prize" title="Shaw Prize">Shaw Prize</a> in mathematical sciences (2008, with <a href="/wiki/Ludvig_Faddeev" title="Ludvig Faddeev">Ludwig Faddeev</a>), "for their widespread and influential contributions to Mathematical Physics."<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup></li></ul> <p>The <a href="/wiki/Minor_planet" title="Minor planet">minor planet</a> <a href="/wiki/10031_Vladarnolda" class="mw-redirect" title="10031 Vladarnolda">10031 Vladarnolda</a> was named after him in 1981 by <a href="/wiki/Lyudmila_Georgievna_Karachkina" class="mw-redirect" title="Lyudmila Georgievna Karachkina">Lyudmila Georgievna Karachkina</a>.<sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> </p><p>The <i><a href="/wiki/Arnold_Mathematical_Journal" title="Arnold Mathematical Journal">Arnold Mathematical Journal</a></i>, published for the first time in 2015, is named after him.<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> </p><p>The Arnold Fellowships, of the <a href="/wiki/London_Institute" class="mw-redirect" title="London Institute">London Institute</a> are named after him.<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> </p><p>He was a plenary speaker at both the 1974 and 1983 <a href="/wiki/International_Congress_of_Mathematicians" title="International Congress of Mathematicians">International Congress of Mathematicians</a> in Vancouver and <a href="/wiki/Warsaw" title="Warsaw">Warsaw</a>, respectively.<sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Fields_Medal_omission">Fields Medal omission</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=15" title="Edit section: Fields Medal omission"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Even though Arnold was nominated for the 1974 <a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medal</a>, one of the highest honours a mathematician could receive, interference from the Soviet government led to it being withdrawn. Arnold's public opposition to the persecution of <a href="/wiki/Dissident#Eastern_bloc" title="Dissident">dissidents</a> had led him into direct conflict with influential Soviet officials, and he suffered persecution himself, including not being allowed to leave the Soviet Union during most of the 1970s and 1980s.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Selected_bibliography">Selected bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=16" title="Edit section: Selected bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>1966: <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFArnold1966" class="citation journal cs1">Arnold, Vladimir (1966). <a rel="nofollow" class="external text" href="https://aif.centre-mersenne.org/article/AIF_1966__16_1_319_0.pdf">"Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Annales_de_l%27Institut_Fourier" title="Annales de l'Institut Fourier">Annales de l'Institut Fourier</a></i>. <b>16</b> (1): <span class="nowrap">319–</span>361. <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/10.5802%2Faif.233">10.5802/aif.233</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annales+de+l%27Institut+Fourier&rft.atitle=Sur+la+g%C3%A9om%C3%A9trie+diff%C3%A9rentielle+des+groupes+de+Lie+de+dimension+infinie+et+ses+applications+%C3%A0+l%27hydrodynamique+des+fluides+parfaits&rft.volume=16&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E319-%3C%2Fspan%3E361&rft.date=1966&rft_id=info%3Adoi%2F10.5802%2Faif.233&rft.aulast=Arnold&rft.aufirst=Vladimir&rft_id=https%3A%2F%2Faif.centre-mersenne.org%2Farticle%2FAIF_1966__16_1_319_0.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li>1978: <i>Ordinary Differential Equations</i>, The MIT 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/0-262-51018-9" title="Special:BookSources/0-262-51018-9">0-262-51018-9</a>.<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup></li> <li>1985: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArnoldGusein-ZadeVarchenko1985" class="citation book cs1">Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. (1985). <i>Singularities of Differentiable Maps, Volume I: The Classification of Critical Points Caustics and Wave Fronts</i>. Monographs in Mathematics. Vol. 82. <a href="/wiki/Birkh%C3%A4user" title="Birkhäuser">Birkhäuser</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4612-5154-5">10.1007/978-1-4612-5154-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4612-9589-1" title="Special:BookSources/978-1-4612-9589-1"><bdi>978-1-4612-9589-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Singularities+of+Differentiable+Maps%2C+Volume+I%3A+The+Classification+of+Critical+Points+Caustics+and+Wave+Fronts&rft.series=Monographs+in+Mathematics&rft.pub=Birkh%C3%A4user&rft.date=1985&rft_id=info%3Adoi%2F10.1007%2F978-1-4612-5154-5&rft.isbn=978-1-4612-9589-1&rft.aulast=Arnold&rft.aufirst=V.+I.&rft.au=Gusein-Zade%2C+S.+M.&rft.au=Varchenko%2C+A.+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li>1988: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArnoldGusein-ZadeVarchenko1988" class="citation book cs1">Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. (1988). Arnold, V. I; Gusein-Zade, S. M; Varchenko, A. N (eds.). <a rel="nofollow" class="external text" href="http://www.numdam.org/item/PMIHES_1967__33__21_0/"><i>Singularities of Differentiable Maps, Volume II: Monodromy and Asymptotics of Integrals</i></a>. Monographs in Mathematics. Vol. 83. <a href="/wiki/Birkh%C3%A4user" title="Birkhäuser">Birkhäuser</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4612-3940-6">10.1007/978-1-4612-3940-6</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4612-8408-6" title="Special:BookSources/978-1-4612-8408-6"><bdi>978-1-4612-8408-6</bdi></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:131768406">131768406</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Singularities+of+Differentiable+Maps%2C+Volume+II%3A+Monodromy+and+Asymptotics+of+Integrals&rft.series=Monographs+in+Mathematics&rft.pub=Birkh%C3%A4user&rft.date=1988&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A131768406%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2F978-1-4612-3940-6&rft.isbn=978-1-4612-8408-6&rft.aulast=Arnold&rft.aufirst=V.+I.&rft.au=Gusein-Zade%2C+S.+M.&rft.au=Varchenko%2C+A.+N.&rft_id=http%3A%2F%2Fwww.numdam.org%2Fitem%2FPMIHES_1967__33__21_0%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li>1988: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArnold1988" class="citation book cs1">Arnold, V.I. (1988). <i>Geometrical Methods in the Theory of Ordinary Differential Equations</i>. Grundlehren der mathematischen Wissenschaften. Vol. 250 (2nd ed.). <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4612-1037-5">10.1007/978-1-4612-1037-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4612-6994-6" title="Special:BookSources/978-1-4612-6994-6"><bdi>978-1-4612-6994-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometrical+Methods+in+the+Theory+of+Ordinary+Differential+Equations&rft.series=Grundlehren+der+mathematischen+Wissenschaften&rft.edition=2nd&rft.pub=Springer&rft.date=1988&rft_id=info%3Adoi%2F10.1007%2F978-1-4612-1037-5&rft.isbn=978-1-4612-6994-6&rft.aulast=Arnold&rft.aufirst=V.I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li>1989: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArnold1989" class="citation book cs1">Arnold, V.I. (1989). <i><a href="/wiki/Mathematical_Methods_of_Classical_Mechanics" title="Mathematical Methods of Classical Mechanics">Mathematical Methods of Classical Mechanics</a></i>. Graduate Texts in Mathematics. Vol. 60 (2nd ed.). <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4757-2063-1">10.1007/978-1-4757-2063-1</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4419-3087-3" title="Special:BookSources/978-1-4419-3087-3"><bdi>978-1-4419-3087-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Methods+of+Classical+Mechanics&rft.series=Graduate+Texts+in+Mathematics&rft.edition=2nd&rft.pub=Springer&rft.date=1989&rft_id=info%3Adoi%2F10.1007%2F978-1-4757-2063-1&rft.isbn=978-1-4419-3087-3&rft.aulast=Arnold&rft.aufirst=V.I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span><sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup></li> <li>1989 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFАрнольд1989" class="citation book cs1"><a class="mw-selflink selflink">Арнольд, В. И.</a> (1989). <i>Гюйгенс и Барроу, Ньютон и Гук - Первые шаги математического анализа и теории катастроф</i>. М.: <a href="/wiki/Nauka_(publisher)" title="Nauka (publisher)">Наука</a>. p. 98. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/5-02-013935-1" title="Special:BookSources/5-02-013935-1"><bdi>5-02-013935-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%D0%93%D1%8E%D0%B9%D0%B3%D0%B5%D0%BD%D1%81+%D0%B8+%D0%91%D0%B0%D1%80%D1%80%D0%BE%D1%83%2C+%D0%9D%D1%8C%D1%8E%D1%82%D0%BE%D0%BD+%D0%B8+%D0%93%D1%83%D0%BA+-+%D0%9F%D0%B5%D1%80%D0%B2%D1%8B%D0%B5+%D1%88%D0%B0%D0%B3%D0%B8+%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B3%D0%BE+%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0+%D0%B8+%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B8+%D0%BA%D0%B0%D1%82%D0%B0%D1%81%D1%82%D1%80%D0%BE%D1%84&rft.place=%D0%9C.&rft.pages=98&rft.pub=%D0%9D%D0%B0%D1%83%D0%BA%D0%B0&rft.date=1989&rft.isbn=5-02-013935-1&rft.aulast=%D0%90%D1%80%D0%BD%D0%BE%D0%BB%D1%8C%D0%B4&rft.aufirst=%D0%92.+%D0%98.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li>1989: (with A. Avez) <i>Ergodic Problems of Classical Mechanics</i>, Addison-Wesley <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/0-201-09406-1" title="Special:BookSources/0-201-09406-1">0-201-09406-1</a>.