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class="vector-toc-list"> </ul> </li> <li id="toc-Index_theory_(1963–1984)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Index_theory_(1963–1984)"> <div class="vector-toc-text"> 2.4 Index theory (1963–1984) </div> </a> <ul id="toc-Index_theory_(1963–1984)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gauge_theory_(1977–1985)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gauge_theory_(1977–1985)"> <div class="vector-toc-text"> 2.5 Gauge theory (1977–1985) </div> </a> <ul id="toc-Gauge_theory_(1977–1985)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Later_work_(1986–2019)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Later_work_(1986–2019)"> <div class="vector-toc-text"> 2.6 Later work (1986–2019) </div> </a> <ul id="toc-Later_work_(1986–2019)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> 3 Bibliography </div> </a> <button aria-controls="toc-Bibliography-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Bibliography subsection </button> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> <li id="toc-Books" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Books"> <div class="vector-toc-text"> 3.1 Books </div> </a> <ul id="toc-Books-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Selected_papers" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Selected_papers"> <div class="vector-toc-text"> 3.2 Selected papers </div> </a> <ul id="toc-Selected_papers-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Awards_and_honours" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Awards_and_honours"> <div class="vector-toc-text"> 4 Awards and honours </div> </a> <ul id="toc-Awards_and_honours-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Personal_life" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Personal_life"> <div class="vector-toc-text"> 5 Personal life </div> </a> <ul id="toc-Personal_life-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 6 See also </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"> 7 References </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle References subsection </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> 7.1 Sources </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </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"> 8 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </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">Michael Atiyah</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 47 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-47" aria-hidden="true" > 47 languages </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%85%D8%A7%D9%8A%D9%83%D9%84_%D8%B9%D8%B7%D9%8A%D8%A9" title="مايكل عطية – Arabic" lang="ar" hreflang="ar" data-title="مايكل عطية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%A7%DB%8C%DA%A9%D9%84_%D8%A2%D8%AA%DB%8C%D8%A7" title="مایکل آتیا – South Azerbaijani" lang="azb" hreflang="azb" data-title="مایکل آتیا" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A6%BE%E0%A6%87%E0%A6%95%E0%A7%87%E0%A6%B2_%E0%A6%AB%E0%A7%8D%E0%A6%B0%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%B8%E0%A6%BF%E0%A6%B8_%E0%A6%86%E0%A6%9F%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE" title="মাইকেল ফ্রান্সিস আটিয়া – Bangla" lang="bn" hreflang="bn" data-title="মাইকেল ফ্রান্সিস আটিয়া" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Minnan" lang="nan" hreflang="nan" data-title="Michael Atiyah" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D0%BA%D0%BB_%D0%90%D1%86%D1%8C%D1%8F" title="Майкл Ацья – Belarusian" lang="be" hreflang="be" data-title="Майкл Ацья" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Catalan" lang="ca" hreflang="ca" data-title="Michael Atiyah" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Czech" lang="cs" hreflang="cs" data-title="Michael Atiyah" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Danish" lang="da" hreflang="da" data-title="Michael Atiyah" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Michael_Francis_Atiyah" title="Michael Francis Atiyah – German" lang="de" hreflang="de" data-title="Michael Francis Atiyah" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%AC%CE%B9%CE%BA%CE%BB_%CE%91%CF%84%CE%AF%CE%B3%CE%B9%CE%B1" title="Μάικλ Ατίγια – Greek" lang="el" hreflang="el" data-title="Μάικλ Ατίγια" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Spanish" lang="es" hreflang="es" data-title="Michael Atiyah" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Esperanto" lang="eo" hreflang="eo" data-title="Michael Atiyah" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Basque" lang="eu" hreflang="eu" data-title="Michael Atiyah" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%A7%DB%8C%DA%A9%D9%84_%D8%B9%D8%B7%DB%8C%D9%87" title="مایکل عطیه – Persian" lang="fa" hreflang="fa" data-title="مایکل عطیه" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – French" lang="fr" hreflang="fr" data-title="Michael Atiyah" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Scottish Gaelic" lang="gd" hreflang="gd" data-title="Michael Atiyah" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target">Gàidhlig</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Galician" lang="gl" hreflang="gl" data-title="Michael Atiyah" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A7%88%EC%9D%B4%ED%81%B4_%EC%95%84%ED%8B%B0%EC%95%BC" title="마이클 아티야 – Korean" lang="ko" hreflang="ko" data-title="마이클 아티야" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%B5%D6%84%D5%AC_%D4%B1%D5%A9%D5%AB%D5%A1" title="Մայքլ Աթիա – Armenian" lang="hy" hreflang="hy" data-title="Մայքլ Աթիա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Indonesian" lang="id" hreflang="id" data-title="Michael Atiyah" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Italian" lang="it" hreflang="it" data-title="Michael Atiyah" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%99%D7%99%D7%A7%D7%9C_%D7%A2%D7%98%D7%99%D7%94" title="מייקל עטיה – Hebrew" lang="he" hreflang="he" data-title="מייקל עטיה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Haitian Creole" lang="ht" hreflang="ht" data-title="Michael Atiyah" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D0%BA%D0%BB_%D0%A4%D1%80%D1%8D%D0%BD%D1%81%D0%B8%D1%81_%D0%90%D1%82%D0%B8%D1%8F" title="Майкл Фрэнсис Атия – Kyrgyz" lang="ky" hreflang="ky" data-title="Майкл Фрэнсис Атия" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Michael_Francis_Atiyah" title="Michael Francis Atiyah – Hungarian" lang="hu" hreflang="hu" data-title="Michael Francis Atiyah" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D8%A7%D9%8A%D9%83%D9%84_%D8%B9%D8%B7%D9%8A%D9%87" title="مايكل عطيه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="مايكل عطيه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target">مصرى</a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%99%E1%80%AD%E1%80%AF%E1%80%80%E1%80%BA%E1%80%80%E1%80%9A%E1%80%BA_%E1%80%A1%E1%80%AC%E1%80%90%E1%80%AE%E1%80%B8%E1%80%9A%E1%80%AC%E1%80%B8" title="မိုက်ကယ် အာတီးယား – Burmese" lang="my" hreflang="my" data-title="မိုက်ကယ် အာတီးယား" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Dutch" lang="nl" hreflang="nl" data-title="Michael Atiyah" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9E%E3%82%A4%E3%82%B1%E3%83%AB%E3%83%BB%E3%82%A2%E3%83%86%E3%82%A3%E3%83%A4" title="マイケル・アティヤ – Japanese" lang="ja" hreflang="ja" data-title="マイケル・アティヤ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Michael_Francis_Atiyah" title="Michael Francis Atiyah – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Michael Francis Atiyah" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Michael Atiyah" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Uzbek" lang="uz" hreflang="uz" data-title="Michael Atiyah" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%85%D8%A7%D8%A6%DB%8C%DA%A9%D9%84_%D8%A2%D8%AA%DB%8C%D8%A7%DB%81" title="مائیکل آتیاہ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="مائیکل آتیاہ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Polish" lang="pl" hreflang="pl" data-title="Michael Atiyah" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Portuguese" lang="pt" hreflang="pt" data-title="Michael Atiyah" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Romanian" lang="ro" hreflang="ro" data-title="Michael Atiyah" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D1%82%D1%8C%D1%8F,_%D0%9C%D0%B0%D0%B9%D0%BA%D0%BB" title="Атья, Майкл – Russian" lang="ru" hreflang="ru" data-title="Атья, Майкл" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Simple English" lang="en-simple" hreflang="en-simple" data-title="Michael Atiyah" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Slovak" lang="sk" hreflang="sk" data-title="Michael Atiyah" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Michael_Francis_Atiyah" title="Michael Francis Atiyah – Slovenian" lang="sl" hreflang="sl" data-title="Michael Francis Atiyah" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Finnish" lang="fi" hreflang="fi" data-title="Michael Atiyah" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Michael_Francis_Atiyah" title="Michael Francis Atiyah – Swedish" lang="sv" hreflang="sv" data-title="Michael Francis Atiyah" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Turkish" lang="tr" hreflang="tr" data-title="Michael Atiyah" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%B9%D0%BA%D0%BB_%D0%90%D1%82%D1%96%D1%8F" title="Майкл Атія – Ukrainian" lang="uk" hreflang="uk" data-title="Майкл Атія" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Michael_Atiyah" title="Michael Atiyah – Vietnamese" lang="vi" hreflang="vi" data-title="Michael Atiyah" 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Please improve this article by adding <a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research">secondary or tertiary sources</a>. Find sources: <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Michael+Atiyah%22">"Michael Atiyah"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Michael+Atiyah%22+-wikipedia&tbs=ar:1">news</a> · <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Michael+Atiyah%22&tbs=bkt:s&tbm=bks">newspapers</a> · <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Michael+Atiyah%22+-wikipedia">books</a> · <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Michael+Atiyah%22">scholar</a> · <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Michael+Atiyah%22&acc=on&wc=on">JSTOR</a> (January 2022) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> <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="honorific-prefix" style="font-size: 77%; font-weight: normal;"><a href="/wiki/Professor" title="Professor">Professor</a></div><div class="fn">Sir Michael Atiyah</div><div class="honorific-suffix" style="font-size: 77%; font-weight: normal;"><a href="/wiki/Member_of_the_Order_of_Merit" class="mw-redirect" title="Member of the Order of Merit">OM</a> <a href="/wiki/Fellow_of_the_Royal_Society" title="Fellow of the Royal Society">FRS</a> <a href="/wiki/Fellow_of_the_Royal_Society_of_Edinburgh" class="mw-redirect" title="Fellow of the Royal Society of Edinburgh">FRSE</a> <a href="/wiki/Fellow_of_the_Academy_of_Medical_Sciences" title="Fellow of the Academy of Medical Sciences">FMedSci</a> <a href="/wiki/Fellow_of_the_Australian_Academy_of_Science" class="mw-redirect" title="Fellow of the Australian Academy of Science">FAA</a> <a href="/wiki/Honorary_Fellow_of_the_Royal_Academy_of_Engineering" class="mw-redirect" title="Honorary Fellow of the Royal Academy of Engineering">HonFREng</a></div></th></tr><tr><td colspan="2" class="infobox-image"><a href="/wiki/File:Michael_Francis_Atiyah.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Michael_Francis_Atiyah.jpg/220px-Michael_Francis_Atiyah.jpg" decoding="async" width="220" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/af/Michael_Francis_Atiyah.jpg 1.5x" data-file-width="312" data-file-height="300" /></a><div class="infobox-caption">Michael Atiyah in 2007</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="nickname">Michael Francis Atiyah</div> (1929-04-22)22 April 1929 <div style="display:inline" class="birthplace"><a href="/wiki/Hampstead" title="Hampstead">Hampstead</a>, London, England</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">11 January 2019(2019-01-11) (aged 89) <div style="display:inline" class="deathplace">Edinburgh, Scotland</div></td></tr><tr><th scope="row" class="infobox-label">Education</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li><a href="/wiki/Trinity_College,_Cambridge" title="Trinity College, Cambridge">Trinity College, Cambridge</a> (<a href="/wiki/Bachelor_of_Arts" title="Bachelor of Arts">BA</a>, <a href="/wiki/PhD" class="mw-redirect" title="PhD">PhD</a>)</li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Atiyah_algebroid" title="Atiyah algebroid">Atiyah algebroid</a> <a href="/wiki/Atiyah_conjecture" title="Atiyah conjecture">Atiyah conjecture</a> <a href="/wiki/Atiyah_conjecture_on_configurations" title="Atiyah conjecture on configurations">Atiyah conjecture on configurations</a> <a href="/wiki/Flip_(mathematics)#Examples" title="Flip (mathematics)">Atiyah flop</a> <a href="/wiki/Atiyah%E2%80%93Bott_formula" title="Atiyah–Bott formula">Atiyah–Bott formula</a> <a href="/wiki/Atiyah%E2%80%93Bott_fixed-point_theorem" title="Atiyah–Bott fixed-point theorem">Atiyah–Bott fixed-point theorem</a> <a href="/wiki/Floer_homology#Atiyah–Floer_conjecture" title="Floer homology">Atiyah–Floer conjecture</a> <a href="/wiki/Atiyah%E2%80%93Hirzebruch_spectral_sequence" title="Atiyah–Hirzebruch spectral sequence">Atiyah–Hirzebruch spectral sequence</a> <a href="/wiki/Atiyah%E2%80%93Jones_conjecture" title="Atiyah–Jones conjecture">Atiyah–Jones conjecture</a> <a href="/wiki/Atiyah%E2%80%93Hitchin%E2%80%93Singer_theorem" class="mw-redirect" title="Atiyah–Hitchin–Singer theorem">Atiyah–Hitchin–Singer theorem</a> <a href="/wiki/Atiyah%E2%80%93Singer_index_theorem" title="Atiyah–Singer index theorem">Atiyah–Singer index theorem</a> <a href="/wiki/Atiyah%E2%80%93Segal_completion_theorem" title="Atiyah–Segal completion theorem">Atiyah–Segal completion theorem</a> <a href="/wiki/ADHM_construction" title="ADHM construction">ADHM construction</a> <a href="/wiki/Fredholm_module" title="Fredholm module">Fredholm module</a> <a href="/wiki/Eta_invariant" title="Eta invariant">Eta invariant</a> <a href="/wiki/K-theory" title="K-theory">K-theory</a> <a href="/wiki/KR-theory" title="KR-theory">KR-theory</a> <a href="/wiki/Pin_group" title="Pin group">Pin group</a> <a href="/wiki/Toric_manifold" title="Toric manifold">Toric manifold</a></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Berwick_Prize" title="Berwick