</li> <li>1990: <i>Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals</i>, Eric J.F. Primrose translator, <a href="/wiki/Birkh%C3%A4user_Verlag" class="mw-redirect" title="Birkhäuser Verlag">Birkhäuser Verlag</a> (1990) <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/3-7643-2383-3" title="Special:BookSources/3-7643-2383-3">3-7643-2383-3</a>.<sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-84" class="reference"><a href="#cite_note-84"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup></li> <li>1991: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArnolʹd1991" class="citation book cs1">Arnolʹd, Vladimir Igorevich (1991). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=5aCqyTCElNkC"><i>The Theory of Singularities and Its Applications</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521422802" title="Special:BookSources/9780521422802"><bdi>9780521422802</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Singularities+and+Its+Applications&rft.pub=Cambridge+University+Press&rft.date=1991&rft.isbn=9780521422802&rft.aulast=Arnol%CA%B9d&rft.aufirst=Vladimir+Igorevich&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D5aCqyTCElNkC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li>1995:<i>Topological Invariants of Plane Curves and Caustics</i>,<sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> American Mathematical Society (1994) <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/978-0-8218-0308-0" title="Special:BookSources/978-0-8218-0308-0">978-0-8218-0308-0</a></li> <li>1998: "On the teaching of mathematics" (Russian) Uspekhi Mat. Nauk 53 (1998), no. 1(319), 229–234; translation in <i><a href="/wiki/Russian_Mathematical_Surveys" title="Russian Mathematical Surveys">Russian Math. Surveys</a></i> 53(1): 229–236.</li> <li>1999: (with <a href="/wiki/Valentin_Afraimovich" title="Valentin Afraimovich">Valentin Afraimovich</a>) <i>Bifurcation Theory And Catastrophe Theory</i> Springer <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/3-540-65379-1" title="Special:BookSources/3-540-65379-1">3-540-65379-1</a></li> <li>2001: "Tsepniye Drobi" (Continued Fractions, in Russian), Moscow (2001).</li> <li>2002: "Что такое математика?" (What is mathematics?, in Russian) ISBN 978-5-94057-426-2.</li> <li>2004: <i>Teoriya Katastrof</i> (Catastrophe Theory,<sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup> in Russian), 4th ed. Moscow, <a href="/wiki/Editorial-URSS" class="mw-redirect" title="Editorial-URSS">Editorial-URSS</a> (2004), <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/5-354-00674-0" title="Special:BookSources/5-354-00674-0">5-354-00674-0</a>.</li> <li>2004: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVladimir_I._Arnold2004" class="citation book cs1">Vladimir I. Arnold, ed. (15 November 2004). <i>Arnold's Problems</i> (2nd ed.). Springer-Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-20748-1" title="Special:BookSources/978-3-540-20748-1"><bdi>978-3-540-20748-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Arnold%27s+Problems&rft.edition=2nd&rft.pub=Springer-Verlag&rft.date=2004-11-15&rft.isbn=978-3-540-20748-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span> <sup id="cite_ref-88" class="reference"><a href="#cite_note-88"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup></li> <li>2004: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArnold2004" class="citation book cs1">Arnold, Vladimir I. (2004). <a rel="nofollow" class="external text" href="https://cds.cern.ch/record/730993"><i>Lectures on Partial Differential Equations</i></a>. Universitext. <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-662-05441-3">10.1007/978-3-662-05441-3</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-40448-4" title="Special:BookSources/978-3-540-40448-4"><bdi>978-3-540-40448-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lectures+on+Partial+Differential+Equations&rft.series=Universitext&rft.pub=Springer&rft.date=2004&rft_id=info%3Adoi%2F10.1007%2F978-3-662-05441-3&rft.isbn=978-3-540-40448-4&rft.aulast=Arnold&rft.aufirst=Vladimir+I.&rft_id=https%3A%2F%2Fcds.cern.ch%2Frecord%2F730993&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span><sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup></li> <li>2007: <i>Yesterday and Long Ago</i>, Springer (2007), <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/978-3-540-28734-6" title="Special:BookSources/978-3-540-28734-6">978-3-540-28734-6</a>.</li> <li>2013: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArnold2013" class="citation book cs1">Arnold, Vladimir I. (2013). Itenberg, Ilia; Kharlamov, Viatcheslav; Shustin, Eugenii I. (eds.). <i>Real Algebraic Geometry</i>. Unitext. Vol. 66. <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-36243-9">10.1007/978-3-642-36243-9</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-36242-2" title="Special:BookSources/978-3-642-36242-2"><bdi>978-3-642-36242-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Real+Algebraic+Geometry&rft.series=Unitext&rft.pub=Springer&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2F978-3-642-36243-9&rft.isbn=978-3-642-36242-2&rft.aulast=Arnold&rft.aufirst=Vladimir+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span><sup id="cite_ref-91" class="reference"><a href="#cite_note-91"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup></li> <li>2014: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFV._I._Arnold2014" class="citation book cs1">V. I. Arnold (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=9INzBAAAQBAJ"><i>Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians</i></a>. American Mathematical Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4704-1701-7" title="Special:BookSources/978-1-4704-1701-7"><bdi>978-1-4704-1701-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Understanding+of+Nature%3A+Essays+on+Amazing+Physical+Phenomena+and+Their+Understanding+by+Mathematicians&rft.pub=American+Mathematical+Society&rft.date=2014&rft.isbn=978-1-4704-1701-7&rft.au=V.+I.+Arnold&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D9INzBAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li>2015: <i>Experimental Mathematics</i>. American Mathematical Society (translated from Russian, 2015).</li> <li>2015: <i>Lectures and Problems: A Gift to Young Mathematicians</i>, American Math Society, (translated from Russian, 2015)</li> <li>1998: <i>Topological Methods in Hydrodynamics</i><sup id="cite_ref-92" class="reference"><a href="#cite_note-92"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Collected_works">Collected works</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=17" title="Edit section: Collected works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>2010: A. B. Givental; B. A. Khesin; J. E. Marsden; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; V. M. Zakalyukin (editors). <i>Collected Works, Volume I: Representations of Functions, Celestial Mechanics, and KAM Theory (1957–1965)</i>. <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a></li> <li>2013: A. B. Givental; B. A. Khesin; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; (editors). <i>Collected Works, Volume II: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry (1965–1972)</i>. Springer.</li> <li>2016: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). <i>Collected Works, Volume III: Singularity Theory 1972–1979</i>. Springer.</li> <li>2018: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). <i>Collected Works, Volume IV: Singularities in Symplectic and Contact Geometry 1980–1985</i>. Springer.</li> <li>2023: Alexander B. Givental, Boris A. Khesin, Mikhail B. Sevryuk, Victor A. Vassiliev, Oleg Ya. Viro (Eds.). <i>Collected Works, Volume VI: Dynamics, Combinatorics, and Invariants of Knots, Curves, and Wave Fronts 1992–1995</i>. Springer.</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=Vladimir_Arnold&action=edit&section=18" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></span></li></ul> <ul><li><a href="/wiki/List_of_things_named_after_Vladimir_Arnold" title="List of things named after Vladimir Arnold">List of things named after Vladimir Arnold</a></li> <li><a href="/wiki/Independent_University_of_Moscow" title="Independent University of Moscow">Independent University of Moscow</a></li> <li><a href="/wiki/Geometric_mechanics" title="Geometric mechanics">Geometric mechanics</a></li></ul> <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=Vladimir_Arnold&action=edit&section=19" 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: 30em;"> <ol class="references"> <li id="cite_note-rsbm-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-rsbm_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-rsbm_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-rsbm_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKhesinTabachnikov2018" class="citation journal cs1"><a href="/wiki/Boris_Khesin" title="Boris Khesin">Khesin, Boris</a>; <a href="/wiki/Sergei_Tabachnikov" title="Sergei Tabachnikov">Tabachnikov, Sergei</a> (2018). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsbm.2017.0016">"Vladimir Igorevich Arnold. 12 June 1937 – 3 June 2010"</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>64</b>: <span class="nowrap">7–</span>26. <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.2017.0016">10.1098/rsbm.2017.0016</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0080-4606">0080-4606</a>.</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=Vladimir+Igorevich+Arnold.+12+June+1937+%E2%80%93+3+June+2010&rft.volume=64&rft.pages=%3Cspan+class%3D%22nowrap%22%3E7-%3C%2Fspan%3E26&rft.date=2018&rft_id=info%3Adoi%2F10.1098%2Frsbm.2017.0016&rft.issn=0080-4606&rft.aulast=Khesin&rft.aufirst=Boris&rft.au=Tabachnikov%2C+Sergei&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frsbm.2017.0016&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-mathgene-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-mathgene_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-mathgene_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=17493">Vladimir Arnold</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></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://www.lefigaro.fr/flash-actu/2010/06/03/97001-20100603FILWWW00719-mort-d-un-grand-mathematicien-russe.php">Mort d'un grand mathématicien russe</a>, AFP (<i>Le Figaro</i>)</span> </li> <li id="cite_note-obituary-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-obituary_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-obituary_4-1"><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="CITEREFGusein-ZadeVarchenko2010" class="citation cs2"><a href="/wiki/Sabir_Gusein-Zade" title="Sabir Gusein-Zade">Gusein-Zade, Sabir M.</a>; <a href="/wiki/Alexander_Varchenko" title="Alexander Varchenko">Varchenko, Alexander N</a> (December 2010), <a rel="nofollow" class="external text" href="http://www.ems-ph.org/journals/newsletter/pdf/2010-12-78.pdf">"Obituary: Vladimir Arnold (12 June 1937 – 3 June 2010)"</a> <span class="cs1-format">(PDF)</span>, <i>Newsletter of the European Mathematical Society</i>, <b>78</b>: <span class="nowrap">28–</span>29</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Newsletter+of+the+European+Mathematical+Society&rft.atitle=Obituary%3A+Vladimir+Arnold+%2812+June+1937+%E2%80%93+3+June+2010%29&rft.volume=78&rft.pages=%3Cspan+class%3D%22nowrap%22%3E28-%3C%2Fspan%3E29&rft.date=2010-12&rft.aulast=Gusein-Zade&rft.aufirst=Sabir+M.&rft.au=Varchenko%2C+Alexander+N&rft_id=http%3A%2F%2Fwww.ems-ph.org%2Fjournals%2Fnewsletter%2Fpdf%2F2010-12-78.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-MacTutor-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-MacTutor_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-MacTutor_5-1"><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="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/Arnold.html">"Vladimir Arnold"</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=Vladimir+Arnold&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%2FArnold.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBartocciBettiGuerraggioLucchetti2010" class="citation book cs1">Bartocci, Claudio; Betti, Renato; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=J4nk1U3qjh0C&pg=PA211"><i>Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles</i></a>. Springer. p. 211. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783642136061" title="Special:BookSources/9783642136061"><bdi>9783642136061</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Lives%3A+Protagonists+of+the+Twentieth+Century+From+Hilbert+to+Wiles&rft.pages=211&rft.pub=Springer&rft.date=2010&rft.isbn=9783642136061&rft.aulast=Bartocci&rft.aufirst=Claudio&rft.au=Betti%2C+Renato&rft.au=Guerraggio%2C+Angelo&rft.au=Lucchetti%2C+Roberto&rft.au=Williams%2C+Kim&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DJ4nk1U3qjh0C%26pg%3DPA211&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-Arnold2007-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Arnold2007_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVladimir_I._Arnold2007" class="citation book cs1">Vladimir I. Arnold (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7c4oAQAAIAAJ"><i>Yesterday and Long Ago</i></a>. Springer. pp. <span class="nowrap">19–</span>26. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-28734-6" title="Special:BookSources/978-3-540-28734-6"><bdi>978-3-540-28734-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Yesterday+and+Long+Ago&rft.pages=%3Cspan+class%3D%22nowrap%22%3E19-%3C%2Fspan%3E26&rft.pub=Springer&rft.date=2007&rft.isbn=978-3-540-28734-6&rft.au=Vladimir+I.+Arnold&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7c4oAQAAIAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-earlylife-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-earlylife_8-0">^</a></b></span> <span class="reference-text"><i>Arnold: Swimming Against the Tide</i>, p. 3</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">Табачников, С. Л. . "Интервью с В.И.Арнольдом", <i><a href="/wiki/Kvant_(magazine)" title="Kvant (magazine)">Квант</a></i>, 1990, Nº 7, pp. 2–7. (<i>in Russian</i>)</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">Sevryuk, M.B. <i>Translation of the V. I. Arnold paper “From Superpositions to KAM Theory” (Vladimir Igorevich Arnold. Selected — 60, Moscow: PHASIS, 1997, pp. 727–740). Regul. Chaot. Dyn. 19, 734–744 (2014)</i>. <a rel="nofollow" class="external free" href="https://doi.org/10.1134/S1560354714060100">https://doi.org/10.1134/S1560354714060100</a></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.ams.org/journals/notices/199704/arnold.pdf">"An Interview with Vladimir Arnol'd"</a> <span class="cs1-format">(PDF)</span>, <i><a href="/wiki/Notices_of_the_American_Mathematical_Society" title="Notices of the American Mathematical Society">Notices of the AMS</a></i>, <b>44</b> (4): <span class="nowrap">432–</span>438, April 1997</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+AMS&rft.atitle=An+Interview+with+Vladimir+Arnol%27d&rft.volume=44&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E432-%3C%2Fspan%3E438&rft.date=1997-04&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fnotices%2F199704%2Farnold.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDaniel_Robertz2014" class="citation book cs1">Daniel Robertz (13 October 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0kvPBAAAQBAJ&pg=PA192"><i>Formal Algorithmic Elimination for PDEs</i></a>. Springer. p. 192. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-11445-3" title="Special:BookSources/978-3-319-11445-3"><bdi>978-3-319-11445-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Formal+Algorithmic+Elimination+for+PDEs&rft.pages=192&rft.pub=Springer&rft.date=2014-10-13&rft.isbn=978-3-319-11445-3&rft.au=Daniel+Robertz&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D0kvPBAAAQBAJ%26pg%3DPA192&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=17493">"Vladimir Arnold - the Mathematics Genealogy Project"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Vladimir+Arnold+-+the+Mathematics+Genealogy+Project&rft_id=https%3A%2F%2Fmathgenealogy.org%2Fid.php%3Fid%3D17493&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-GRE-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-GRE_14-0">^</a></b></span> <span class="reference-text"><a href="/wiki/Great_Russian_Encyclopedia" title="Great Russian Encyclopedia">Great Russian Encyclopedia</a> (2005), Moscow: Bol'shaya Rossiyskaya Enciklopediya Publisher, vol. 2.</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArnold2007" class="citation book cs1">Arnold, Vladimir I. (2007). <i>Yesterday and Long Ago</i>. Berlin ; New York : Moscow: Springer ; Phasis. p. V. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-28734-6" title="Special:BookSources/978-3-540-28734-6"><bdi>978-3-540-28734-6</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/76794406">76794406</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Yesterday+and+Long+Ago&rft.place=Berlin+%3B+New+York+%3A+Moscow&rft.pages=V&rft.pub=Springer+%3B+Phasis&rft.date=2007&rft_id=info%3Aoclcnum%2F76794406&rft.isbn=978-3-540-28734-6&rft.aulast=Arnold&rft.aufirst=Vladimir+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></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">Polterovich and Scherbak (2011)</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 news cs1"><a rel="nofollow" class="external text" href="https://www.telegraph.co.uk/news/obituaries/science-obituaries/7886200/Vladimir-Arnold.html">"Vladimir Arnold"</a>. <i>The Daily Telegraph</i>. London. 12 July 2010.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Daily+Telegraph&rft.atitle=Vladimir+Arnold&rft.date=2010-07-12&rft_id=https%3A%2F%2Fwww.telegraph.co.uk%2Fnews%2Fobituaries%2Fscience-obituaries%2F7886200%2FVladimir-Arnold.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKenneth_Chang2010" class="citation news cs1">Kenneth Chang (11 June 2010). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2010/06/11/science/11arnold.html">"Vladimir Arnold Dies at 72; Pioneering Mathematician"</a>. <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">12 June</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Vladimir+Arnold+Dies+at+72%3B+Pioneering+Mathematician&rft.date=2010-06-11&rft.au=Kenneth+Chang&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2010%2F06%2F11%2Fscience%2F11arnold.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110614172804/http://www.heraldsun.com.au/news/breaking-news/numbers-up-as-top-mathematician-vladimir-arnold-dies/story-e6frf7jx-1225875367896">"Number's up as top mathematician Vladimir Arnold dies"</a>. <i><a href="/wiki/Herald_Sun" title="Herald Sun">Herald Sun</a></i>. 