Prize">Berwick Prize</a> (1961)</li> <li><a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medal</a> (1966)</li> <li><a href="/wiki/Royal_Medal" title="Royal Medal">Royal Medal</a> (1968)</li> <li><a href="/wiki/De_Morgan_Medal" title="De Morgan Medal">De Morgan Medal</a> (1980)</li> <li><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a> (1988)</li> <li><a href="/wiki/Abel_Prize" title="Abel Prize">Abel Prize</a> (2004)</li></ul> </div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546">Scientific career</td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/University_of_Oxford" title="University of Oxford">University of Oxford</a></li> <li><a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a></li> <li><a href="/wiki/University_of_Leicester" title="University of Leicester">University of Leicester</a></li> <li><a href="/wiki/University_of_Edinburgh" title="University of Edinburgh">University of Edinburgh</a></li> <li><a href="/wiki/University_of_Cambridge" title="University of Cambridge">University of Cambridge</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><a rel="nofollow" class="external text" href="https://www.repository.cam.ac.uk/handle/1810/251002">Some Applications of Topological Methods in Algebraic Geometry</a> (1955)</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/W._V._D._Hodge" title="W. V. D. Hodge">W. V. D. Hodge</a><a href="#cite_note-aphd-1">[1]</a><a href="#cite_note-genealogy-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Simon_Donaldson" title="Simon Donaldson">Simon Donaldson</a></li> <li><a href="/wiki/K._David_Elworthy" title="K. David Elworthy">K. David Elworthy</a></li> <li><a href="/wiki/Nigel_Hitchin" title="Nigel Hitchin">Nigel Hitchin</a><a href="#cite_note-3">[3]</a></li> <li><a href="/wiki/Lisa_Jeffrey" title="Lisa Jeffrey">Lisa Jeffrey</a></li> <li><a href="/wiki/Frances_Kirwan" title="Frances Kirwan">Frances Kirwan</a></li> <li><a href="/wiki/Peter_Kronheimer" class="mw-redirect" title="Peter Kronheimer">Peter Kronheimer</a></li> <li><a href="/wiki/Ruth_Lawrence" title="Ruth Lawrence">Ruth Lawrence</a></li> <li><a href="/wiki/George_Lusztig" title="George Lusztig">George Lusztig</a></li> <li><a href="/wiki/Ian_R._Porteous" title="Ian R. Porteous">Ian R. Porteous</a></li> <li><a href="/wiki/Graeme_Segal" title="Graeme Segal">Graeme Segal</a></li> <li><a href="/wiki/David_O._Tall" class="mw-redirect" title="David O. Tall">David O. Tall</a><a href="#cite_note-genealogy-2">[2]</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Other notable students</th><td class="infobox-data"><a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> Sir Michael Francis Atiyah (<a href="/wiki/Help:IPA/English" title="Help:IPA/English">/əˈtiːə/</a>; 22 April 1929 – 11 January 2019) was a British-Lebanese <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> specialising in <a href="/wiki/Geometry" title="Geometry">geometry</a>.<a href="#cite_note-mactutor-4">[4]</a> His contributions include the <a href="/wiki/Atiyah%E2%80%93Singer_index_theorem" title="Atiyah–Singer index theorem">Atiyah–Singer index theorem</a> and co-founding <a href="/wiki/Topological_K-theory" title="Topological K-theory">topological K-theory</a>. He was awarded the <a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medal</a> in 1966 and the <a href="/wiki/Abel_Prize" title="Abel Prize">Abel Prize</a> in 2004. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_life_and_education">Early life and education</h2>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=1" title="Edit section: Early life and education">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:TrinityCollegeCamGreatCourt.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/TrinityCollegeCamGreatCourt.jpg/220px-TrinityCollegeCamGreatCourt.jpg" decoding="async" width="220" height="143" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/TrinityCollegeCamGreatCourt.jpg/330px-TrinityCollegeCamGreatCourt.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/TrinityCollegeCamGreatCourt.jpg/440px-TrinityCollegeCamGreatCourt.jpg 2x" data-file-width="1181" data-file-height="768" /></a><figcaption><a href="/wiki/Trinity_Great_Court" class="mw-redirect" title="Trinity Great Court">Great Court</a> of <a href="/wiki/Trinity_College,_Cambridge" title="Trinity College, Cambridge">Trinity College, Cambridge</a>, where Atiyah was a student and later <a href="/wiki/Master_of_Trinity_College,_Cambridge" class="mw-redirect" title="Master of Trinity College, Cambridge">Master</a></figcaption></figure> Atiyah was born on 22 April 1929 in <a href="/wiki/Hampstead" title="Hampstead">Hampstead</a>, <a href="/wiki/London" title="London">London</a>, England, the son of Jean (née Levens) and <a href="/wiki/Edward_Atiyah" title="Edward Atiyah">Edward Atiyah</a>.<a href="#cite_note-whoswho-5">[5]</a> His mother was Scottish and his father was a Lebanese <a href="/wiki/Eastern_Orthodox_Christianity_in_Lebanon" class="mw-redirect" title="Eastern Orthodox Christianity in Lebanon">Orthodox Christian</a>. He had two brothers, <a href="/wiki/Patrick_Atiyah" title="Patrick Atiyah">Patrick</a> (deceased) and Joe, and a sister, Selma (deceased).<a href="#cite_note-ja-6">[6]</a> Atiyah went to primary school at the Diocesan school in <a href="/wiki/Khartoum" title="Khartoum">Khartoum</a>, Sudan (1934–1941), and to secondary school at <a href="/wiki/Victoria_College,_Alexandria" title="Victoria College, Alexandria">Victoria College</a> in <a href="/wiki/Cairo" title="Cairo">Cairo</a> and <a href="/wiki/Alexandria" title="Alexandria">Alexandria</a> (1941–1945); the school was also attended by <a href="/wiki/European_nobility" class="mw-redirect" title="European nobility">European nobility</a> displaced by the <a href="/wiki/Second_World_War" class="mw-redirect" title="Second World War">Second World War</a> and some future leaders of Arab nations.<a href="#cite_note-7">[7]</a> He returned to England and <a href="/wiki/Manchester_Grammar_School" title="Manchester Grammar School">Manchester Grammar School</a> for his <a href="/wiki/Higher_School_Certificate_(UK)" class="mw-redirect" title="Higher School Certificate (UK)">HSC</a> studies (1945–1947) and did his <a href="/wiki/National_Service_in_the_United_Kingdom" class="mw-redirect" title="National Service in the United Kingdom">national service</a> with the <a href="/wiki/Royal_Electrical_and_Mechanical_Engineers" title="Royal Electrical and Mechanical Engineers">Royal Electrical and Mechanical Engineers</a> (1947–1949). His <a href="/wiki/Undergraduate" class="mw-redirect" title="Undergraduate">undergraduate</a> and <a href="/wiki/Postgraduate" class="mw-redirect" title="Postgraduate">postgraduate</a> studies took place at <a href="/wiki/Trinity_College,_Cambridge" title="Trinity College, Cambridge">Trinity College, Cambridge</a> (1949–1955).<a href="#cite_note-cv1-8">[8]</a> He was a <a href="/wiki/Doctoral" class="mw-redirect" title="Doctoral">doctoral</a> student of <a href="/wiki/William_V._D._Hodge" class="mw-redirect" title="William V. D. Hodge">William V. D. Hodge</a><a href="#cite_note-genealogy-2">[2]</a> and was awarded a doctorate in 1955 for a thesis entitled Some Applications of Topological Methods in Algebraic Geometry.<a href="#cite_note-aphd-1">[1]</a><a href="#cite_note-genealogy-2">[2]</a> Atiyah was a member of the <a href="/wiki/British_Humanist_Association" class="mw-redirect" title="British Humanist Association">British Humanist Association</a>.<a href="#cite_note-9">[9]</a> During his time at Cambridge, he was president of <a href="/wiki/The_Archimedeans" title="The Archimedeans">The Archimedeans</a>.<a href="#cite_note-10">[10]</a> <div class="mw-heading mw-heading2"><h2 id="Career_and_research">Career and research</h2>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=2" title="Edit section: Career and research">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Fuld_Hall,_Institute_for_Advanced_Study,_Princeton,_NJ.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Fuld_Hall%2C_Institute_for_Advanced_Study%2C_Princeton%2C_NJ.jpg/220px-Fuld_Hall%2C_Institute_for_Advanced_Study%2C_Princeton%2C_NJ.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Fuld_Hall%2C_Institute_for_Advanced_Study%2C_Princeton%2C_NJ.jpg/330px-Fuld_Hall%2C_Institute_for_Advanced_Study%2C_Princeton%2C_NJ.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Fuld_Hall%2C_Institute_for_Advanced_Study%2C_Princeton%2C_NJ.jpg/440px-Fuld_Hall%2C_Institute_for_Advanced_Study%2C_Princeton%2C_NJ.jpg 2x" data-file-width="2469" data-file-height="1646" /></a><figcaption>The <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> in Princeton, where Atiyah was professor from 1969 to 1972</figcaption></figure> Atiyah spent the academic year 1955–1956 at the <a href="/wiki/Institute_for_Advanced_Study,_Princeton" class="mw-redirect" title="Institute for Advanced Study, Princeton">Institute for Advanced Study, Princeton</a>, then returned to <a href="/wiki/Cambridge_University" class="mw-redirect" title="Cambridge University">Cambridge University</a>, where he was a research fellow and assistant <a href="/wiki/Lecturer" title="Lecturer">lecturer</a> (1957–1958), then a university <a href="/wiki/Lecturer" title="Lecturer">lecturer</a> and tutorial <a href="/wiki/Fellow" title="Fellow">fellow</a> at <a href="/wiki/Pembroke_College,_Cambridge" title="Pembroke College, Cambridge">Pembroke College, Cambridge</a> (1958–1961). In 1961, he moved to the <a href="/wiki/University_of_Oxford" title="University of Oxford">University of Oxford</a>, where he was a <a href="/wiki/Reader_(academic_rank)" title="Reader (academic rank)">reader</a> and <a href="/wiki/Professor" title="Professor">professorial</a> fellow at <a href="/wiki/St_Catherine%27s_College,_Oxford" title="St Catherine's College, Oxford">St Catherine's College</a> (1961–1963).<a href="#cite_note-cv1-8">[8]</a> He became <a href="/wiki/Savilian_Professor_of_Geometry" title="Savilian Professor of Geometry">Savilian Professor of Geometry</a> and a professorial fellow of <a href="/wiki/New_College,_Oxford" title="New College, Oxford">New College, Oxford</a>, from 1963 to 1969. He took up a three-year professorship at the Institute for Advanced Study in <a href="/wiki/Princeton,_New_Jersey" title="Princeton, New Jersey">Princeton</a> after which he returned to Oxford as a <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> Research Professor and professorial fellow of St Catherine's College. He was president of the <a href="/wiki/London_Mathematical_Society" title="London Mathematical Society">London Mathematical Society</a> from 1974 to 1976.<a href="#cite_note-cv1-8">[8]</a> <style data-mw-deduplicate="TemplateStyles:r1224211176">.mw-parser-output .quotebox{background-color:#F9F9F9;border:1px solid #aaa;box-sizing:border-box;padding:10px;font-size:88%;max-width:100%}.mw-parser-output .quotebox.floatleft{margin:.5em 1.4em .8em 0}.mw-parser-output .quotebox.floatright{margin:.5em 0 .8em 1.4em}.mw-parser-output .quotebox.centered{overflow:hidden;position:relative;margin:.5em auto .8em auto}.mw-parser-output .quotebox.floatleft span,.mw-parser-output .quotebox.floatright span{font-style:inherit}.mw-parser-output .quotebox>blockquote{margin:0;padding:0;border-left:0;font-family:inherit;font-size:inherit}.mw-parser-output .quotebox-title{text-align:center;font-size:110%;font-weight:bold}.mw-parser-output .quotebox-quote>:first-child{margin-top:0}.mw-parser-output .quotebox-quote:last-child>:last-child{margin-bottom:0}.mw-parser-output .quotebox-quote.quoted:before{font-family:"Times New Roman",serif;font-weight:bold;font-size:large;color:gray;content:" “ ";vertical-align:-45%;line-height:0}.mw-parser-output .quotebox-quote.quoted:after{font-family:"Times New Roman",serif;font-weight:bold;font-size:large;color:gray;content:" ” ";line-height:0}.mw-parser-output .quotebox .left-aligned{text-align:left}.mw-parser-output .quotebox .right-aligned{text-align:right}.mw-parser-output .quotebox .center-aligned{text-align:center}.mw-parser-output .quotebox .quote-title,.mw-parser-output .quotebox .quotebox-quote{display:block}.mw-parser-output .quotebox cite{display:block;font-style:normal}@media screen and (max-width:640px){.mw-parser-output .quotebox{width:100%!important;margin:0 0 .8em!important;float:none!important}}</style><div class="quotebox pullquote floatright" style="width:33%; ;"> <blockquote class="quotebox-quote left-aligned" style=""> I started out by changing local currency into foreign currency everywhere I travelled as a child and ended up making money. That's when my father realised that I would be a mathematician some day. </blockquote> <cite class="left-aligned" style="">Michael Atiyah<a href="#cite_note-11">[11]</a></cite> </div> Atiyah was president of the <a href="/wiki/Pugwash_Conferences_on_Science_and_World_Affairs" title="Pugwash Conferences on Science and World Affairs">Pugwash Conferences on Science and World Affairs</a> from 1997 to 2002.<a href="#cite_note-cv2-12">[12]</a> He also contributed to the foundation of the <a href="/wiki/InterAcademy_Panel_on_International_Issues" class="mw-redirect" title="InterAcademy Panel on International Issues">InterAcademy Panel on International Issues</a>, the Association of European Academies (ALLEA), and the <a href="/wiki/European_Mathematical_Society" title="European Mathematical Society">European Mathematical Society</a> (EMS).<a href="#cite_note-13">[13]</a> Within the United Kingdom, he was involved in the creation of the <a href="/wiki/Isaac_Newton_Institute_for_Mathematical_Sciences" class="mw-redirect" title="Isaac Newton Institute for Mathematical Sciences">Isaac Newton Institute for Mathematical Sciences</a> in Cambridge and was its first director (1990–1996). He was <a href="/wiki/President_of_the_Royal_Society" class="mw-redirect" title="President of the Royal Society">President of the Royal Society</a> (1990–1995), <a href="/wiki/Master_of_Trinity_College,_Cambridge" class="mw-redirect" title="Master of Trinity College, Cambridge">Master of Trinity College, Cambridge</a> (1990–1997),<a href="#cite_note-cv2-12">[12]</a> <a href="/wiki/Chancellor_(education)" title="Chancellor (education)">Chancellor</a> of the <a href="/wiki/University_of_Leicester" title="University of Leicester">University of Leicester</a> (1995–2005),<a href="#cite_note-cv2-12">[12]</a> and president of the <a href="/wiki/Royal_Society_of_Edinburgh" title="Royal Society of Edinburgh">Royal Society of Edinburgh</a> (2005–2008).