4 June 2010. Archived from <a rel="nofollow" class="external text" href="http://www.heraldsun.com.au/news/breaking-news/numbers-up-as-top-mathematician-vladimir-arnold-dies/story-e6frf7jx-1225875367896">the original</a> on 14 June 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">6 June</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Herald+Sun&rft.atitle=Number%27s+up+as+top+mathematician+Vladimir+Arnold+dies&rft.date=2010-06-04&rft_id=http%3A%2F%2Fwww.heraldsun.com.au%2Fnews%2Fbreaking-news%2Fnumbers-up-as-top-mathematician-vladimir-arnold-dies%2Fstory-e6frf7jx-1225875367896&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" 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"> <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.pdmi.ras.ru/~arnsem/Arnold/">"From V. I. Arnold's web page"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">12 June</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=From+V.+I.+Arnold%27s+web+page&rft_id=http%3A%2F%2Fwww.pdmi.ras.ru%2F~arnsem%2FArnold%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://eng.kremlin.ru/news/437#sel=3:1,5:29">"Condolences to the family of Vladimir Arnold"</a>. <a href="/wiki/Presidential_Press_and_Information_Office" class="mw-redirect" title="Presidential Press and Information Office">Presidential Press and Information Office</a>. 15 June 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">1 September</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Condolences+to+the+family+of+Vladimir+Arnold&rft.date=2010-06-15&rft_id=http%3A%2F%2Feng.kremlin.ru%2Fnews%2F437%23sel%3D3%3A1%2C5%3A29&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" 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">Carmen Chicone (2007), Book review of "Ordinary Differential Equations", by Vladimir I. Arnold. Springer-Verlag, Berlin, 2006. <i>SIAM Review</i> <b>49</b>(2):335–336. <i>(Chicone mentions the criticism but does not agree with it.)</i></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">See <a rel="nofollow" class="external autonumber" href="https://iopscience.iop.org/article/10.1070/RM1998v053n01ABEH000005/https://archive.today/20210331201831/https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html">[1]</a> (archived from <a rel="nofollow" class="external autonumber" href="http://pauli.uni-muenster.de/~munsteg/arnold.html">[2]</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170428233041/http://pauli.uni-muenster.de/~munsteg/arnold.html">Archived</a> 28 April 2017 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>) and other essays in <a rel="nofollow" class="external autonumber" href="http://www.pdmi.ras.ru/~arnsem/Arnold/">[3]</a>.</span> </li> <li id="cite_note-interview1-24"><span class="mw-cite-backlink">^ <a href="#cite_ref-interview1_24-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-interview1_24-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.ams.org/notices/199704/arnold.pdf">An Interview with Vladimir Arnol'd</a>, by S. H. Lui, <i><a href="/wiki/AMS_Notices" class="mw-redirect" title="AMS Notices">AMS Notices</a></i>, 1991.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEzraWiggins2010" class="citation journal cs1">Ezra, Gregory S.; Wiggins, Stephen (1 December 2010). "Vladimir Igorevich Arnold". <i><a href="/wiki/Physics_Today" title="Physics Today">Physics Today</a></i>. <b>63</b> (12): <span class="nowrap">74–</span>76. <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/2010PhT....63l..74E">2010PhT....63l..74E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3529010">10.1063/1.3529010</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/0031-9228">0031-9228</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=Vladimir+Igorevich+Arnold&rft.volume=63&rft.issue=12&rft.pages=%3Cspan+class%3D%22nowrap%22%3E74-%3C%2Fspan%3E76&rft.date=2010-12-01&rft.issn=0031-9228&rft_id=info%3Adoi%2F10.1063%2F1.3529010&rft_id=info%3Abibcode%2F2010PhT....63l..74E&rft.aulast=Ezra&rft.aufirst=Gregory+S.&rft.au=Wiggins%2C+Stephen&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" 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"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1007.0688">Oleg Karpenkov. "Vladimir Igorevich Arnold"</a></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"><a href="/wiki/Boris_Khesin" title="Boris Khesin">B. Khesin</a> and <a href="/wiki/Sergei_Tabachnikov" title="Sergei Tabachnikov">S. Tabachnikov</a>, Tribute to Vladimir Arnold, <i>Notices of the AMS</i>, <b>59</b>:3 (2012) 378–399.</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoryunovZakalyukin2011" class="citation cs2">Goryunov, V.; Zakalyukin, V. (2011), <a rel="nofollow" class="external text" href="http://www.ams.org/distribution/mmj/vol11-3-2011/vladimir-arnold.html">"Vladimir I. Arnold"</a>, <i><a href="/wiki/Moscow_Mathematical_Journal" title="Moscow Mathematical Journal">Moscow Mathematical Journal</a></i>, <b>11</b> (3)</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Moscow+Mathematical+Journal&rft.atitle=Vladimir+I.+Arnold&rft.volume=11&rft.issue=3&rft.date=2011&rft.aulast=Goryunov&rft.aufirst=V.&rft.au=Zakalyukin%2C+V.&rft_id=http%3A%2F%2Fwww.ams.org%2Fdistribution%2Fmmj%2Fvol11-3-2011%2Fvladimir-arnold.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span>.</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">See for example: Arnold, V. I.; Vasilev, V. A. (1989), "Newton's Principia read 300 years later" and Arnold, V. I. (2006); "Forgotten and neglected theories of Poincaré".</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">"Vladimir Igorevich Arnold and the Invention of Symplectic Topology", chapter I in the book <i>Contact and Symplectic Topology</i> (editors: Frédéric Bourgeois, Vincent Colin, András Stipsicz)</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOrnes2021" class="citation web cs1">Ornes, Stephen (14 January 2021). <a rel="nofollow" class="external text" href="https://www.quantamagazine.org/mathematicians-resurrect-hilberts-13th-problem-20210114/">"Mathematicians Resurrect Hilbert's 13th Problem"</a>. <i><a href="/wiki/Quanta_Magazine" title="Quanta Magazine">Quanta Magazine</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Quanta+Magazine&rft.atitle=Mathematicians+Resurrect+Hilbert%27s+13th+Problem&rft.date=2021-01-14&rft.aulast=Ornes&rft.aufirst=Stephen&rft_id=https%3A%2F%2Fwww.quantamagazine.org%2Fmathematicians-resurrect-hilberts-13th-problem-20210114%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSzpiro2008" class="citation book cs1"><a href="/wiki/George_Szpiro" title="George Szpiro">Szpiro, George G.</a> (29 July 2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=iEBOce-4S2EC&pg=PT39"><i>Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles</i></a>. Penguin. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781440634284" title="Special:BookSources/9781440634284"><bdi>9781440634284</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Poincare%27s+Prize%3A+The+Hundred-Year+Quest+to+Solve+One+of+Math%27s+Greatest+Puzzles&rft.pub=Penguin&rft.date=2008-07-29&rft.isbn=9781440634284&rft.aulast=Szpiro&rft.aufirst=George+G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DiEBOce-4S2EC%26pg%3DPT39&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text">Phase Space Crystals, by Lingzhen Guo <a rel="nofollow" class="external free" href="https://iopscience.iop.org/book/978-0-7503-3563-8.pdf">https://iopscience.iop.org/book/978-0-7503-3563-8.pdf</a></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text">Zaslavsky web map, by George Zaslavsky <a rel="nofollow" class="external free" href="http://www.scholarpedia.org/article/Zaslavsky_web_map">http://www.scholarpedia.org/article/Zaslavsky_web_map</a></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150714123033/https://www.math.upenn.edu/Arnold/Arnold-interview1997.pdf">"Archived copy"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.math.upenn.edu/Arnold/Arnold-interview1997.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 14 July 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">22 February</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=Archived+copy&rft_id=http%3A%2F%2Fwww.math.upenn.edu%2FArnold%2FArnold-interview1997.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_web" title="Template:Cite web">cite web</a>}}</code>: CS1 maint: archived copy as title (<a href="/wiki/Category:CS1_maint:_archived_copy_as_title" title="Category:CS1 maint: archived copy as title">link</a>)</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"><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.ias.ac.in/resonance/Volumes/19/09/0787-0796.pdf">"Resonance – Journal of Science Education | Indian Academy of Sciences"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Resonance+%E2%80%93+Journal+of+Science+Education+%26%23124%3B+Indian+Academy+of+Sciences&rft_id=http%3A%2F%2Fwww.ias.ac.in%2Fresonance%2FVolumes%2F19%2F09%2F0787-0796.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></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">Note: It also appears in another article by him, but in English: <i>Local Normal Forms of Functions</i>, <a rel="nofollow" class="external free" href="http://www.maths.ed.ac.uk/~aar/papers/arnold15.pdf">http://www.maths.ed.ac.uk/~aar/papers/arnold15.pdf</a></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDirk_SiersmaCharles_WallV._Zakalyukin2001" class="citation book cs1">Dirk Siersma; Charles Wall; V. Zakalyukin (30 June 2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rK77kWeRNqYC&pg=PA29"><i>New Developments in Singularity Theory</i></a>. Springer Science & Business Media. p. 29. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7923-6996-7" title="Special:BookSources/978-0-7923-6996-7"><bdi>978-0-7923-6996-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=New+Developments+in+Singularity+Theory&rft.pages=29&rft.pub=Springer+Science+%26+Business+Media&rft.date=2001-06-30&rft.isbn=978-0-7923-6996-7&rft.au=Dirk+Siersma&rft.au=Charles+Wall&rft.au=V.+Zakalyukin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DrK77kWeRNqYC%26pg%3DPA29&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></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="CITEREFLandsbergManivel2002" class="citation arxiv cs1">Landsberg, J. M.; Manivel, L. (2002). "Representation theory and projective geometry". <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/math/0203260">math/0203260</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Representation+theory+and+projective+geometry&rft.date=2002&rft_id=info%3Aarxiv%2Fmath%2F0203260&rft.aulast=Landsberg&rft.aufirst=J.+M.&rft.au=Manivel%2C+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" 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="CITEREFTerence_Tao2013" class="citation book cs1"><a href="/wiki/Terence_Tao" title="Terence Tao">Terence Tao</a> (22 March 2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BawxAAAAQBAJ&pg=PA205"><i>Compactness and Contradiction</i></a>. American Mathematical Soc. pp. <span class="nowrap">205–</span>206. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-9492-7" title="Special:BookSources/978-0-8218-9492-7"><bdi>978-0-8218-9492-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Compactness+and+Contradiction&rft.pages=%3Cspan+class%3D%22nowrap%22%3E205-%3C%2Fspan%3E206&rft.pub=American+Mathematical+Soc.&rft.date=2013-03-22&rft.isbn=978-0-8218-9492-7&rft.au=Terence+Tao&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBawxAAAAQBAJ%26pg%3DPA205&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMacKayStewart2010" class="citation news cs1">MacKay, Robert Sinclair; Stewart, Ian (19 August 2010). <a rel="nofollow" class="external text" href="https://www.theguardian.com/science/2010/aug/19/v-i-arnold-obituary">"VI Arnold obituary"</a>. <i>The Guardian</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Guardian&rft.atitle=VI+Arnold+obituary&rft.date=2010-08-19&rft.aulast=MacKay&rft.aufirst=Robert+Sinclair&rft.au=Stewart%2C+Ian&rft_id=https%3A%2F%2Fwww.theguardian.com%2Fscience%2F2010%2Faug%2F19%2Fv-i-arnold-obituary&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.iamp.org/bulletins/old-bulletins/201007.pdf">IAMP News Bulletin, July 2010, pp. 25–26</a></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text">Note: The paper also appears with other names, as in <a rel="nofollow" class="external free" href="http://perso.univ-rennes1.fr/marie-francoise.roy/cirm07/arnold.pdf">http://perso.univ-rennes1.fr/marie-francoise.roy/cirm07/arnold.pdf</a></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA._G._KhovanskiiAleksandr_Nikolaevich_VarchenkoV._A._Vasiliev1997" class="citation book cs1">A. G. Khovanskii; Aleksandr Nikolaevich Varchenko; V. A. Vasiliev (1997). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=n6MlbFDp5UwC&pg=PR10"><i>Topics in Singularity Theory: V. I. Arnold's 60th Anniversary Collection (preface)</i></a>. American Mathematical Soc. p. 10. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-0807-8" title="Special:BookSources/978-0-8218-0807-8"><bdi>978-0-8218-0807-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Topics+in+Singularity+Theory%3A+V.+I.+Arnold%27s+60th+Anniversary+Collection+%28preface%29&rft.pages=10&rft.pub=American+Mathematical+Soc.&rft.date=1997&rft.isbn=978-0-8218-0807-8&rft.au=A.+G.+Khovanskii&rft.au=Aleksandr+Nikolaevich+Varchenko&rft.au=V.+A.+Vasiliev&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dn6MlbFDp5UwC%26pg%3DPR10&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKhesinTabachnikov2014" class="citation book cs1">Khesin, Boris A.; Tabachnikov, Serge L. (10 September 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=aBWHBAAAQBAJ&pg=PA159"><i>Arnold: Swimming Against the Tide</i></a>. American Mathematical Society. p. 159. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781470416997" title="Special:BookSources/9781470416997"><bdi>9781470416997</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Arnold%3A+Swimming+Against+the+Tide&rft.pages=159&rft.pub=American+Mathematical+Society&rft.date=2014-09-10&rft.isbn=9781470416997&rft.aulast=Khesin&rft.aufirst=Boris+A.&rft.au=Tabachnikov%2C+Serge+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DaBWHBAAAQBAJ%26pg%3DPA159&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDegtyarevKharlamov2000" class="citation journal cs1">Degtyarev, A. I.; Kharlamov, V. M. (2000). "Topological properties of real algebraic varieties: Du coté de chez Rokhlin". <i>Russian Mathematical Surveys</i>. <b>55</b> (4): <span class="nowrap">735–</span>814. <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/math/0004134">math/0004134</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/2000RuMaS..55..735D">2000RuMaS..55..735D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1070%2FRM2000v055n04ABEH000315">10.1070/RM2000v055n04ABEH000315</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:250775854">250775854</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Russian+Mathematical+Surveys&rft.atitle=Topological+properties+of+real+algebraic+varieties%3A+Du+cot%C3%A9+de+chez+Rokhlin&rft.volume=55&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E735-%3C%2Fspan%3E814&rft.date=2000&rft_id=info%3Aarxiv%2Fmath%2F0004134&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A250775854%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1070%2FRM2000v055n04ABEH000315&rft_id=info%3Abibcode%2F2000RuMaS..55..735D&rft.aulast=Degtyarev&rft.aufirst=A.+I.&rft.au=Kharlamov%2C+V.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text">"Arnold and Symplectic Geometry", by <a href="/wiki/Helmut_Hofer" title="Helmut Hofer">Helmut Hofer</a> (in the book <i>Arnold: Swimming Against the Tide</i>)</span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text">"<a rel="nofollow" class="external text" href="http://www-irma.u-strasbg.fr/~maudin/Arnold.pdf">Vladimir Igorevich Arnold and the invention of symplectic topology</a>", by <a href="/wiki/Mich%C3%A8le_Audin" title="Michèle Audin">Michèle Audin</a> <a rel="nofollow" class="external free" href="https://web.archive.org/web/20160303175152/http://www-irma.u-strasbg.fr/~maudin/Arnold.pdf">https://web.archive.org/web/20160303175152/http://www-irma.u-strasbg.fr/~maudin/Arnold.pdf</a></span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text">"Topology in Arnold's work", by <a href="/wiki/Victor_Vassiliev" class="mw-redirect" title="Victor Vassiliev">Victor Vassiliev</a></span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external free" href="http://www.ams.org/journals/bull/2008-45-02/S0273-0979-07-01165-2/S0273-0979-07-01165-2.pdf">http://www.ams.org/journals/bull/2008-45-02/S0273-0979-07-01165-2/S0273-0979-07-01165-2.pdf</a> Bulletin (New Series) of The American Mathematical Society Volume 45, Number 2, April 2008, pp. 329–334</span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBerger" class="citation book cs1"><a href="/wiki/Marcel_Berger" title="Marcel Berger">Berger, Marcel</a>. <i>A Panoramic View of Riemannian Geometry</i>. pp. <span class="nowrap">24–</span>25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Panoramic+View+of+Riemannian+Geometry&rft.pages=%3Cspan+class%3D%22nowrap%22%3E24-%3C%2Fspan%3E25&rft.aulast=Berger&rft.aufirst=Marcel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://hosted.math.rochester.edu/ojac/vol9/90.pdf">"On computational complexity of plane curve invariants", by Duzhin and Biaoshuai</a></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text">Extrema of Arnold's invariants of curves on surfaces, by Vladimir Chernov <a rel="nofollow" class="external free" href="https://math.dartmouth.edu/~chernov-china/">https://math.dartmouth.edu/~chernov-china/</a></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text">V. I. Arnold, "Plane curves, their invariants, perestroikas and classifications" (May 1993)</span> </li> <li id="cite_note-wolfram-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-wolfram_55-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1">Weisstein, Eric W. <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Gomboc.html">"Gömböc"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">29 April</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=G%C3%B6mb%C3%B6c&rft.aulast=Weisstein&rft.aufirst=Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FGomboc.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMackenzie2010" class="citation book cs1">Mackenzie, Dana (29 December 2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=la0xAAAAQBAJ&pg=PA104"><i>What's Happening in the Mathematical Sciences</i></a>. American Mathematical Soc. p. 104. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780821849996" title="Special:BookSources/9780821849996"><bdi>9780821849996</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=What%27s+Happening+in+the+Mathematical+Sciences&rft.pages=104&rft.pub=American+Mathematical+Soc.