<a href="#cite_note-14">[14]</a> From 1997 until his death in 2019 he was an honorary professor in the <a href="/wiki/University_of_Edinburgh" title="University of Edinburgh">University of Edinburgh</a>. He was a Trustee of the <a href="/wiki/James_Clerk_Maxwell_Foundation" title="James Clerk Maxwell Foundation">James Clerk Maxwell Foundation</a>.<a href="#cite_note-15">[15]</a> Atiyah's mathematical collaborators included <a href="/wiki/Raoul_Bott" title="Raoul Bott">Raoul Bott</a>, <a href="/wiki/Friedrich_Hirzebruch" title="Friedrich Hirzebruch">Friedrich Hirzebruch</a><a href="#cite_note-16">[16]</a> and <a href="/wiki/Isadore_Singer" title="Isadore Singer">Isadore Singer</a>, and his students included <a href="/wiki/Graeme_Segal" title="Graeme Segal">Graeme Segal</a>, <a href="/wiki/Nigel_Hitchin" title="Nigel Hitchin">Nigel Hitchin</a>, <a href="/wiki/Simon_Donaldson" title="Simon Donaldson">Simon Donaldson</a>, and <a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a>.<a href="#cite_note-Adv-17">[17]</a> Together with Hirzebruch, he laid the foundations for <a href="/wiki/Topological_K-theory" title="Topological K-theory">topological K-theory</a>, an important tool in <a href="/wiki/Algebraic_topology" title="Algebraic topology">algebraic topology</a>, which, informally speaking, describes ways in which spaces can be twisted. His best known result, the <a href="/wiki/Atiyah%E2%80%93Singer_index_theorem" title="Atiyah–Singer index theorem">Atiyah–Singer index theorem</a>, was proved with Singer in 1963 and is used in counting the number of independent solutions to <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a>. Some of his more recent work was inspired by <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>, in particular <a href="/wiki/Instanton" title="Instanton">instantons</a> and <a href="/wiki/Monopole_(mathematics)" title="Monopole (mathematics)">monopoles</a>, which are responsible for some corrections in <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>. He was awarded the <a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medal</a> in 1966 and the <a href="/wiki/Abel_Prize" title="Abel Prize">Abel Prize</a> in 2004. <div class="mw-heading mw-heading3"><h3 id="Collaborations">Collaborations</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=3" title="Edit section: Collaborations">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Mathematical_Institute,_University_of_Oxford.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Mathematical_Institute%2C_University_of_Oxford.jpg/220px-Mathematical_Institute%2C_University_of_Oxford.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Mathematical_Institute%2C_University_of_Oxford.jpg/330px-Mathematical_Institute%2C_University_of_Oxford.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Mathematical_Institute%2C_University_of_Oxford.jpg/440px-Mathematical_Institute%2C_University_of_Oxford.jpg 2x" data-file-width="2576" data-file-height="1932" /></a><figcaption>The old <a href="/wiki/The_Mathematical_Institute,_University_of_Oxford" class="mw-redirect" title="The Mathematical Institute, University of Oxford">Mathematical Institute</a> (now the Department of Statistics) in <a href="/wiki/Oxford" title="Oxford">Oxford</a>, where Atiyah supervised many of his students</figcaption></figure> Atiyah collaborated with many mathematicians. His three main collaborations were with <a href="/wiki/Raoul_Bott" title="Raoul Bott">Raoul Bott</a> on the <a href="/wiki/Atiyah%E2%80%93Bott_fixed-point_theorem" title="Atiyah–Bott fixed-point theorem">Atiyah–Bott fixed-point theorem</a> and many other topics, with <a href="/wiki/Isadore_M._Singer" class="mw-redirect" title="Isadore M. Singer">Isadore M. Singer</a> on the <a href="/wiki/Atiyah%E2%80%93Singer_index_theorem" title="Atiyah–Singer index theorem">Atiyah–Singer index theorem</a>, and with <a href="/wiki/Friedrich_Hirzebruch" title="Friedrich Hirzebruch">Friedrich Hirzebruch</a> on topological K-theory,<a href="#cite_note-18">[18]</a> all of whom he met at the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> in Princeton in 1955.<a href="#cite_note-19">[19]</a> His other collaborators included; <a href="/wiki/J._Frank_Adams" class="mw-redirect" title="J. Frank Adams">J. Frank Adams</a> (<a href="/wiki/Hopf_invariant" title="Hopf invariant">Hopf invariant</a> problem), Jürgen Berndt (projective planes), Roger Bielawski (Berry–Robbins problem), Howard Donnelly (<a href="/wiki/L-function" title="L-function">L-functions</a>), <a href="/wiki/Vladimir_Drinfeld" title="Vladimir Drinfeld">Vladimir G. Drinfeld</a> (instantons), Johan L. Dupont (singularities of <a href="/wiki/Vector_field" title="Vector field">vector fields</a>), <a href="/wiki/Lars_G%C3%A5rding" title="Lars Gårding">Lars Gårding</a> (<a href="/wiki/Hyperbolic_partial_differential_equation" title="Hyperbolic partial differential equation">hyperbolic differential equations</a>), <a href="/wiki/Nigel_Hitchin" title="Nigel Hitchin">Nigel J. Hitchin</a> (monopoles), <a href="/wiki/William_V._D._Hodge" class="mw-redirect" title="William V. D. Hodge">William V. D. Hodge</a> (Integrals of the second kind), <a href="/wiki/Michael_Hopkins_(mathematician)" class="mw-redirect" title="Michael Hopkins (mathematician)">Michael Hopkins</a> (<a href="/wiki/K-theory" title="K-theory">K-theory</a>), <a href="/wiki/Lisa_Jeffrey" title="Lisa Jeffrey">Lisa Jeffrey</a> (topological Lagrangians), John D. S. Jones (Yang–Mills theory), <a href="/wiki/Juan_Maldacena" title="Juan Maldacena">Juan Maldacena</a> (M-theory), <a href="/wiki/Yuri_I._Manin" class="mw-redirect" title="Yuri I. Manin">Yuri I. Manin</a> (instantons), <a href="/wiki/Nick_Manton" class="mw-redirect" title="Nick Manton">Nick S. Manton</a> (Skyrmions), <a href="/wiki/Vijay_Kumar_Patodi" title="Vijay Kumar Patodi">Vijay K. Patodi</a> (spectral asymmetry), A. N. Pressley (convexity), <a href="/wiki/Elmer_Rees" title="Elmer Rees">Elmer Rees</a> (vector bundles), <a href="/wiki/Wilfried_Schmid" title="Wilfried Schmid">Wilfried Schmid</a> (discrete series representations), <a href="/wiki/Graeme_Segal" title="Graeme Segal">Graeme Segal</a> (<a href="/wiki/K-theory" title="K-theory">equivariant K-theory</a>), Alexander Shapiro<a href="#cite_note-20">[20]</a> (Clifford algebras), L. Smith (homotopy groups of spheres), <a href="/wiki/Paul_Sutcliffe" title="Paul Sutcliffe">Paul Sutcliffe</a> (polyhedra), <a href="/wiki/David_O._Tall" class="mw-redirect" title="David O. Tall">David O. Tall</a> (lambda rings), <a href="/wiki/J._A._Todd" title="J. A. Todd">John A. Todd</a> (<a href="/wiki/Stiefel_manifold" title="Stiefel manifold">Stiefel manifolds</a>), <a href="/wiki/Cumrun_Vafa" title="Cumrun Vafa">Cumrun Vafa</a> (M-theory), <a href="/wiki/Richard_S._Ward" title="Richard S. Ward">Richard S. Ward</a> (instantons) and <a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a> (M-theory, topological quantum field theories).<a href="#cite_note-21">[21]</a> His later research on <a href="/wiki/Gauge_field_theories" class="mw-redirect" title="Gauge field theories">gauge field theories</a>, particularly <a href="/wiki/Yang%E2%80%93Mills" class="mw-redirect" title="Yang–Mills">Yang–Mills</a> theory, stimulated important interactions between <a href="/wiki/Geometry" title="Geometry">geometry</a> and <a href="/wiki/Theoretical_physics" title="Theoretical physics">physics</a>, most notably in the work of Edward Witten.<a href="#cite_note-22">[22]</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1224211176"><div class="quotebox pullquote floatright" style="width:33%; ;"> <blockquote class="quotebox-quote left-aligned" style=""> If you attack a mathematical problem directly, very often you come to a dead end, nothing you do seems to work and you feel that if only you could peer round the corner there might be an easy solution. There is nothing like having somebody else beside you, because he can usually peer round the corner. </blockquote> <cite class="left-aligned" style="">Michael Atiyah<a href="#cite_note-23">[23]</a></cite> </div> Atiyah's students included Peter Braam 1987, <a href="/wiki/Simon_Donaldson" title="Simon Donaldson">Simon Donaldson</a> 1983, <a href="/wiki/K._David_Elworthy" title="K. David Elworthy">K. David Elworthy</a> 1967, Howard Fegan 1977, Eric Grunwald 1977, <a href="/wiki/Nigel_Hitchin" title="Nigel Hitchin">Nigel Hitchin</a> 1972, Lisa Jeffrey 1991, <a href="/wiki/Frances_Kirwan" title="Frances Kirwan">Frances Kirwan</a> 1984, <a href="/wiki/Peter_Kronheimer" class="mw-redirect" title="Peter Kronheimer">Peter Kronheimer</a> 1986, <a href="/wiki/Ruth_Lawrence" title="Ruth Lawrence">Ruth Lawrence</a> 1989, <a href="/wiki/George_Lusztig" title="George Lusztig">George Lusztig</a> 1971, <a href="/wiki/Jack_Morava" title="Jack Morava">Jack Morava</a> 1968, Michael Murray 1983, Peter Newstead 1966, <a href="/wiki/Ian_R._Porteous" title="Ian R. Porteous">Ian R. Porteous</a> 1961, <a href="/wiki/John_Roe_(mathematician)" title="John Roe (mathematician)">John Roe</a> 1985, Brian Sanderson 1963, <a href="/wiki/Rolph_Ludwig_Edward_Schwarzenberger" title="Rolph Ludwig Edward Schwarzenberger">Rolph Schwarzenberger</a> 1960, Graeme Segal 1967, David Tall 1966, and Graham White 1982.<a href="#cite_note-genealogy-2">[2]</a> Other contemporary mathematicians who influenced Atiyah include <a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a>, <a href="/wiki/Lars_H%C3%B6rmander" title="Lars Hörmander">Lars Hörmander</a>, <a href="/wiki/Alain_Connes" title="Alain Connes">Alain Connes</a> and <a href="/wiki/Jean-Michel_Bismut" title="Jean-Michel Bismut">Jean-Michel Bismut</a>.<a href="#cite_note-24">[24]</a> Atiyah said that the mathematician he most admired was <a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Hermann Weyl</a>,<a href="#cite_note-25">[25]</a> and that his favourite mathematicians from before the 20th century were <a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Bernhard Riemann</a> and <a href="/wiki/William_Rowan_Hamilton" title="William Rowan Hamilton">William Rowan Hamilton</a>.<a href="#cite_note-26">[26]</a> The seven volumes of Atiyah's collected papers include most of his work, except for his commutative algebra textbook;<a href="#cite_note-27">[27]</a> the first five volumes are divided thematically and the sixth and seventh arranged by date. <div class="mw-heading mw-heading3"><h3 id="Algebraic_geometry_(1952–1958)">Algebraic geometry (1952–1958)</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=4" title="Edit section: Algebraic geometry (1952–1958)">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Algebraic_geometry" title="Algebraic geometry">Algebraic geometry</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Twisted_cubic_curve.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Twisted_cubic_curve.png/250px-Twisted_cubic_curve.png" decoding="async" width="250" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Twisted_cubic_curve.png/375px-Twisted_cubic_curve.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Twisted_cubic_curve.png/500px-Twisted_cubic_curve.png 2x" data-file-width="541" data-file-height="536" /></a><figcaption>A <a href="/wiki/Twisted_cubic_curve" class="mw-redirect" title="Twisted cubic curve">twisted cubic curve</a>, the subject of Atiyah's first paper</figcaption></figure> Atiyah's early papers on algebraic geometry (and some general papers) are reprinted in the first volume of his collected works.<a href="#cite_note-28">[28]</a> As an undergraduate Atiyah was interested in classical projective geometry, and wrote his first paper: a short note on <a href="/wiki/Twisted_cubics" class="mw-redirect" title="Twisted cubics">twisted cubics</a>.<a href="#cite_note-29">[29]</a> He started research under <a href="/wiki/W._V._D._Hodge" title="W. V. D. Hodge">W. V. D. Hodge</a> and won the <a href="/wiki/Smith%27s_prize" class="mw-redirect" title="Smith's prize">Smith's prize</a> for 1954 for a <a href="/wiki/Sheaf_(mathematics)" title="Sheaf (mathematics)">sheaf-theoretic</a> approach to <a href="/wiki/Ruled_surface" title="Ruled surface">ruled surfaces</a>,<a href="#cite_note-30">[30]</a> which encouraged Atiyah to continue in mathematics, rather than switch to his other interests—architecture and archaeology.<a href="#cite_note-31">[31]</a> His PhD thesis with Hodge was on a sheaf-theoretic approach to <a href="/wiki/Solomon_Lefschetz" title="Solomon Lefschetz">Solomon Lefschetz</a>'s theory of integrals of the second kind on algebraic varieties, and resulted in an invitation to visit the Institute for Advanced Study in Princeton for a year.<a href="#cite_note-32">[32]</a> While in Princeton he classified <a href="/wiki/Vector_bundle" title="Vector bundle">vector bundles</a> on an <a href="/wiki/Elliptic_curve" title="Elliptic curve">elliptic curve</a> (extending <a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Alexander Grothendieck</a>'s classification of vector bundles on a genus 0 curve), by showing that any vector bundle is a sum of (essentially unique) indecomposable vector bundles,<a href="#cite_note-33">[33]</a> and then showing that the space of indecomposable vector bundles of given degree and positive dimension can be identified with the elliptic curve.<a href="#cite_note-34">[34]</a> He also studied double points on surfaces,<a href="#cite_note-35">[35]</a> giving the first example of a <a href="/wiki/Flop_(algebraic_geometry)" class="mw-redirect" title="Flop (algebraic geometry)">flop</a>, a special birational transformation of <a href="/wiki/3-fold" title="3-fold">3-folds</a> that was later heavily used in <a href="/wiki/Shigefumi_Mori" title="Shigefumi Mori">Shigefumi Mori</a>'s work on <a href="/wiki/Minimal_model_(birational_geometry)" class="mw-redirect" title="Minimal model (birational geometry)">minimal models</a> for 3-folds.<a href="#cite_note-36">[36]</a> Atiyah's flop can also be used to show that the universal marked family of <a href="/wiki/K3_surface" title="K3 surface">K3 surfaces</a> is not <a href="/wiki/Hausdorff_space" title="Hausdorff space">Hausdorff</a>.<a href="#cite_note-37">[37]</a> <div class="mw-heading mw-heading3"><h3 id="K-theory_(1959–1974)">K-theory (1959–1974)</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=5" title="Edit section: K-theory (1959–1974)">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/K-theory" title="K-theory">K-theory</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:M%C3%B6bius_strip.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/M%C3%B6bius_strip.jpg/250px-M%C3%B6bius_strip.jpg" decoding="async" width="250" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/M%C3%B6bius_strip.jpg/375px-M%C3%B6bius_strip.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/M%C3%B6bius_strip.jpg/500px-M%C3%B6bius_strip.jpg 2x" data-file-width="1328" data-file-height="824" /></a><figcaption>A <a href="/wiki/M%C3%B6bius_band" class="mw-redirect" title="Möbius band">Möbius band</a> is the simplest non-trivial example of a <a href="/wiki/Vector_bundle" title="Vector bundle">vector bundle</a>.</figcaption></figure> Atiyah's works on <a href="/wiki/K-theory" title="K-theory">K-theory</a>, including his book on K-theory<a href="#cite_note-38">[38]</a> are reprinted in volume 2 of his collected works.<a href="#cite_note-39">[39]</a> The simplest nontrivial example of a vector bundle is the <a href="/wiki/M%C3%B6bius_band" class="mw-redirect" title="Möbius band">Möbius band</a> (pictured on the right): a strip of paper with a twist in it, which represents a rank 1 vector bundle over a circle (the circle in question being the centerline of the Möbius band). K-theory is a tool for working with higher-dimensional analogues of this example, or in other words for describing higher-dimensional twistings: elements of the K-group of a space are represented by vector bundles over it, so the Möbius band represents an element of the K-group of a circle.<a href="#cite_note-40">[40]</a> Topological K-theory was discovered by Atiyah and <a href="/wiki/Friedrich_Hirzebruch" title="Friedrich Hirzebruch">Friedrich Hirzebruch</a><a href="#cite_note-41">[41]</a> who were inspired by Grothendieck's proof of the <a href="/wiki/Grothendieck%E2%80%93Riemann%E2%80%93Roch_theorem" title="Grothendieck–Riemann–Roch theorem">Grothendieck–Riemann–Roch theorem</a> and Bott's work on the <a href="/wiki/Bott_periodicity_theorem" title="Bott periodicity theorem">periodicity theorem</a>. This paper only discussed the zeroth K-group; they shortly after extended it to K-groups of all degrees,<a href="#cite_note-paper28-42">[42]</a> giving the first (nontrivial) example of a <a href="/wiki/Generalized_cohomology_theory" class="mw-redirect" title="Generalized cohomology theory">generalized cohomology theory</a>. Several results showed that the newly introduced K-theory was in some ways more powerful than ordinary cohomology theory. Atiyah and Todd<a href="#cite_note-43">[43]</a> used K-theory to improve the lower bounds found using ordinary cohomology by Borel and Serre for the <a href="/w/index.php?title=James_number&action=edit&redlink=1" class="new" title="James number (page does not exist)">James number</a>, describing when a map from a complex <a href="/wiki/Stiefel_manifold" title="Stiefel manifold">Stiefel manifold</a> to a sphere has a cross section. (<a href="/wiki/J._Frank_Adams" class="mw-redirect" title="J. Frank Adams">Adams</a> and Grant-Walker later showed that the bound found by Atiyah and Todd was best possible.) Atiyah and Hirzebruch<a href="#cite_note-44">[44]</a> used K-theory to explain some relations between <a href="/wiki/Steenrod_operation" class="mw-redirect" title="Steenrod operation">Steenrod operations</a> and <a href="/wiki/Todd_class" title="Todd class">Todd classes</a> that Hirzebruch had noticed a few years before. The original solution of the <a href="/wiki/Hopf_invariant_one_problem" class="mw-redirect" title="Hopf invariant one problem">Hopf invariant one problem</a> operations by J. F. Adams was very long and complicated, using secondary cohomology operations. Atiyah showed how primary operations in K-theory could be used to give a short solution taking only a few lines, and in joint work with Adams<a href="#cite_note-45">[45]</a> also proved analogues of the result at odd primes. <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Atiyah-Hirzebruch.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Atiyah-Hirzebruch.jpeg/250px-Atiyah-Hirzebruch.jpeg" decoding="async" width="250" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Atiyah-Hirzebruch.jpeg/375px-Atiyah-Hirzebruch.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/0/09/Atiyah-Hirzebruch.jpeg 2x" data-file-width="400" data-file-height="282" /></a><figcaption>Michael Atiyah and <a href="/wiki/Friedrich_Hirzebruch" title="Friedrich Hirzebruch">Friedrich Hirzebruch</a> (right), the creators of K-theory</figcaption></figure> The <a href="/wiki/Atiyah%E2%80%93Hirzebruch_spectral_sequence" title="Atiyah–Hirzebruch spectral sequence">Atiyah–Hirzebruch spectral sequence</a> relates the ordinary cohomology of a space to its generalized cohomology theory.<a href="#cite_note-paper28-42">[42]</a> (Atiyah and Hirzebruch used the case of K-theory, but their method works for all cohomology theories). Atiyah showed<a href="#cite_note-46">[46]</a> that for a finite group G, the K theory of its <a href="/wiki/Classifying_space" title="Classifying space">classifying space</a>, BG, is isomorphic to the <a href="/wiki/Completion_(ring_theory)" class="mw-redirect" title="Completion (ring theory)">completion</a> of its <a href="/wiki/Representation_ring" title="Representation ring">character ring</a>: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K(BG)\cong R(G)^{\wedge }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>G</mi> <mo stretchy="false">)</mo> <mo>≅</mo> <mi>R</mi> <mo stretchy="false">(</mo> <mi>G</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∧</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K(BG)\cong R(G)^{\wedge }.}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd5822d7ae533e55a63dccfffea81556d247db62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.94ex; height:3.009ex;" alt="{\displaystyle K(BG)\cong R(G)^{\wedge }.}"></dd></dl> The same year<a href="#cite_note-47">[47]</a> they proved the result for G any <a href="/wiki/Compact_group" title="Compact group">compact</a> <a href="/wiki/Connected_space" title="Connected space">connected</a> <a href="/wiki/Lie_group" title="Lie group">Lie group</a>. Although soon the result could be extended to all compact Lie groups by incorporating results from <a href="/wiki/Graeme_Segal" title="Graeme Segal">Graeme Segal</a>'s thesis,<a href="#cite_note-48">[48]</a> that extension was complicated. However a simpler and more general proof was produced by introducing <a href="/wiki/Equivariant_algebraic_K-theory" title="Equivariant algebraic K-theory">equivariant K-theory</a>, i.e. equivalence classes of G-vector bundles over a compact G-space X.<a href="#cite_note-49">[49]</a> It was shown that under suitable conditions the completion of the equivariant K theory of X is <a href="/wiki/Isomorphic" class="mw-redirect" title="Isomorphic">isomorphic</a> to the ordinary K-theory of a space, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{G}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{G}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd1836284184ae41b282ff4a856a2d7e2fb4fce1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.448ex; height:2.509ex;" alt="{\displaystyle X_{G}}">, which fibred over BG with fibre X: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{G}(X)^{\wedge }\cong K(X_{G}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>X</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∧</mo> </mrow> </msup> <mo>≅</mo> <mi>K</mi> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{G}(X)^{\wedge }\cong K(X_{G}).}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd9e9f808e88204fa1ff5974b97d0d8dda465f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.684ex; height:3.009ex;" alt="{\displaystyle K_{G}(X)^{\wedge }\cong K(X_{G}).}"></dd></dl> The original result then followed as a corollary by taking X to be a point: the left hand side reduced to the completion of R(G) and the right to K(BG). See <a href="/wiki/Atiyah%E2%80%93Segal_completion_theorem" title="Atiyah–Segal completion theorem">Atiyah–Segal completion theorem</a> for more details. He defined new generalized homology and cohomology theories called bordism and <a href="/wiki/Cobordism" title="Cobordism">cobordism</a>, and pointed out that many of the deep results on cobordism of manifolds found by <a href="/wiki/Ren%C3%A9_Thom" title="René Thom">René Thom</a>, <a href="/wiki/C._T._C._Wall" title="C. T. C. Wall">C. T. C. Wall</a>, and others could be naturally reinterpreted as statements about these cohomology theories.<a href="#cite_note-50">[50]</a> Some of these cohomology theories, in particular complex cobordism, turned out to be some of the most powerful cohomology theories known. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1224211176"><div class="quotebox pullquote floatright" style="width:33%; ;"> <blockquote class="quotebox-quote left-aligned" style=""> "Algebra is the offer made by the devil to the mathematician. The devil says: `I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine." </blockquote> <cite class="left-aligned" style="">Michael Atiyah<a href="#cite_note-51">[51]</a></cite> </div> He introduced<a href="#cite_note-paper37-52">[52]</a> the <a href="/wiki/J-group" class="mw-redirect" title="J-group">J-group</a> J(X) of a finite complex X, defined as the group of stable fiber homotopy equivalence classes of <a href="/wiki/Sphere_bundle" title="Sphere bundle">sphere bundles</a>; this was later studied in detail by <a href="/wiki/J._F._Adams" class="mw-redirect" title="J. F. Adams">J. F. Adams</a> in a series of papers, leading to the <a href="/wiki/Adams_conjecture" class="mw-redirect" title="Adams conjecture">Adams conjecture</a>. With Hirzebruch he extended the <a href="/wiki/Grothendieck%E2%80%93Riemann%E2%80%93Roch_theorem" title="Grothendieck–Riemann–Roch theorem">Grothendieck–Riemann–Roch theorem</a> to complex analytic embeddings,<a href="#cite_note-paper37-52">[52]</a> and in a related paper<a href="#cite_note-53">[53]</a> they showed that the <a href="/wiki/Hodge_conjecture" title="Hodge conjecture">Hodge conjecture</a> for integral cohomology is false. The Hodge conjecture for rational cohomology is, as of 2008, a major unsolved problem.<a href="#cite_note-54">[54]</a> The <a href="/wiki/Bott_periodicity_theorem" title="Bott periodicity theorem">Bott periodicity theorem</a> was a central theme in Atiyah's work on K-theory, and he repeatedly returned to it, reworking the proof several times to understand it better. With Bott he worked out an elementary proof,<a href="#cite_note-55">[55]</a> and gave another version of it in his book.<a href="#cite_note-56">[56]</a> With Bott and <a href="/wiki/Alexander_Shapiro" title="Alexander Shapiro">Shapiro</a> he analysed the relation of Bott periodicity to the periodicity of <a href="/wiki/Clifford_algebras" class="mw-redirect" title="Clifford algebras">Clifford algebras</a>;<a href="#cite_note-57">[57]</a> although this paper did not have a proof of the periodicity theorem, a proof along similar lines was shortly afterwards found by R. Wood. He found a proof of several generalizations using <a href="/wiki/Elliptic_operator" title="Elliptic operator">elliptic operators</a>;<a href="#cite_note-58">[58]</a> this new proof used an idea that he used to give a particularly short and easy proof of Bott's original periodicity theorem.<a href="#cite_note-59">[59]</a> <div class="mw-heading mw-heading3"><h3 id="Index_theory_(1963–1984)">Index theory (1963–1984)</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=6" title="Edit section: Index theory (1963–1984)">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Isadore_Singer_1977.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Isadore_Singer_1977.jpeg/220px-Isadore_Singer_1977.jpeg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Isadore_Singer_1977.jpeg/330px-Isadore_Singer_1977.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/f/f2/Isadore_Singer_1977.jpeg 2x" data-file-width="400" data-file-height="267" /></a><figcaption><a href="/wiki/Isadore_Singer" title="Isadore Singer">Isadore Singer</a> (in 1977), who worked with Atiyah on index theory</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Atiyah%E2%80%93Singer_index_theorem" title="Atiyah–Singer index theorem">Atiyah–Singer index theorem</a></div> Atiyah's work on index theory is reprinted in volumes 3 and 4 of his collected works.<a href="#cite_note-60">[60]</a><a href="#cite_note-61">[61]</a> The index of a differential operator is closely related to the number of independent solutions (more precisely, it is the differences of the numbers of independent solutions of the differential operator and its adjoint). There are many hard and fundamental problems in mathematics that can easily be reduced to the problem of finding the number of independent solutions of some differential operator, so if one has some means of finding the index of a differential operator these problems can often be solved. This is what the Atiyah–Singer index theorem does: it gives a formula for the index of certain differential operators, in terms of topological invariants that look quite complicated but are in practice usually straightforward to calculate.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] Several deep theorems, such as the <a href="/wiki/Hirzebruch%E2%80%93Riemann%E2%80%93Roch_theorem" title="Hirzebruch–Riemann–Roch theorem">Hirzebruch–Riemann–Roch theorem</a>, are special cases of the Atiyah–Singer index theorem. In fact the index theorem gave a more powerful result, because its proof applied to all compact complex manifolds, while Hirzebruch's proof only worked for projective manifolds. There were also many new applications: a typical one is calculating the dimensions of the moduli spaces of instantons. The index theorem can also be run "in reverse": the index is obviously an integer, so the formula for it must also give an integer, which sometimes gives subtle integrality conditions on invariants of manifolds. A typical example of this is <a href="/wiki/Rochlin%27s_theorem" class="mw-redirect" title="Rochlin's theorem">Rochlin's theorem</a>, which follows from the index theorem.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1224211176"><div class="quotebox pullquote floatright" style="width:33%; ;"> <blockquote class="quotebox-quote left-aligned" style=""> The most useful piece of advice I would give to a mathematics student is always to suspect an impressive sounding Theorem if it does not have a special case which is both simple and non-trivial. </blockquote> <cite class="left-aligned" style="">Michael Atiyah<a href="#cite_note-62">[62]</a></cite> </div> The index problem for <a href="/wiki/Elliptic_differential_operator" class="mw-redirect" title="Elliptic differential operator">elliptic differential operators</a> was posed in 1959 by <a href="/wiki/Israil_Gelfand" class="mw-redirect" title="Israil Gelfand">Gel'fand</a>.