&rft.date=2010-12-29&rft.isbn=9780821849996&rft.aulast=Mackenzie&rft.aufirst=Dana&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dla0xAAAAQBAJ%26pg%3DPA104&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text">Ivan Izmestiev, <a href="/wiki/Serge_Tabachnikov" class="mw-redirect" title="Serge Tabachnikov">Serge Tabachnikov</a>. "Ivory’s theorem revisited", <i>Journal of Integrable Systems</i>, Volume 2, Issue 1, (2017) <a rel="nofollow" class="external free" href="https://doi.org/10.1093/integr/xyx006">https://doi.org/10.1093/integr/xyx006</a></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text">O. Karpenkov, "Vladimir Igorevich Arnold", <i>Internat. Math. Nachrichten</i>, no. 214, pp. 49–57, 2010. (<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1007.0688">link to arXiv preprint</a>)</span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarold_M._Schmeck_Jr.1982" class="citation news cs1">Harold M. Schmeck Jr. (27 June 1982). <a rel="nofollow" class="external text" href="https://www.nytimes.com/1982/06/27/us/american-and-russian-share-prize-in-mathematics.html">"American and Russian Share Prize in Mathematics"</a>. <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=American+and+Russian+Share+Prize+in+Mathematics&rft.date=1982-06-27&rft.au=Harold+M.+Schmeck+Jr.&rft_id=https%3A%2F%2Fwww.nytimes.com%2F1982%2F06%2F27%2Fus%2Famerican-and-russian-share-prize-in-mathematics.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</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/20160126153013/http://www.kva.se/globalassets/priser/crafoord/2014/rattigheter/crafoordprize1982_2014.pdf">"The Crafoord Prize 1982–2014"</a> <span class="cs1-format">(PDF)</span>. The Anna-Greta and Holger Crafoord Fund. 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"Featured Review: Two New Books on Partial Differential Equations". <i>SIAM Review</i>. <b>47</b> (1): <span class="nowrap">165–</span>168. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0036-1445">0036-1445</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/20453608">20453608</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+Review&rft.atitle=Featured+Review%3A+Two+New+Books+on+Partial+Differential+Equations&rft.volume=47&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E165-%3C%2Fspan%3E168&rft.date=2005&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F20453608%23id-name%3DJSTOR&rft.issn=0036-1445&rft.aulast=Guenther&rft.aufirst=Ronald+B.&rft.au=Thomann%2C+Enrique+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-90"><span class="mw-cite-backlink"><b><a href="#cite_ref-90">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGroves2005" class="citation journal cs1">Groves, M. (2005). "Book Review: Vladimir I. Arnold, Lectures on Partial Differential Equations. Universitext". <i>Journal of Applied Mathematics and Mechanics</i>. <b>85</b> (4): 304. <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/2005ZaMM...85..304G">2005ZaMM...85..304G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fzamm.200590023">10.1002/zamm.200590023</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/1521-4001">1521-4001</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Applied+Mathematics+and+Mechanics&rft.atitle=Book+Review%3A+Vladimir+I.+Arnold%2C+Lectures+on+Partial+Differential+Equations.+Universitext&rft.volume=85&rft.issue=4&rft.pages=304&rft.date=2005&rft.issn=1521-4001&rft_id=info%3Adoi%2F10.1002%2Fzamm.200590023&rft_id=info%3Abibcode%2F2005ZaMM...85..304G&rft.aulast=Groves&rft.aufirst=M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-91"><span class="mw-cite-backlink"><b><a href="#cite_ref-91">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGouvêa2013" class="citation web cs1"><a href="/wiki/Fernando_Q._Gouv%C3%AAa" title="Fernando Q. Gouvêa">Gouvêa, Fernando Q.</a> (15 August 2013). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230323231917/https://www.maa.org/press/maa-reviews/real-algebraic-geometry">"Review of <i>Real Algebraic Geometry</i> by Arnold"</a>. <i><a href="/wiki/MAA_Reviews" class="mw-redirect" title="MAA Reviews">MAA Reviews</a></i>. Archived from <a rel="nofollow" class="external text" href="https://old.maa.org/press/maa-reviews/real-algebraic-geometry">the original</a> on 23 March 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MAA+Reviews&rft.atitle=Review+of+Real+Algebraic+Geometry+by+Arnold&rft.date=2013-08-15&rft.aulast=Gouv%C3%AAa&rft.aufirst=Fernando+Q.&rft_id=https%3A%2F%2Fold.maa.org%2Fpress%2Fmaa-reviews%2Freal-algebraic-geometry&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></span> </li> <li id="cite_note-92"><span class="mw-cite-backlink"><b><a href="#cite_ref-92">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://ems.press/content/serial-article-files/28174">Review, by Daniel Peralta-Salas, of the book "Topological Methods in Hydrodynamics", by Vladimir I. Arnold and Boris A. Khesin</a></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=Vladimir_Arnold&action=edit&section=20" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Khesin, Boris; Tabachnikov, Serge (Coordinating Editors). "<a rel="nofollow" class="external text" href="http://www.ams.org/notices/201203/rtx120300378p.pdf">Tribute to Vladimir Arnold</a>", <i><a href="/wiki/Notices_of_the_American_Mathematical_Society" title="Notices of the American Mathematical Society">Notices of the American Mathematical Society</a></i>, March 2012, Volume 59, Number 3, pp. 378–399.</li> <li>Khesin, Boris; Tabachnikov, Serge (Coordinating Editors). "<a rel="nofollow" class="external text" href="http://www.ams.org/notices/201204/rtx120400482p.pdf">Memories of Vladimir Arnold</a>", <i>Notices of the American Mathematical Society</i>, April 2012, Volume 59, Number 4, pp. 482–502.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoris_A._KhesinSerge_L._Tabachnikov2014" class="citation book cs1">Boris A. Khesin; Serge L. Tabachnikov (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=aBWHBAAAQBAJ"><i>Arnold: Swimming Against the Tide</i></a>. American Mathematical Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4704-1699-7" title="Special:BookSources/978-1-4704-1699-7"><bdi>978-1-4704-1699-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Arnold%3A+Swimming+Against+the+Tide&rft.pub=American+Mathematical+Society&rft.date=2014&rft.isbn=978-1-4704-1699-7&rft.au=Boris+A.+Khesin&rft.au=Serge+L.+Tabachnikov&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DaBWHBAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeonid_PolterovichInna_Scherbak2011" class="citation journal cs1"><a href="/wiki/Leonid_Polterovich" title="Leonid Polterovich">Leonid Polterovich</a>; Inna Scherbak (7 September 2011). "V.I. Arnold (1937–2010)". <i>Jahresbericht der Deutschen Mathematiker-Vereinigung</i>. <b>113</b> (4): <span class="nowrap">185–</span>219. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1365%2Fs13291-011-0027-6">10.1365/s13291-011-0027-6</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:122052411">122052411</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Jahresbericht+der+Deutschen+Mathematiker-Vereinigung&rft.atitle=V.I.+Arnold+%281937%E2%80%932010%29&rft.volume=113&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E185-%3C%2Fspan%3E219&rft.date=2011-09-07&rft_id=info%3Adoi%2F10.1365%2Fs13291-011-0027-6&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122052411%23id-name%3DS2CID&rft.au=Leonid+Polterovich&rft.au=Inna+Scherbak&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="http://www.ems-ph.org/journals/newsletter/pdf/2015-06-96.pdf">"Features: "Knotted Vortex Lines and Vortex Tubes in Stationary Fluid Flows"; "On Delusive Nodal Sets of Free Oscillations"<span class="cs1-kern-right"></span>"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Newsletter_of_the_European_Mathematical_Society" class="mw-redirect" title="Newsletter of the European Mathematical Society">EMS Newsletter</a></i> (96): <span class="nowrap">26–</span>48. June 2015. <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/1027-488X">1027-488X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=EMS+Newsletter&rft.atitle=Features%3A+%22Knotted+Vortex+Lines+and+Vortex+Tubes+in+Stationary+Fluid+Flows%22%3B+%22On+Delusive+Nodal+Sets+of+Free+Oscillations%22&rft.issue=96&rft.pages=%3Cspan+class%3D%22nowrap%22%3E26-%3C%2Fspan%3E48&rft.date=2015-06&rft.issn=1027-488X&rft_id=http%3A%2F%2Fwww.ems-ph.org%2Fjournals%2Fnewsletter%2Fpdf%2F2015-06-96.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVladimir+Arnold" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vladimir_Arnold&action=edit&section=21" 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 .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Vladimir_Arnold" class="extiw" title="commons:Category:Vladimir Arnold">Vladimir Arnold</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikiquote-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Vladimir_Arnold" class="extiw" title="q:Special:Search/Vladimir Arnold">Vladimir Arnold</a></b></i>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.pdmi.ras.ru/~arnsem/Arnold/">V. I. Arnold's web page</a></li> <li><a rel="nofollow" class="external text" href="https://www.mi.ras.ru/~arnold/">Personal web page</a></li> <li><a rel="nofollow" class="external text" href="http://www.msri.org/communications/vmath/VMathVideos/VideoInfo/3152/show_video">V. I. Arnold lecturing on Continued Fractions</a></li> <li><a rel="nofollow" class="external text" href="http://www.mccme.ru/ium/~arnold/">A short curriculum vitae</a></li> <li><a rel="nofollow" class="external text" href="https://www.math.fsu.edu/%7Ewxm/Arnold.htm"><i>On Teaching Mathematics</i></a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170428233041/http://pauli.uni-muenster.de/~munsteg/arnold.html">Archived</a> 28 April 2017 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, text of a talk from 1997 espousing Arnold's opinions on mathematical instruction</li> <li><a rel="nofollow" class="external text" href="https://www.mathunion.org/fileadmin/IMU/Publications/Bulletins/1994_1999/39/Arnold.html"><i>Topology of Plane Curves, Wave Fronts, Legendrian Knots, Sturm Theory and Flattenings of Projective Curves</i></a></li> <li><a rel="nofollow" class="external text" href="http://imaginary.org/sites/default/files/taskbook_arnold_en_0.pdf">Problems from 5 to 15</a>, a text by Arnold for school students, available at the <a rel="nofollow" class="external text" href="http://www.imaginary.org">IMAGINARY platform</a></li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=17493">Vladimir Arnold</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="http://www.math.nsc.ru/LBRT/g2/english/ssk/arnold_e.html">S. Kutateladze, Arnold Is Gone</a></li> <li><a rel="nofollow" class="external text" href="http://www.math.ru/lib/files/pdf/mehmat/mm3.pdf">В.Б.Демидовичем (2009), МЕХМАТЯНЕ ВСПОМИНАЮТ 2: В.И.Арнольд, pp. 25–58</a></li> <li><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:arnold.vladimir-igorevich">Author profile</a> in the database <a href="/wiki/Zentralblatt_MATH" class="mw-redirect" title="Zentralblatt MATH">zbMATH</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output 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id="Laureates_of_the_Wolf_Prize_in_Mathematics235" style="font-size:114%;margin:0 4em">Laureates of the <a href="/wiki/Wolf_Prize_in_Mathematics" title="Wolf Prize in Mathematics">Wolf Prize in Mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">1970s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Israel_Gelfand" title="Israel Gelfand">Israel Gelfand</a> / <a href="/wiki/Carl_Ludwig_Siegel" title="Carl Ludwig Siegel">Carl L. Siegel</a> (1978)</li> <li><a href="/wiki/Jean_Leray" title="Jean Leray">Jean Leray</a> / <a href="/wiki/Andr%C3%A9_Weil" title="André Weil">André Weil</a> (1979)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">1980s</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Henri_Cartan" title="Henri Cartan">Henri Cartan</a> / <a href="/wiki/Andrey_Kolmogorov" title="Andrey Kolmogorov">Andrey Kolmogorov</a> (1980)</li> <li><a href="/wiki/Lars_Ahlfors" title="Lars Ahlfors">Lars Ahlfors</a> / <a href="/wiki/Oscar_Zariski" title="Oscar Zariski">Oscar Zariski</a> (1981)</li> <li><a href="/wiki/Hassler_Whitney" title="Hassler Whitney">Hassler Whitney</a> / <a href="/wiki/Mark_Krein" title="Mark Krein">Mark Krein</a> (1982)</li> <li><a href="/wiki/Shiing-Shen_Chern" title="Shiing-Shen Chern">Shiing-Shen Chern</a> / <a href="/wiki/Paul_Erd%C5%91s" title="Paul Erdős">Paul Erdős</a> (1983/84)</li> <li><a href="/wiki/Kunihiko_Kodaira" title="Kunihiko Kodaira">Kunihiko Kodaira</a> / <a href="/wiki/Hans_Lewy" title="Hans Lewy">Hans Lewy</a> (1984/85)</li> <li><a href="/wiki/Samuel_Eilenberg" title="Samuel Eilenberg">Samuel Eilenberg</a> / <a href="/wiki/Atle_Selberg" title="Atle Selberg">Atle Selberg</a> (1986)</li> <li><a href="/wiki/Kiyosi_It%C3%B4" title="Kiyosi Itô">Kiyosi Itô</a> / <a href="/wiki/Peter_Lax" title="Peter Lax">Peter Lax</a> (1987)</li> <li><a href="/wiki/Friedrich_Hirzebruch" title="Friedrich Hirzebruch">Friedrich Hirzebruch</a> / <a href="/wiki/Lars_H%C3%B6rmander" title="Lars Hörmander">Lars Hörmander</a> (1988)</li> <li><a href="/wiki/Alberto_Calder%C3%B3n" title="Alberto Calderón">Alberto Calderón</a> / <a href="/wiki/John_Milnor" title="John Milnor">John Milnor</a> (1989)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">1990s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ennio_De_Giorgi" title="Ennio De Giorgi">Ennio De Giorgi</a> / <a href="/wiki/Ilya_Piatetski-Shapiro" title="Ilya Piatetski-Shapiro">Ilya Piatetski-Shapiro</a> (1990)</li> <li><a href="/wiki/Lennart_Carleson" title="Lennart Carleson">Lennart Carleson</a> / <a href="/wiki/John_G._Thompson" title="John G. Thompson">John G. Thompson</a> (1992)</li> <li><a href="/wiki/Mikhail_Leonidovich_Gromov" class="mw-redirect" title="Mikhail Leonidovich Gromov">Mikhail Gromov</a> / <a href="/wiki/Jacques_Tits" title="Jacques Tits">Jacques Tits</a> (1993)</li> <li><a href="/wiki/J%C3%BCrgen_Moser" title="Jürgen Moser">Jürgen Moser</a> (1994/95)</li> <li><a href="/wiki/Robert_Langlands" title="Robert Langlands">Robert Langlands</a> / <a href="/wiki/Andrew_Wiles" title="Andrew Wiles">Andrew Wiles</a> (1995/96)</li> <li><a href="/wiki/Joseph_Keller" title="Joseph Keller">Joseph Keller</a> / <a href="/wiki/Yakov_Sinai" title="Yakov Sinai">Yakov G. Sinai</a> (1996/97)</li> <li><a href="/wiki/L%C3%A1szl%C3%B3_Lov%C3%A1sz" title="László Lovász">László Lovász</a> / <a href="/wiki/Elias_M._Stein" title="Elias M. Stein">Elias M. Stein</a> (1999)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">2000s</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Raoul_Bott" title="Raoul Bott">Raoul Bott</a> / <a href="/wiki/Jean-Pierre_Serre" title="Jean-Pierre Serre">Jean-Pierre Serre</a> (2000)</li> <li><a class="mw-selflink selflink">Vladimir Arnold</a> / <a href="/wiki/Saharon_Shelah" title="Saharon Shelah">Saharon Shelah</a> (2001)</li> <li><a href="/wiki/Mikio_Sato" title="Mikio Sato">Mikio Sato</a> / <a href="/wiki/John_Tate_(mathematician)" title="John Tate (mathematician)">John Tate</a> (2002/03)</li> <li><a href="/wiki/Grigory_Margulis" title="Grigory Margulis">Grigory Margulis</a> / <a href="/wiki/Sergei_Novikov_(mathematician)" title="Sergei Novikov (mathematician)">Sergei Novikov</a> (2005)</li> <li><a href="/wiki/Stephen_Smale" title="Stephen Smale">Stephen Smale</a> / <a href="/wiki/Hillel_Furstenberg" title="Hillel Furstenberg">Hillel Furstenberg</a> (2006/07)</li> <li><a href="/wiki/Pierre_Deligne" title="Pierre Deligne">Pierre Deligne</a> / <a href="/wiki/Phillip_Griffiths" title="Phillip Griffiths">Phillip A. Griffiths</a> / <a href="/wiki/David_Mumford" title="David Mumford">David B. Mumford</a> (2008)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">2010s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dennis_Sullivan" title="Dennis Sullivan">Dennis Sullivan</a> / <a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Shing-Tung Yau</a> (2010)</li> <li><a href="/wiki/Michael_Aschbacher" title="Michael Aschbacher">Michael Aschbacher</a> / <a href="/wiki/Luis_Caffarelli" title="Luis Caffarelli">Luis Caffarelli</a> (2012)</li> <li><a href="/wiki/George_Mostow" title="George Mostow">George Mostow</a> / <a href="/wiki/Michael_Artin" title="Michael Artin">Michael Artin</a> (2013)</li> <li><a href="/wiki/Peter_Sarnak" title="Peter Sarnak">Peter Sarnak</a> (2014)</li> <li><a href="/wiki/James_Arthur_(mathematician)" title="James Arthur (mathematician)">James G. Arthur</a> (2015)</li> <li><a href="/wiki/Richard_Schoen" title="Richard Schoen">Richard Schoen</a> / <a href="/wiki/Charles_Fefferman" title="Charles Fefferman">Charles Fefferman</a> (2017)</li> <li><a href="/wiki/Alexander_Beilinson" title="Alexander Beilinson">Alexander Beilinson</a> / <a href="/wiki/Vladimir_Drinfeld" title="Vladimir Drinfeld">Vladimir Drinfeld</a> (2018)</li> <li><a href="/wiki/Jean-Fran%C3%A7ois_Le_Gall" title="Jean-François Le Gall">Jean-François Le Gall</a> / <a href="/wiki/Greg_Lawler" title="Greg Lawler">Gregory Lawler</a> (2019)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">2020s</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Simon_Donaldson" title="Simon Donaldson">Simon K. Donaldson</a> / <a href="/wiki/Yakov_Eliashberg" title="Yakov Eliashberg">Yakov Eliashberg</a> (2020)</li> <li><a href="/wiki/George_Lusztig" title="George Lusztig">George Lusztig</a> (2022)</li> <li><a href="/wiki/Ingrid_Daubechies" title="Ingrid Daubechies">Ingrid Daubechies</a> (2023)</li> <li><a href="/wiki/Noga_Alon" title="Noga Alon">Noga Alon</a> / <a href="/wiki/Adi_Shamir" title="Adi Shamir">Adi Shamir</a> (2024)</li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="background:#d3d3d3;"><div><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/16px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/24px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/32px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></b></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Shaw_Prize_laureates86" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="background:#d3d3d3;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Shaw_Prize_laureates" title="Template:Shaw Prize laureates"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Shaw_Prize_laureates" title="Template talk:Shaw Prize laureates"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Shaw_Prize_laureates" title="Special:EditPage/Template:Shaw Prize laureates"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Shaw_Prize_laureates86" style="font-size:114%;margin:0 4em"><a href="/wiki/Shaw_Prize" title="Shaw Prize">Shaw Prize</a> laureates</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">Astronomy</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jim_Peebles" title="Jim Peebles">Jim Peebles</a> (2004)</li> <li><a href="/wiki/Geoffrey_Marcy" title="Geoffrey Marcy">Geoffrey Marcy</a> and <a href="/wiki/Michel_Mayor" title="Michel Mayor">Michel Mayor</a> (2005)</li> <li><a