<a href="#cite_note-63">[63]</a> He noticed the homotopy invariance of the index, and asked for a formula for it by means of <a href="/wiki/Topological_invariant" class="mw-redirect" title="Topological invariant">topological invariants</a>. Some of the motivating examples included the <a href="/wiki/Riemann%E2%80%93Roch_theorem" title="Riemann–Roch theorem">Riemann–Roch theorem</a> and its generalization the <a href="/wiki/Hirzebruch%E2%80%93Riemann%E2%80%93Roch_theorem" title="Hirzebruch–Riemann–Roch theorem">Hirzebruch–Riemann–Roch theorem</a>, and the <a href="/wiki/Hirzebruch_signature_theorem" title="Hirzebruch signature theorem">Hirzebruch signature theorem</a>. <a href="/wiki/Friedrich_Hirzebruch" title="Friedrich Hirzebruch">Hirzebruch</a> and <a href="/wiki/Armand_Borel" title="Armand Borel">Borel</a> had proved the integrality of the <a href="/wiki/%C3%82_genus" class="mw-redirect" title="Â genus">Â genus</a> of a spin manifold, and Atiyah suggested that this integrality could be explained if it were the index of the <a href="/wiki/Dirac_operator" title="Dirac operator">Dirac operator</a> (which was rediscovered by Atiyah and Singer in 1961). The first announcement of the Atiyah–Singer theorem was their 1963 paper.<a href="#cite_note-64">[64]</a> The proof sketched in this announcement was inspired by Hirzebruch's proof of the <a href="/wiki/Hirzebruch%E2%80%93Riemann%E2%80%93Roch_theorem" title="Hirzebruch–Riemann–Roch theorem">Hirzebruch–Riemann–Roch theorem</a> and was never published by them, though it is described in the book by Palais.<a href="#cite_note-65">[65]</a> Their first published proof<a href="#cite_note-66">[66]</a> was more similar to Grothendieck's proof of the <a href="/wiki/Grothendieck%E2%80%93Riemann%E2%80%93Roch_theorem" title="Grothendieck–Riemann–Roch theorem">Grothendieck–Riemann–Roch theorem</a>, replacing the <a href="/wiki/Cobordism" title="Cobordism">cobordism</a> theory of the first proof with <a href="/wiki/K-theory" title="K-theory">K-theory</a>, and they used this approach to give proofs of various generalizations in a sequence of papers from 1968 to 1971. Instead of just one elliptic operator, one can consider a family of elliptic operators parameterized by some space Y. In this case the index is an element of the K theory of Y, rather than an integer.<a href="#cite_note-67">[67]</a> If the operators in the family are real, then the index lies in the real K theory of Y. This gives a little extra information, as the map from the real K theory of Y to the <a href="/wiki/Complex_K-theory" class="mw-redirect" title="Complex K-theory">complex K-theory</a> is not always injective.<a href="#cite_note-68">[68]</a> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Graeme_Segal.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Graeme_Segal.jpeg/220px-Graeme_Segal.jpeg" decoding="async" width="220" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Graeme_Segal.jpeg/330px-Graeme_Segal.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/1/1f/Graeme_Segal.jpeg 2x" data-file-width="400" data-file-height="280" /></a><figcaption>Atiyah's former student <a href="/wiki/Graeme_Segal" title="Graeme Segal">Graeme Segal</a> (in 1982), who worked with Atiyah on <a href="/wiki/K-theory" title="K-theory">equivariant K-theory</a></figcaption></figure> With Bott, Atiyah found an analogue of the <a href="/wiki/Lefschetz_fixed-point_formula" class="mw-redirect" title="Lefschetz fixed-point formula">Lefschetz fixed-point formula</a> for elliptic operators, giving the Lefschetz number of an endomorphism of an <a href="/wiki/Elliptic_complex" title="Elliptic complex">elliptic complex</a> in terms of a sum over the fixed points of the endomorphism.<a href="#cite_note-69">[69]</a> As special cases their formula included the <a href="/wiki/Weyl_character_formula" title="Weyl character formula">Weyl character formula</a>, and several new results about elliptic curves with complex multiplication, some of which were initially disbelieved by experts.<a href="#cite_note-70">[70]</a> Atiyah and Segal combined this fixed point theorem with the index theorem as follows. If there is a compact <a href="/wiki/Group_action_(mathematics)" class="mw-redirect" title="Group action (mathematics)">group action</a> of a group G on the compact manifold X, commuting with the elliptic operator, then one can replace ordinary K-theory in the index theorem with <a href="/wiki/Equivariant_algebraic_K-theory" title="Equivariant algebraic K-theory">equivariant K-theory</a>. For trivial groups G this gives the index theorem, and for a finite group G acting with isolated fixed points it gives the Atiyah–Bott fixed point theorem. In general it gives the index as a sum over fixed point submanifolds of the group G.<a href="#cite_note-71">[71]</a> Atiyah<a href="#cite_note-72">[72]</a> solved a problem asked independently by <a href="/wiki/Lars_H%C3%B6rmander" title="Lars Hörmander">Hörmander</a> and Gel'fand, about whether complex powers of analytic functions define <a href="/wiki/Distribution_(mathematics)" title="Distribution (mathematics)">distributions</a>. Atiyah used <a href="/wiki/Heisuke_Hironaka" title="Heisuke Hironaka">Hironaka</a>'s resolution of singularities to answer this affirmatively. An ingenious and elementary solution was found at about the same time by <a href="/wiki/J._Bernstein" class="mw-redirect" title="J. Bernstein">J. Bernstein</a>, and discussed by Atiyah.<a href="#cite_note-73">[73]</a> As an application of the equivariant index theorem, Atiyah and Hirzebruch showed that manifolds with effective circle actions have vanishing <a href="/wiki/%C3%82-genus" class="mw-redirect" title="Â-genus">Â-genus</a>.<a href="#cite_note-74">[74]</a> (Lichnerowicz showed that if a manifold has a metric of positive scalar curvature then the Â-genus vanishes.) With <a href="/wiki/Elmer_Rees" title="Elmer Rees">Elmer Rees</a>, Atiyah studied the problem of the relation between topological and holomorphic vector bundles on projective space. They solved the simplest unknown case, by showing that all rank 2 vector bundles over projective 3-space have a holomorphic structure.<a href="#cite_note-75">[75]</a> <a href="/wiki/Geoffrey_Horrocks_(mathematician)" title="Geoffrey Horrocks (mathematician)">Horrocks</a> had previously found some non-trivial examples of such vector bundles, which were later used by Atiyah in his study of instantons on the 4-sphere. <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Raoul_Bott_1986.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Raoul_Bott_1986.jpeg/220px-Raoul_Bott_1986.jpeg" decoding="async" width="220" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Raoul_Bott_1986.jpeg/330px-Raoul_Bott_1986.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c8/Raoul_Bott_1986.jpeg 2x" data-file-width="400" data-file-height="271" /></a><figcaption><a href="/wiki/Raoul_Bott" title="Raoul Bott">Raoul Bott</a>, who worked with Atiyah on fixed point formulas and several other topics</figcaption></figure> Atiyah, Bott and <a href="/wiki/Vijay_Kumar_Patodi" title="Vijay Kumar Patodi">Vijay K. Patodi</a><a href="#cite_note-76">[76]</a> gave a new proof of the index theorem using the <a href="/wiki/Heat_equation" title="Heat equation">heat equation</a>. If the <a href="/wiki/Manifold" title="Manifold">manifold</a> is allowed to have boundary, then some restrictions must be put on the domain of the elliptic operator in order to ensure a finite index. These conditions can be local (like demanding that the sections in the domain vanish at the boundary) or more complicated global conditions (like requiring that the sections in the domain solve some differential equation). The local case was worked out by Atiyah and Bott, but they showed that many interesting operators (e.g., the <a href="/wiki/Signature_operator" title="Signature operator">signature operator</a>) do not admit local boundary conditions. To handle these operators, Atiyah, Patodi and Singer introduced global boundary conditions equivalent to attaching a cylinder to the manifold along the boundary and then restricting the domain to those sections that are square integrable along the cylinder, and also introduced the <a href="/wiki/Atiyah%E2%80%93Patodi%E2%80%93Singer_eta_invariant" class="mw-redirect" title="Atiyah–Patodi–Singer eta invariant">Atiyah–Patodi–Singer eta invariant</a>. This resulted in a series of papers on spectral asymmetry,<a href="#cite_note-77">[77]</a> which were later unexpectedly used in <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>, in particular in Witten's work on anomalies. <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Schlierenfoto_Mach_1-2_Pfeilfl%C3%BCgel_-_NASA.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Schlierenfoto_Mach_1-2_Pfeilfl%C3%BCgel_-_NASA.jpg/220px-Schlierenfoto_Mach_1-2_Pfeilfl%C3%BCgel_-_NASA.jpg" decoding="async" width="220" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Schlierenfoto_Mach_1-2_Pfeilfl%C3%BCgel_-_NASA.jpg/330px-Schlierenfoto_Mach_1-2_Pfeilfl%C3%BCgel_-_NASA.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/7/7b/Schlierenfoto_Mach_1-2_Pfeilfl%C3%BCgel_-_NASA.jpg 2x" data-file-width="390" data-file-height="398" /></a><figcaption>The lacunas discussed by Petrovsky, Atiyah, Bott and Gårding are similar to the spaces between shockwaves of a supersonic object.</figcaption></figure> The fundamental solutions of linear <a href="/wiki/Hyperbolic_partial_differential_equation" title="Hyperbolic partial differential equation">hyperbolic partial differential equations</a> often have <a href="/wiki/Petrovsky_lacuna" title="Petrovsky lacuna">Petrovsky lacunas</a>: regions where they vanish identically. These were studied in 1945 by <a href="/wiki/I._G._Petrovsky" class="mw-redirect" title="I. G. Petrovsky">I. G. Petrovsky</a>, who found topological conditions describing which regions were lacunas. In collaboration with Bott and <a href="/wiki/Lars_G%C3%A5rding" title="Lars Gårding">Lars Gårding</a>, Atiyah wrote three papers updating and generalizing Petrovsky's work.<a href="#cite_note-78">[78]</a> Atiyah<a href="#cite_note-79">[79]</a> showed how to extend the index theorem to some non-compact manifolds, acted on by a discrete group with compact quotient. The kernel of the elliptic operator is in general infinite-dimensional in this case, but it is possible to get a finite index using the dimension of a module over a <a href="/wiki/Von_Neumann_algebra" title="Von Neumann algebra">von Neumann algebra</a>; this index is in general real rather than integer valued. This version is called the L2 index theorem, and was used by Atiyah and Schmid<a href="#cite_note-80">[80]</a> to give a geometric construction, using square integrable harmonic spinors, of Harish-Chandra's <a href="/wiki/Discrete_series_representation" title="Discrete series representation">discrete series representations</a> of <a href="/wiki/Semisimple_Lie_group" class="mw-redirect" title="Semisimple Lie group">semisimple Lie groups</a>. In the course of this work they found a more elementary proof of Harish-Chandra's fundamental theorem on the local integrability of characters of Lie groups.<a href="#cite_note-81">[81]</a> With H. Donnelly and I. Singer, he extended Hirzebruch's formula (relating the signature defect at cusps of Hilbert modular surfaces to values of L-functions) from real quadratic fields to all totally real fields.<a href="#cite_note-82">[82]</a> <div class="mw-heading mw-heading3"><h3 id="Gauge_theory_(1977–1985)">Gauge theory (1977–1985)</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=7" title="Edit section: Gauge theory (1977–1985)">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Gauge_theory_(mathematics)" title="Gauge theory (mathematics)">Gauge theory (mathematics)</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Camposcargas.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Camposcargas.svg/220px-Camposcargas.svg.png" decoding="async" width="220" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Camposcargas.svg/330px-Camposcargas.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Camposcargas.svg/440px-Camposcargas.svg.png 2x" data-file-width="512" data-file-height="224" /></a><figcaption>On the left, two nearby monopoles of the same polarity repel each other, and on the right two nearby monopoles of opposite polarity form a <a href="/wiki/Dipole" title="Dipole">dipole</a>. These are abelian monopoles; the non-abelian ones studied by Atiyah are more complicated.</figcaption></figure> Many of his papers on gauge theory and related topics are reprinted in volume 5 of his collected works.<a href="#cite_note-FOOTNOTEAtiyah1988e-83">[83]</a> A common theme of these papers is the study of moduli spaces of solutions to certain <a href="/wiki/Non-linear_partial_differential_equation" class="mw-redirect" title="Non-linear partial differential equation">non-linear partial differential equations</a>, in particular the equations for instantons and monopoles. This often involves finding a subtle correspondence between solutions of two seemingly quite different equations. An early example of this which Atiyah used repeatedly is the <a href="/wiki/Penrose_transform" title="Penrose transform">Penrose transform</a>, which can sometimes convert solutions of a non-linear equation over some real manifold into solutions of some linear holomorphic equations over a different complex manifold. In a series of papers with several authors, Atiyah classified all instantons on 4-dimensional Euclidean space. It is more convenient to classify instantons on a sphere as this is compact, and this is essentially equivalent to classifying instantons on Euclidean space as this is conformally equivalent to a sphere and the equations for instantons are conformally invariant. With Hitchin and Singer<a href="#cite_note-84">[84]</a> he calculated the dimension of the moduli space of irreducible self-dual connections (instantons) for any principal bundle over a compact 4-dimensional Riemannian manifold (the <a href="/wiki/Atiyah%E2%80%93Hitchin%E2%80%93Singer_theorem" class="mw-redirect" title="Atiyah–Hitchin–Singer theorem">Atiyah–Hitchin–Singer theorem</a>). For example, the dimension of the space of SU2 instantons of rank k>0 is 8k−3. To do this they used the Atiyah–Singer index theorem to calculate the dimension of the tangent space of the moduli space at a point; the tangent space is essentially the space of solutions of an elliptic differential operator, given by the linearization of the non-linear Yang–Mills equations. These moduli spaces were later used by Donaldson to construct his <a href="/wiki/Donaldson_invariant" class="mw-redirect" title="Donaldson invariant">invariants of 4-manifolds</a>. Atiyah and Ward used the Penrose correspondence to reduce the classification of all instantons on the 4-sphere to a problem in algebraic geometry.<a href="#cite_note-85">[85]</a> With Hitchin he used ideas of Horrocks to solve this problem, giving the <a href="/wiki/ADHM_construction" title="ADHM construction">ADHM construction</a> of all instantons on a sphere; Manin and Drinfeld found the same construction at the same time, leading to a joint paper by all four authors.<a href="#cite_note-86">[86]</a> Atiyah reformulated this construction using <a href="/wiki/Quaternion" title="Quaternion">quaternions</a> and wrote up a leisurely account of this classification of instantons on Euclidean space as a book.<a href="#cite_note-87">[87]</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1224211176"><div class="quotebox pullquote floatright" style="width:33%; ;"> <blockquote class="quotebox-quote left-aligned" style=""> The mathematical problems that have been solved or techniques that have arisen out of physics in the past have been the lifeblood of mathematics. </blockquote> <cite class="left-aligned" style="">Michael Atiyah<a href="#cite_note-88">[88]</a></cite> </div> Atiyah's work on instanton moduli spaces was used in Donaldson's work on <a href="/wiki/Donaldson_theory" title="Donaldson theory">Donaldson theory</a>. Donaldson showed that the moduli space of (degree 1) instantons over a compact simply connected <a href="/wiki/4-manifold" title="4-manifold">4-manifold</a> with positive definite intersection form can be compactified to give a cobordism between the manifold and a sum of copies of complex projective space. He deduced from this that the intersection form must be a sum of one-dimensional ones, which led to several spectacular applications to smooth 4-manifolds, such as the existence of non-equivalent <a href="/wiki/Smooth_structure" title="Smooth structure">smooth structures</a> on 4-dimensional Euclidean space. Donaldson went on to use the other moduli spaces studied by Atiyah to define <a href="/wiki/Donaldson_invariant" class="mw-redirect" title="Donaldson invariant">Donaldson invariants</a>, which revolutionized the study of smooth 4-manifolds, and showed that they were more subtle than smooth manifolds in any other dimension, and also quite different from topological 4-manifolds. Atiyah described some of these results in a survey talk.<a href="#cite_note-89">[89]</a> <a href="/wiki/Green%27s_function" title="Green's function">Green's functions</a> for linear partial differential equations can often be found by using the <a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transform</a> to convert this into an algebraic problem. Atiyah used a non-linear version of this idea.<a href="#cite_note-90">[90]</a> He used the Penrose transform to convert the Green's function for the conformally invariant Laplacian into a complex analytic object, which turned out to be essentially the diagonal embedding of the Penrose twistor space into its square. This allowed him to find an explicit formula for the conformally invariant Green's function on a 4-manifold. In his paper with Jones,<a href="#cite_note-91">[91]</a> he studied the topology of the moduli space of SU(2) instantons over a 4-sphere. They showed that the natural map from this moduli space to the space of all connections induces epimorphisms of <a href="/wiki/Homology_group" class="mw-redirect" title="Homology group">homology groups</a> in a certain range of dimensions, and suggested that it might induce isomorphisms of homology groups in the same range of dimensions. This became known as the <a href="/wiki/Atiyah%E2%80%93Jones_conjecture" title="Atiyah–Jones conjecture">Atiyah–Jones conjecture</a>, and was later proved by several mathematicians.<a href="#cite_note-92">[92]</a> Harder and <a href="/wiki/M._S._Narasimhan" title="M. S. Narasimhan">M. S. Narasimhan</a> described the cohomology of the <a href="/wiki/Moduli_space" title="Moduli space">moduli spaces</a> of <a href="/wiki/Stable_vector_bundle" title="Stable vector bundle">stable vector bundles</a> over <a href="/wiki/Riemann_surface" title="Riemann surface">Riemann surfaces</a> by counting the number of points of the moduli spaces over finite fields, and then using the Weil conjectures to recover the cohomology over the complex numbers.<a href="#cite_note-93">[93]</a> Atiyah and <a href="/wiki/R._Bott" class="mw-redirect" title="R. Bott">R. Bott</a> used <a href="/wiki/Morse_theory" title="Morse theory">Morse theory</a> and the <a href="/wiki/Yang%E2%80%93Mills_equation" class="mw-redirect" title="Yang–Mills equation">Yang–Mills equations</a> over a <a href="/wiki/Riemann_surface" title="Riemann surface">Riemann surface</a> to reproduce and extending the results of Harder and Narasimhan.<a href="#cite_note-94">[94]</a> An old result due to <a href="/wiki/Issai_Schur" title="Issai Schur">Schur</a> and Horn states that the set of possible diagonal vectors of an Hermitian matrix with given eigenvalues is the convex hull of all the permutations of the eigenvalues. Atiyah proved a generalization of this that applies to all compact <a href="/wiki/Symplectic_manifold" title="Symplectic manifold">symplectic manifolds</a> acted on by a torus, showing that the image of the manifold under the moment map is a convex polyhedron,<a href="#cite_note-95">[95]</a> and with Pressley gave a related generalization to infinite-dimensional loop groups.<a href="#cite_note-96">[96]</a> Duistermaat and Heckman found a striking formula, saying that the push-forward of the <a href="/wiki/Liouville_measure" class="mw-redirect" title="Liouville measure">Liouville measure</a> of a <a href="/wiki/Moment_map" class="mw-redirect" title="Moment map">moment map</a> for a torus action is given exactly by the stationary phase approximation (which is in general just an asymptotic expansion rather than exact). Atiyah and Bott<a href="#cite_note-97">[97]</a> showed that this could be deduced from a more general formula in <a href="/wiki/Equivariant_cohomology" title="Equivariant cohomology">equivariant cohomology</a>, which was a consequence of well-known <a href="/wiki/Localization_formula_for_equivariant_cohomology" title="Localization formula for equivariant cohomology">localization theorems</a>. Atiyah showed<a href="#cite_note-98">[98]</a> that the moment map was closely related to <a href="/wiki/Geometric_invariant_theory" title="Geometric invariant theory">geometric invariant theory</a>, and this idea was later developed much further by his student <a href="/wiki/F._Kirwan" class="mw-redirect" title="F. Kirwan">F. Kirwan</a>. Witten shortly after applied the <a href="/wiki/Duistermaat%E2%80%93Heckman_formula" title="Duistermaat–Heckman formula">Duistermaat–Heckman formula</a> to loop spaces and showed that this formally gave the Atiyah–Singer index theorem for the Dirac operator; this idea was lectured on by Atiyah.<a href="#cite_note-99">[99]</a> With Hitchin he worked on <a href="/wiki/Magnetic_monopole" title="Magnetic monopole">magnetic monopoles</a>, and studied their scattering using an idea of <a href="/wiki/Nick_Manton" class="mw-redirect" title="Nick Manton">Nick Manton</a>.<a href="#cite_note-100">[100]</a> His book<a href="#cite_note-101">[101]</a> with Hitchin gives a detailed description of their work on <a href="/wiki/Magnetic_monopoles" class="mw-redirect" title="Magnetic monopoles">magnetic monopoles</a>. The main theme of the book is a study of a moduli space of <a href="/wiki/Magnetic_monopoles" class="mw-redirect" title="Magnetic monopoles">magnetic monopoles</a>; this has a natural Riemannian metric, and a key point is that this metric is complete and <a href="/wiki/Hyperk%C3%A4hler" class="mw-redirect" title="Hyperkähler">hyperkähler</a>. The metric is then used to study the scattering of two monopoles, using a suggestion of N. Manton that the geodesic flow on the moduli space is the low energy approximation to the scattering. For example, they show that a head-on collision between two monopoles results in 90-degree scattering, with the direction of scattering depending on the relative phases of the two monopoles. He also studied monopoles on hyperbolic space.<a href="#cite_note-102">[102]</a> Atiyah showed<a href="#cite_note-103">[103]</a> that instantons in 4 dimensions can be identified with instantons in 2 dimensions, which are much easier to handle. There is of course a catch: in going from 4 to 2 dimensions the structure group of the gauge theory changes from a finite-dimensional group to an infinite-dimensional loop group. This gives another example where the moduli spaces of solutions of two apparently unrelated nonlinear partial differential equations turn out to be essentially the same. Atiyah and Singer found that anomalies in quantum field theory could be interpreted in terms of index theory of the Dirac operator;<a href="#cite_note-104">[104]</a> this idea later became widely used by physicists. <div class="mw-heading mw-heading3"><h3 id="Later_work_(1986–2019)">Later work (1986–2019)</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=8" title="Edit section: Later work (1986–2019)">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Edward_Witten_at_Harvard.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/dd/Edward_Witten_at_Harvard.jpg" decoding="async" width="189" height="229" class="mw-file-element" data-file-width="189" data-file-height="229" /></a><figcaption><a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a>, whose work on invariants of manifolds and <a href="/wiki/Topological_quantum_field_theories" class="mw-redirect" title="Topological quantum field theories">topological quantum field theories</a> was influenced by Atiyah</figcaption></figure> Many of the papers in the 6th volume<a href="#cite_note-105">[105]</a> of his collected works are surveys, obituaries, and general talks. Atiyah continued to publish subsequently, including several surveys, a popular book,<a href="#cite_note-106">[106]</a> and another paper with <a href="/wiki/Graeme_Segal" title="Graeme Segal">Segal</a> on <a href="/wiki/Twisted_K-theory" title="Twisted K-theory">twisted K-theory</a>. One paper<a href="#cite_note-107">[107]</a> is a detailed study of the <a href="/wiki/Dedekind_eta_function" title="Dedekind eta function">Dedekind eta function</a> from the point of view of topology and the index theorem. Several of his papers from around this time study the connections between <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, <a href="/wiki/Knot_theory" title="Knot theory">knots</a>, and <a href="/wiki/Donaldson_theory" title="Donaldson theory">Donaldson theory</a>. He introduced the concept of a <a href="/wiki/Topological_quantum_field_theory" title="Topological quantum field theory">topological quantum field theory</a>, inspired by Witten's work and Segal's definition of a conformal field theory.<a href="#cite_note-108">[108]</a> His book "The Geometry and Physics of Knots"<a href="#cite_note-109">[109]</a> describes the new <a href="/wiki/Knot_invariant" title="Knot invariant">knot invariants</a> found by <a href="/wiki/Vaughan_Jones" title="Vaughan Jones">Vaughan Jones</a> and <a href="/wiki/Edward_Witten" title="Edward Witten">Edward Witten</a> in terms of topological quantum field theories, and his paper with L. Jeffrey<a href="#cite_note-110">[110]</a> explains Witten's Lagrangian giving the <a href="/wiki/Donaldson_invariant" class="mw-redirect" title="Donaldson invariant">Donaldson invariants</a>. He studied <a href="/wiki/Skyrmion" title="Skyrmion">skyrmions</a> with Nick Manton,<a href="#cite_note-111">[111]</a> finding a relation with <a href="/wiki/Magnetic_monopoles" class="mw-redirect" title="Magnetic monopoles">magnetic monopoles</a> and <a href="/wiki/Instanton" title="Instanton">instantons</a>, and giving a conjecture for the structure of the <a href="/wiki/Moduli_space" title="Moduli space">moduli space</a> of two <a href="/wiki/Skyrmions" class="mw-redirect" title="Skyrmions">skyrmions</a> as a certain <a href="/wiki/Subquotient" title="Subquotient">subquotient</a> of complex <a href="/wiki/Projective_3-space" class="mw-redirect" title="Projective 3-space">projective 3-space</a>. Several papers<a href="#cite_note-112">[112]</a> were inspired by a question of <a rel="nofollow" class="external text" href="https://research-information.bristol.ac.uk/en/persons/jonathan-m-robbins(60101278-f877-4e14-946f-262f3b95d5ae).html">Jonathan Robbins</a> (called the <a href="/wiki/Berry%E2%80%93Robbins_problem" title="Berry–Robbins problem">Berry–Robbins problem</a>), who asked if there is a map from the configuration space of n points in 3-space to the flag manifold of the unitary group. Atiyah gave an affirmative answer to this question, but felt his solution was too computational and studied a conjecture that would give a more natural solution. He also related the question to <a href="/wiki/Nahm%27s_equation" class="mw-redirect" title="Nahm's equation">Nahm's equation</a>, and introduced the <a href="/wiki/Atiyah_conjecture_on_configurations" title="Atiyah conjecture on configurations">Atiyah conjecture on configurations</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1224211176"><div class="quotebox pullquote floatright" style="width:33%; ;"> <blockquote class="quotebox-quote left-aligned" style=""> But for most practical purposes, you just use the classical groups. The exceptional Lie groups are just there to show you that the theory is a bit bigger; it is pretty rare that they ever turn up. </blockquote> <cite class="left-aligned" style="">Michael Atiyah<a href="#cite_note-ReferenceA-113">[113]</a></cite> </div> With <a href="/wiki/Juan_Maldacena" title="Juan Maldacena">Juan Maldacena</a> and <a href="/wiki/Cumrun_Vafa" title="Cumrun Vafa">Cumrun Vafa</a>,<a href="#cite_note-114">[114]</a> and <a href="/wiki/E._Witten" class="mw-redirect" title="E. Witten">E. Witten</a><a href="#cite_note-115">[115]</a> he described the dynamics of <a href="/wiki/M-theory" title="M-theory">M-theory</a> on <a href="/wiki/Joyce_manifold" class="mw-redirect" title="Joyce manifold">manifolds with G2 holonomy</a>. These papers seem to be the first time that Atiyah worked on exceptional Lie groups. In his papers with <a href="/wiki/Michael_J._Hopkins" title="Michael J. Hopkins">M. Hopkins</a><a href="#cite_note-116">[116]</a> and G. Segal<a href="#cite_note-117">[117]</a> he returned to his earlier interest of K-theory, describing some twisted forms of K-theory with applications in <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>. In October 2016, he claimed<a href="#cite_note-118">[118]</a> a short proof of the non-existence of <a href="/wiki/Complex_manifold" title="Complex manifold">complex structures</a> on the 6-sphere. His proof, like many predecessors, is considered flawed by the mathematical community, even after the proof was rewritten in a revised form.