href="/wiki/Saul_Perlmutter" title="Saul Perlmutter">Saul Perlmutter</a>, <a href="/wiki/Adam_Riess" title="Adam Riess">Adam Riess</a> and <a href="/wiki/Brian_Schmidt" title="Brian Schmidt">Brian Schmidt</a> (2006)</li> <li><a href="/wiki/Peter_Goldreich" title="Peter Goldreich">Peter Goldreich</a> (2007)</li> <li><a href="/wiki/Reinhard_Genzel" title="Reinhard Genzel">Reinhard Genzel</a> (2008)</li> <li><a href="/wiki/Frank_Shu" title="Frank Shu">Frank Shu</a> (2009)</li> <li><a href="/wiki/Charles_L._Bennett" title="Charles L. Bennett">Charles Bennett</a>, <a href="/wiki/Lyman_Page" title="Lyman Page">Lyman Page</a> and <a href="/wiki/David_Spergel" title="David Spergel">David Spergel</a> (2010)</li> <li><a href="/wiki/Enrico_Costa_(physicist)" title="Enrico Costa (physicist)">Enrico Costa</a> and <a href="/wiki/Gerald_J._Fishman" title="Gerald J. Fishman">Gerald Fishman</a> (2011)</li> <li><a href="/wiki/David_C._Jewitt" title="David C. Jewitt">David C. Jewitt</a> and <a href="/wiki/Jane_Luu" title="Jane Luu">Jane Luu</a> (2012)</li> <li><a href="/wiki/Steven_Balbus" title="Steven Balbus">Steven Balbus</a> and <a href="/wiki/John_F._Hawley" title="John F. Hawley">John F. Hawley</a> (2013)</li> <li><a href="/wiki/Daniel_Eisenstein" title="Daniel Eisenstein">Daniel Eisenstein</a>, <a href="/wiki/Shaun_Cole" title="Shaun Cole">Shaun Cole</a> and <a href="/wiki/John_A._Peacock" title="John A. Peacock">John A. Peacock</a> (2014)</li> <li><a href="/wiki/William_J._Borucki" title="William J. Borucki">William J. Borucki</a> (2015)</li> <li><a href="/wiki/Ronald_Drever" title="Ronald Drever">Ronald Drever</a>, <a href="/wiki/Kip_Thorne" title="Kip Thorne">Kip Thorne</a> and <a href="/wiki/Rainer_Weiss" title="Rainer Weiss">Rainer Weiss</a> (2016)</li> <li><a href="/wiki/Simon_White" title="Simon White">Simon White</a> (2017)</li> <li><a href="/wiki/Jean-Loup_Puget" title="Jean-Loup Puget">Jean-Loup Puget</a> (2018)</li> <li><a href="/wiki/Edward_C._Stone" title="Edward C. Stone">Edward C. Stone</a> (2019)</li> <li><a href="/wiki/Roger_Blandford" title="Roger Blandford">Roger Blandford</a> (2020)</li> <li><a href="/wiki/Victoria_Kaspi" title="Victoria Kaspi">Victoria Kaspi</a> and <a href="/wiki/Chryssa_Kouveliotou" title="Chryssa Kouveliotou">Chryssa Kouveliotou</a> (2021)</li> <li><a href="/wiki/Lennart_Lindegren" title="Lennart Lindegren">Lennart Lindegren</a> and <a href="/wiki/Michael_Perryman" title="Michael Perryman">Michael Perryman</a> (2022)</li> <li><a href="/wiki/Matthew_Bailes" title="Matthew Bailes">Matthew Bailes</a>, <a href="/wiki/Duncan_Lorimer" title="Duncan Lorimer">Duncan Lorimer</a> and <a href="/wiki/Maura_McLaughlin" title="Maura McLaughlin">Maura McLaughlin</a> (2023)</li> <li><a href="/wiki/Shrinivas_R._Kulkarni" class="mw-redirect" title="Shrinivas R. Kulkarni">Shrinivas R. Kulkarni</a> (2024)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">Life science<br />and medicine</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/Stanley_Norman_Cohen" title="Stanley Norman Cohen">Stanley Norman Cohen</a>, <a href="/wiki/Herbert_Boyer" title="Herbert Boyer">Herbert Boyer</a>, <a href="/wiki/Yuet_Wai_Kan" title="Yuet Wai Kan">Yuet-Wai Kan</a> and <a href="/wiki/Richard_Doll" title="Richard Doll">Richard Doll</a> (2004)</li> <li><a href="/wiki/Michael_Berridge" title="Michael Berridge">Michael Berridge</a> (2005)</li> <li><a href="/wiki/Xiaodong_Wang_(biochemist)" title="Xiaodong Wang (biochemist)">Xiaodong Wang</a> (2006)</li> <li><a href="/wiki/Robert_Lefkowitz" title="Robert Lefkowitz">Robert Lefkowitz</a> (2007)</li> <li><a href="/wiki/Ian_Wilmut" title="Ian Wilmut">Ian Wilmut</a>, <a href="/wiki/Keith_Campbell_(biologist)" title="Keith Campbell (biologist)">Keith H. S. Campbell</a> and <a href="/wiki/Shinya_Yamanaka" title="Shinya Yamanaka">Shinya Yamanaka</a> (2008)</li> <li><a href="/wiki/Douglas_L._Coleman" title="Douglas L. Coleman">Douglas Coleman</a> and <a href="/wiki/Jeffrey_M._Friedman" title="Jeffrey M. Friedman">Jeffrey Friedman</a> (2009)</li> <li><a href="/wiki/David_Julius" title="David Julius">David Julius</a> (2010)</li> <li><a href="/wiki/Jules_A._Hoffmann" title="Jules A. Hoffmann">Jules Hoffmann</a>, <a href="/wiki/Ruslan_Medzhitov" title="Ruslan Medzhitov">Ruslan Medzhitov</a> and <a href="/wiki/Bruce_Beutler" title="Bruce Beutler">Bruce Beutler</a> (2011)</li> <li><a href="/wiki/Franz-Ulrich_Hartl" title="Franz-Ulrich Hartl">Franz-Ulrich Hartl</a> and <a href="/wiki/Arthur_L._Horwich" title="Arthur L. Horwich">Arthur L. Horwich</a> (2012)</li> <li><a href="/wiki/Jeffrey_C._Hall" title="Jeffrey C. Hall">Jeffrey C. Hall</a>, <a href="/wiki/Michael_Rosbash" title="Michael Rosbash">Michael Rosbash</a> and <a href="/wiki/Michael_W._Young" title="Michael W. Young">Michael W. Young</a> (2013)</li> <li><a href="/wiki/Kazutoshi_Mori" title="Kazutoshi Mori">Kazutoshi Mori</a> and <a href="/wiki/Peter_Walter" title="Peter Walter">Peter Walter</a> (2014)</li> <li><a href="/wiki/Bonnie_Bassler" title="Bonnie Bassler">Bonnie Bassler</a> and <a href="/wiki/Everett_Peter_Greenberg" title="Everett Peter Greenberg">Everett Peter Greenberg</a> (2015)</li> <li><a href="/wiki/Adrian_Bird" title="Adrian Bird">Adrian Bird</a> and <a href="/wiki/Huda_Zoghbi" title="Huda Zoghbi">Huda Zoghbi</a> (2016)</li> <li><a href="/wiki/Ian_R._Gibbons" title="Ian R. Gibbons">Ian R. Gibbons</a> and <a href="/wiki/Ronald_Vale" title="Ronald Vale">Ronald Vale</a> (2017)</li> <li><a href="/wiki/Mary-Claire_King" title="Mary-Claire King">Mary-Claire King</a> (2018)</li> <li><a href="/wiki/Maria_Jasin" title="Maria Jasin">Maria Jasin</a> (2019)</li> <li><a href="/wiki/Gero_Miesenb%C3%B6ck" title="Gero Miesenböck">Gero Miesenböck</a>, <a href="/wiki/Peter_Hegemann" title="Peter Hegemann">Peter Hegemann</a> and <a href="/wiki/Georg_Nagel" title="Georg Nagel">Georg Nagel</a> (2020)</li> <li><a href="/wiki/Scott_D._Emr" title="Scott D. Emr">Scott D. Emr</a> (2021)</li> <li><a href="/wiki/Paul_Negulescu" title="Paul Negulescu">Paul A. Negulescu</a> and <a href="/wiki/Michael_J._Welsh_(biologist)" title="Michael J. Welsh (biologist)">Michael J. Welsh</a> (2022)</li> <li><a href="/wiki/Patrick_Cramer" title="Patrick Cramer">Patrick Cramer</a> and <a href="/wiki/Eva_Nogales" title="Eva Nogales">Eva Nogales</a> (2023)</li> <li><a href="/wiki/Stuart_H._Orkin" class="mw-redirect" title="Stuart H. Orkin">Stuart H. Orkin</a> and <a href="/wiki/Swee_Lay_Thein" title="Swee Lay Thein">Swee Lay Thein</a> (2024)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;background:#d3d3d3;">Mathematical<br />science</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Shiing-Shen_Chern" title="Shiing-Shen Chern">Shiing-Shen Chern</a> (2004)</li> <li><a href="/wiki/Andrew_Wiles" title="Andrew Wiles">Andrew Wiles</a> (2005)</li> <li><a href="/wiki/David_Mumford" title="David Mumford">David Mumford</a> and <a href="/wiki/Wu_Wenjun" title="Wu Wenjun">Wentsun Wu</a> (2006)</li> <li><a href="/wiki/Robert_Langlands" title="Robert Langlands">Robert Langlands</a> and <a href="/wiki/Richard_Taylor_(mathematician)" title="Richard Taylor (mathematician)">Richard Taylor</a> (2007)</li> <li><a class="mw-selflink selflink">Vladimir Arnold</a> and <a href="/wiki/Ludvig_Faddeev" title="Ludvig Faddeev">Ludwig Faddeev</a> (2008)</li> <li><a href="/wiki/Simon_Donaldson" title="Simon Donaldson">Simon Donaldson</a> and <a href="/wiki/Clifford_Taubes" title="Clifford Taubes">Clifford Taubes</a> (2009)</li> <li><a href="/wiki/Jean_Bourgain" title="Jean Bourgain">Jean Bourgain</a> (2010)</li> <li><a href="/wiki/Demetrios_Christodoulou" title="Demetrios Christodoulou">Demetrios Christodoulou</a> and <a href="/wiki/Richard_S._Hamilton" title="Richard S. Hamilton">Richard S. Hamilton</a> (2011)</li> <li><a href="/wiki/Maxim_Kontsevich" title="Maxim Kontsevich">Maxim Kontsevich</a> (2012)</li> <li><a href="/wiki/David_Donoho" title="David Donoho">David Donoho</a> (2013)</li> <li><a href="/wiki/George_Lusztig" title="George Lusztig">George Lusztig</a> (2014)</li> <li><a href="/wiki/Gerd_Faltings" title="Gerd Faltings">Gerd Faltings</a> and <a href="/wiki/Henryk_Iwaniec" title="Henryk Iwaniec">Henryk Iwaniec</a> (2015)</li> <li><a href="/wiki/Nigel_Hitchin" title="Nigel Hitchin">Nigel Hitchin</a> (2016)</li> <li><a href="/wiki/J%C3%A1nos_Koll%C3%A1r" title="János Kollár">János Kollár</a> and <a href="/wiki/Claire_Voisin" title="Claire Voisin">Claire Voisin</a> (2017)</li> <li><a href="/wiki/Luis_Caffarelli" title="Luis Caffarelli">Luis Caffarelli</a> (2018)</li> <li><a href="/wiki/Michel_Talagrand" title="Michel Talagrand">Michel Talagrand</a> (2019)</li> <li><a href="/wiki/Alexander_Beilinson" title="Alexander Beilinson">Alexander Beilinson</a> and <a href="/wiki/David_Kazhdan" title="David Kazhdan">David Kazhdan</a> (2020)</li> <li><a href="/wiki/Jean-Michel_Bismut" title="Jean-Michel Bismut">Jean-Michel Bismut</a> and <a href="/wiki/Jeff_Cheeger" title="Jeff Cheeger">Jeff Cheeger</a> (2021)</li> <li><a href="/wiki/Noga_Alon" title="Noga Alon">Noga Alon</a> and <a href="/wiki/Ehud_Hrushovski" title="Ehud Hrushovski">Ehud Hrushovski</a> (2022)</li> <li><a href="/wiki/Vladimir_Drinfeld" title="Vladimir Drinfeld">Vladimir Drinfeld</a> and <a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Shing-Tung Yau</a> (2023)</li> <li><a href="/wiki/Peter_Sarnak" title="Peter Sarnak">Peter Sarnak</a> (2024)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output 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