<a href="#cite_note-119">[119]</a><a href="#cite_note-120">[120]</a> At the 2018 <a href="/wiki/Klaus_Tschira_Foundation" title="Klaus Tschira Foundation">Heidelberg Laureate Forum</a>, he claimed to have solved the <a href="/wiki/Riemann_hypothesis" title="Riemann hypothesis">Riemann hypothesis</a>, <a href="/wiki/Hilbert%27s_eighth_problem" title="Hilbert's eighth problem">Hilbert's eighth problem</a>, <a href="/wiki/Proof_by_contradiction" title="Proof by contradiction">by contradiction</a> using the <a href="/wiki/Fine-structure_constant" title="Fine-structure constant">fine-structure constant</a>. Again, the proof did not hold up and the hypothesis remains one of the six unsolved <a href="/wiki/Millennium_Prize_Problems" title="Millennium Prize Problems">Millennium Prize Problems</a> in mathematics, as of 2024.<a href="#cite_note-121">[121]</a><a href="#cite_note-122">[122]</a> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=9" title="Edit section: Bibliography">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Books">Books</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=10" title="Edit section: Books">edit</a>]</div> This subsection lists all books written by Atiyah; it omits a few books that he edited. <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 35em;"> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFAtiyahMacdonald1969" class="citation cs2">Atiyah, Michael F.; <a href="/wiki/Ian_G._Macdonald" title="Ian G. Macdonald">Macdonald, Ian G.</a> (1969), Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0242802">0242802</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+commutative+algebra&rft.pub=Addison-Wesley+Publishing+Co.%2C+Reading%2C+Mass.-London-Don+Mills%2C+Ont.&rft.date=1969&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0242802%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Macdonald%2C+Ian+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. A classic textbook covering standard commutative algebra.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1970" class="citation cs2">Atiyah, Michael F. (1970), Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Cologne: Westdeutscher Verlag, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0263102">0263102</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vector+fields+on+manifolds&rft.place=Cologne&rft.series=Arbeitsgemeinschaft+f%C3%BCr+Forschung+des+Landes+Nordrhein-Westfalen%2C+Heft+200&rft.pub=Westdeutscher+Verlag&rft.date=1970&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0263102%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted as (<a href="#CITEREFAtiyah1988b">Atiyah 1988b</a>, item 50).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1974" class="citation cs2">Atiyah, Michael F. (1974), Elliptic operators and compact groups, Lecture Notes in Mathematics, Vol. 401, Berlin, New York: <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0482866">0482866</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elliptic+operators+and+compact+groups&rft.place=Berlin%2C+New+York&rft.series=Lecture+Notes+in+Mathematics%2C+Vol.+401&rft.pub=Springer-Verlag&rft.date=1974&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0482866%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted as (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, item 78).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1979" class="citation cs2">Atiyah, Michael F. (1979), Geometry of Yang–Mills fields, Scuola Normale Superiore Pisa, Pisa, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0554924">0554924</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometry+of+Yang%E2%80%93Mills+fields&rft.pub=Scuola+Normale+Superiore+Pisa%2C+Pisa&rft.date=1979&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D554924%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted as (<a href="#CITEREFAtiyah1988e">Atiyah 1988e</a>, item 99).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahHitchin1988" class="citation cs2">Atiyah, Michael F.; Hitchin, Nigel (1988), The geometry and dynamics of magnetic monopoles, M. B. Porter Lectures, <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1515%2F9781400859306">10.1515/9781400859306</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-08480-0" title="Special:BookSources/978-0-691-08480-0"><bdi>978-0-691-08480-0</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0934202">0934202</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+geometry+and+dynamics+of+magnetic+monopoles&rft.series=M.+B.+Porter+Lectures&rft.pub=Princeton+University+Press&rft.date=1988&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D934202%23id-name%3DMR&rft_id=info%3Adoi%2F10.1515%2F9781400859306&rft.isbn=978-0-691-08480-0&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Hitchin%2C+Nigel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted as (<a href="#CITEREFAtiyah2004">Atiyah 2004</a>, item 126).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1988a" class="citation cs2">Atiyah, Michael F. (1988a), Collected works. Vol. 1 Early papers: general papers, Oxford Science Publications, The Clarendon Press Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-853275-0" title="Special:BookSources/978-0-19-853275-0"><bdi>978-0-19-853275-0</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0951892">0951892</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collected+works.+Vol.+1+Early+papers%3A+general+papers&rft.series=Oxford+Science+Publications&rft.pub=The+Clarendon+Press+Oxford+University+Press&rft.date=1988&rft.isbn=978-0-19-853275-0&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D951892%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1988b" class="citation cs2">Atiyah, Michael F. (1988b), Collected works. Vol. 2 K-theory, Oxford Science Publications, The Clarendon Press Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-853276-7" title="Special:BookSources/978-0-19-853276-7"><bdi>978-0-19-853276-7</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0951892">0951892</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collected+works.+Vol.+2+K-theory&rft.series=Oxford+Science+Publications&rft.pub=The+Clarendon+Press+Oxford+University+Press&rft.date=1988&rft.isbn=978-0-19-853276-7&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D951892%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1988c" class="citation cs2">Atiyah, Michael F. (1988c), Collected works. Vol. 3 Index theory: 1, Oxford Science Publications, The Clarendon Press Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-853277-4" title="Special:BookSources/978-0-19-853277-4"><bdi>978-0-19-853277-4</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0951892">0951892</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collected+works.+Vol.+3+Index+theory%3A+1&rft.series=Oxford+Science+Publications&rft.pub=The+Clarendon+Press+Oxford+University+Press&rft.date=1988&rft.isbn=978-0-19-853277-4&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D951892%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1988d" class="citation cs2">Atiyah, Michael F. (1988d), Collected works. Vol. 4 Index theory: 2, Oxford Science Publications, The Clarendon Press Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-853278-1" title="Special:BookSources/978-0-19-853278-1"><bdi>978-0-19-853278-1</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0951892">0951892</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collected+works.+Vol.+4+Index+theory%3A+2&rft.series=Oxford+Science+Publications&rft.pub=The+Clarendon+Press+Oxford+University+Press&rft.date=1988&rft.isbn=978-0-19-853278-1&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D951892%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1988e" class="citation cs2">Atiyah, Michael F. (1988e), Collected works. Vol. 5 Gauge theories, Oxford Science Publications, The Clarendon Press Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-853279-8" title="Special:BookSources/978-0-19-853279-8"><bdi>978-0-19-853279-8</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0951892">0951892</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collected+works.+Vol.+5+Gauge+theories&rft.series=Oxford+Science+Publications&rft.pub=The+Clarendon+Press+Oxford+University+Press&rft.date=1988&rft.isbn=978-0-19-853279-8&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D951892%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1989" class="citation cs2">Atiyah, Michael F. (1989), K-theory, Advanced Book Classics (2nd ed.), <a href="/wiki/Addison-Wesley" title="Addison-Wesley">Addison-Wesley</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-09394-0" title="Special:BookSources/978-0-201-09394-0"><bdi>978-0-201-09394-0</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1043170">1043170</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=K-theory&rft.series=Advanced+Book+Classics&rft.edition=2nd&rft.pub=Addison-Wesley&rft.date=1989&rft.isbn=978-0-201-09394-0&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1043170%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. First edition (1967) reprinted as (<a href="#CITEREFAtiyah1988b">Atiyah 1988b</a>, item 45).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1990" class="citation cs2">Atiyah, Michael F. (1990), <a rel="nofollow" class="external text" href="https://archive.org/details/geometryphysicso0000atiy">The geometry and physics of knots</a>, Lezioni Lincee. [Lincei Lectures], <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FCBO9780511623868">10.1017/CBO9780511623868</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-39521-2" title="Special:BookSources/978-0-521-39521-2"><bdi>978-0-521-39521-2</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1078014">1078014</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+geometry+and+physics+of+knots&rft.series=Lezioni+Lincee.+%5BLincei+Lectures%5D&rft.pub=Cambridge+University+Press&rft.date=1990&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1078014%23id-name%3DMR&rft_id=info%3Adoi%2F10.1017%2FCBO9780511623868&rft.isbn=978-0-521-39521-2&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgeometryphysicso0000atiy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted as (<a href="#CITEREFAtiyah2004">Atiyah 2004</a>, item 136).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah2004" class="citation cs2">Atiyah, Michael F. (2004), Collected works. Vol. 6, Oxford Science Publications, The Clarendon Press Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-853099-2" title="Special:BookSources/978-0-19-853099-2"><bdi>978-0-19-853099-2</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=2160826">2160826</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collected+works.+Vol.+6&rft.series=Oxford+Science+Publications&rft.pub=The+Clarendon+Press+Oxford+University+Press&rft.date=2004&rft.isbn=978-0-19-853099-2&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D2160826%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah2007" class="citation cs2">Atiyah, Michael F. (2007), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190114153347/https://tuttimatematici.info/">Siamo tutti matematici (Italian: We are all mathematicians)</a>, Roma: Di Renzo Editore, p. 96, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-88-8323-157-5" title="Special:BookSources/978-88-8323-157-5"><bdi>978-88-8323-157-5</bdi></a>, archived from <a rel="nofollow" class="external text" href="http://www.tuttimatematici.info/">the original</a> on 14 January 2019, retrieved 23 July 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Siamo+tutti+matematici+%28Italian%3A+We+are+all+mathematicians%29&rft.place=Roma&rft.pages=96&rft.pub=Di+Renzo+Editore&rft.date=2007&rft.isbn=978-88-8323-157-5&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft_id=http%3A%2F%2Fwww.tuttimatematici.info%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah2014" class="citation cs2">Atiyah, Michael (2014), Collected works. Vol. 7. 2002-2013, Oxford Science Publications, The Clarendon Press Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-968926-2" title="Special:BookSources/978-0-19-968926-2"><bdi>978-0-19-968926-2</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=3223085">3223085</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collected+works.+Vol.+7.+2002-2013&rft.series=Oxford+Science+Publications&rft.pub=The+Clarendon+Press+Oxford+University+Press&rft.date=2014&rft.isbn=978-0-19-968926-2&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D3223085%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahIagolnitzerChong2015" class="citation cs2">Atiyah, Michael F.; Iagolnitzer, Daniel; Chong, Chitat (2015), Fields Medallists' Lectures (3rd Edition), World Scientific, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2F9652">10.1142/9652</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-4696-18-0" title="Special:BookSources/978-981-4696-18-0"><bdi>978-981-4696-18-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fields+Medallists%27+Lectures+%283rd+Edition%29&rft.pub=World+Scientific&rft.date=2015&rft_id=info%3Adoi%2F10.1142%2F9652&rft.isbn=978-981-4696-18-0&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Iagolnitzer%2C+Daniel&rft.au=Chong%2C+Chitat&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Selected_papers">Selected papers</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=11" title="Edit section: Selected papers">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 35em;"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1961" class="citation cs2">Atiyah, Michael F. (1961), <a rel="nofollow" class="external text" href="http://www.numdam.org/item?id=PMIHES_1961__9__23_0">"Characters and cohomology of finite groups"</a>, Inst. Hautes Études Sci. Publ. Math., 9: 23–64, <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%2FBF02698718">10.1007/BF02698718</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:54764252">54764252</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Inst.+Hautes+%C3%89tudes+Sci.+Publ.+Math.&rft.atitle=Characters+and+cohomology+of+finite+groups&rft.volume=9&rft.pages=23-64&rft.date=1961&rft_id=info%3Adoi%2F10.1007%2FBF02698718&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A54764252%23id-name%3DS2CID&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft_id=http%3A%2F%2Fwww.numdam.org%2Fitem%3Fid%3DPMIHES_1961__9__23_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted in (<a href="#CITEREFAtiyah1988b">Atiyah 1988b</a>, paper 29).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahHirzebruch1961" class="citation cs2">Atiyah, Michael F.; <a href="/wiki/Friedrich_Hirzebruch" title="Friedrich Hirzebruch">Hirzebruch, Friedrich</a> (1961), Vector bundles and homogeneous spaces, Proceedings of Symposia in Pure Mathematics, vol. 3, pp. 7–38, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fpspum%2F003%2F0139181">10.1090/pspum/003/0139181</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-1403-1" title="Special:BookSources/978-0-8218-1403-1"><bdi>978-0-8218-1403-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vector+bundles+and+homogeneous+spaces&rft.series=Proceedings+of+Symposia+in+Pure+Mathematics&rft.pages=7-38&rft.date=1961&rft_id=info%3Adoi%2F10.1090%2Fpspum%2F003%2F0139181&rft.isbn=978-0-8218-1403-1&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Hirzebruch%2C+Friedrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted in (<a href="#CITEREFAtiyah1988b">Atiyah 1988b</a>, paper 28).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahSegal1969" class="citation cs2">Atiyah, Michael F.; <a href="/wiki/Graeme_Segal" title="Graeme Segal">Segal, Graeme B.</a> (1969), "Equivariant K-Theory and Completion", Journal of Differential Geometry, 3 (1–2): 1–18, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4310%2Fjdg%2F1214428815">10.4310/jdg/1214428815</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+Differential+Geometry&rft.atitle=Equivariant+K-Theory+and+Completion&rft.volume=3&rft.issue=1%E2%80%932&rft.pages=1-18&rft.date=1969&rft_id=info%3Adoi%2F10.4310%2Fjdg%2F1214428815&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Segal%2C+Graeme+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted in (<a href="#CITEREFAtiyah1988b">Atiyah 1988b</a>, paper 49).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1976" class="citation cs2 cs1-prop-long-vol">Atiyah, Michael F. (1976), "Elliptic operators, discrete groups and von Neumann algebras", Colloque "Analyse et Topologie" en l'Honneur de Henri Cartan (Orsay, 1974), Asterisque, vol. 32–33, Soc. Math. France, Paris, pp. 43–72, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0420729">0420729</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Elliptic+operators%2C+discrete+groups+and+von+Neumann+algebras&rft.btitle=Colloque+%22Analyse+et+Topologie%22+en+l%27Honneur+de+Henri+Cartan+%28Orsay%2C+1974%29&rft.series=Asterisque&rft.pages=43-72&rft.pub=Soc.+Math.+France%2C+Paris&rft.date=1976&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0420729%23id-name%3DMR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted in (<a href="#CITEREFAtiyah1988d">Atiyah 1988d</a>, paper 89). Formulation of the <a href="/wiki/Atiyah_conjecture" title="Atiyah conjecture">Atiyah "Conjecture"</a> on the rationality of the L2-Betti numbers.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahSinger1963" class="citation cs2">Atiyah, Michael F.; Singer, Isadore M. (1963), "The Index of Elliptic Operators on Compact Manifolds", Bull. Amer. Math. Soc., 69 (3): 322–433, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9904-1963-10957-X">10.1090/S0002-9904-1963-10957-X</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=The+Index+of+Elliptic+Operators+on+Compact+Manifolds&rft.volume=69&rft.issue=3&rft.pages=322-433&rft.date=1963&rft_id=info%3Adoi%2F10.1090%2FS0002-9904-1963-10957-X&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Singer%2C+Isadore+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. An announcement of the index theorem. Reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 56).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahSinger1968a" class="citation cs2">Atiyah, Michael F.; Singer, Isadore M. (1968a), "The Index of Elliptic Operators I", <a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a>, 87 (3): 484–530, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1970715">10.2307/1970715</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/1970715">1970715</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=The+Index+of+Elliptic+Operators+I&rft.volume=87&rft.issue=3&rft.pages=484-530&rft.date=1968&rft_id=info%3Adoi%2F10.2307%2F1970715&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1970715%23id-name%3DJSTOR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Singer%2C+Isadore+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. This gives a proof using K-theory instead of <a href="/wiki/Cohomology" title="Cohomology">cohomology</a>. Reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 64).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahSegal1968" class="citation cs2">Atiyah, Michael F.; Segal, Graeme B. (1968), "The Index of Elliptic Operators: II", <a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a>, Second Series, 87 (3): 531–545, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1970716">10.2307/1970716</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/1970716">1970716</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=The+Index+of+Elliptic+Operators%3A+II&rft.volume=87&rft.issue=3&rft.pages=531-545&rft.date=1968&rft_id=info%3Adoi%2F10.2307%2F1970716&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1970716%23id-name%3DJSTOR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Segal%2C+Graeme+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. This reformulates the result as a sort of Lefschetz fixed point theorem, using <a href="/wiki/K-theory" title="K-theory">equivariant K-theory</a>. Reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 65).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahSinger1968b" class="citation cs2">Atiyah, Michael F.; Singer, Isadore M. (1968b), "The Index of Elliptic Operators III", <a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a>, Second Series, 87 (3): 546–604, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1970717">10.2307/1970717</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/1970717">1970717</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=The+Index+of+Elliptic+Operators+III&rft.volume=87&rft.issue=3&rft.pages=546-604&rft.date=1968&rft_id=info%3Adoi%2F10.2307%2F1970717&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1970717%23id-name%3DJSTOR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Singer%2C+Isadore+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. This paper shows how to convert from the K-theory version to a version using cohomology. Reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 66).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahSinger1971" class="citation cs2">Atiyah, Michael F.; Singer, Isadore M. (1971), "The Index of Elliptic Operators IV", Annals of Mathematics, Second Series, 93 (1): 119–138, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1970756">10.2307/1970756</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/1970756">1970756</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=The+Index+of+Elliptic+Operators+IV&rft.volume=93&rft.issue=1&rft.pages=119-138&rft.date=1971&rft_id=info%3Adoi%2F10.2307%2F1970756&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1970756%23id-name%3DJSTOR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Singer%2C+Isadore+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> This paper studies families of elliptic operators, where the index is now an element of the K-theory of the space parametrizing the family. Reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 67).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahSinger1971" class="citation cs2">Atiyah, Michael F.; Singer, Isadore M. (1971), "The Index of Elliptic Operators V", <a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a>, Second Series, 93 (1): 139–149, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1970757">10.2307/1970757</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/1970757">1970757</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=The+Index+of+Elliptic+Operators+V&rft.volume=93&rft.issue=1&rft.pages=139-149&rft.date=1971&rft_id=info%3Adoi%2F10.2307%2F1970757&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1970757%23id-name%3DJSTOR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Singer%2C+Isadore+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. This studies families of real (rather than complex) elliptic operators, when one can sometimes squeeze out a little extra information. Reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 68).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahBott1966" class="citation cs2">Atiyah, Michael F.; Bott, Raoul (1966), "A Lefschetz Fixed Point Formula for Elliptic Differential Operators", Bull. Am. Math. Soc., 72 (2): 245–50, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9904-1966-11483-0">10.1090/S0002-9904-1966-11483-0</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Am.+Math.+Soc.&rft.atitle=A+Lefschetz+Fixed+Point+Formula+for+Elliptic+Differential+Operators&rft.volume=72&rft.issue=2&rft.pages=245-50&rft.date=1966&rft_id=info%3Adoi%2F10.1090%2FS0002-9904-1966-11483-0&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Bott%2C+Raoul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. This states a theorem calculating the Lefschetz number of an endomorphism of an elliptic complex. Reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 61).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahBott1967" class="citation cs2">Atiyah, Michael F.; Bott, Raoul (1967), "A Lefschetz Fixed Point Formula for Elliptic Complexes: I", <a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a>, Second Series, 86 (2): 374–407, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1970694">10.2307/1970694</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/1970694">1970694</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=A+Lefschetz+Fixed+Point+Formula+for+Elliptic+Complexes%3A+I&rft.volume=86&rft.issue=2&rft.pages=374-407&rft.date=1967&rft_id=info%3Adoi%2F10.2307%2F1970694&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1970694%23id-name%3DJSTOR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Bott%2C+Raoul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> (reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 61))and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahBott1968" class="citation cs2">Atiyah, Michael F.; Bott, Raoul (1968), "A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications", <a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a>, Second Series, 88 (3): 451–491, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1970721">10.2307/1970721</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/1970721">1970721</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=A+Lefschetz+Fixed+Point+Formula+for+Elliptic+Complexes%3A+II.+Applications&rft.volume=88&rft.issue=3&rft.pages=451-491&rft.date=1968&rft_id=info%3Adoi%2F10.2307%2F1970721&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1970721%23id-name%3DJSTOR&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Bott%2C+Raoul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted in (<a href="#CITEREFAtiyah1988c">Atiyah 1988c</a>, paper 62). These give the proofs and some applications of the results announced in the previous paper.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahBottPatodi1973" class="citation cs2">Atiyah, Michael F.; Bott, Raoul; Patodi, Vijay K. (1973), <a rel="nofollow" class="external text" href="https://link.springer.com/content/pdf/10.1007%2FBF01425562.pdf">"On the heat equation and the index theorem"</a> (PDF), Invent. Math., 19 (4): 279–330, <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/1973InMat..19..279A">1973InMat..19..279A</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%2FBF01425417">10.1007/BF01425417</a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0650828">0650828</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:115700319">115700319</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Invent.+Math.&rft.atitle=On+the+heat+equation+and+the+index+theorem&rft.volume=19&rft.issue=4&rft.pages=279-330&rft.date=1973&rft_id=info%3Adoi%2F10.1007%2FBF01425417&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0650828%23id-name%3DMR&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A115700319%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1973InMat..19..279A&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Bott%2C+Raoul&rft.au=Patodi%2C+Vijay+K.&rft_id=https%3A%2F%2Flink.springer.com%2Fcontent%2Fpdf%2F10.1007%252FBF01425562.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah,_Michael_F.BottPatodi1975" class="citation cs2">Atiyah, Michael F.; Bott, R.; Patodi, V. K. (1975), "Errata", Invent. Math., 28 (3): 277–280, <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/1975InMat..28..277A">1975InMat..28..277A</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%2FBF01425562">10.1007/BF01425562</a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0650829">0650829</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Invent.+Math.&rft.atitle=Errata&rft.volume=28&rft.issue=3&rft.pages=277-280&rft.date=1975&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0650829%23id-name%3DMR&rft_id=info%3Adoi%2F10.1007%2FBF01425562&rft_id=info%3Abibcode%2F1975InMat..28..277A&rft.au=Atiyah%2C+Michael+F.&rft.au=Bott%2C+R.&rft.au=Patodi%2C+V.+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> Reprinted in (<a href="#CITEREFAtiyah1988d">Atiyah 1988d</a>, paper 79, 79a).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyahSchmid1977" class="citation cs2">Atiyah, Michael F.; Schmid, Wilfried (1977), "A geometric construction of the discrete series for semisimple Lie groups", Invent. Math., 42: 1–62, <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/1977InMat..42....1A">1977InMat..42....1A</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%2FBF01389783">10.1007/BF01389783</a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0463358">0463358</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:189831012">189831012</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Invent.+Math.&rft.atitle=A+geometric+construction+of+the+discrete+series+for+semisimple+Lie+groups&rft.volume=42&rft.pages=1-62&rft.date=1977&rft_id=info%3Adoi%2F10.1007%2FBF01389783&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0463358%23id-name%3DMR&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A189831012%23id-name%3DS2CID&rft_id=info%3Abibcode%2F1977InMat..42....1A&rft.aulast=Atiyah&rft.aufirst=Michael+F.&rft.au=Schmid%2C+Wilfried&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah,_Michael_F.Schmid1979" class="citation cs2">Atiyah, Michael F.; Schmid, Wilfried (1979), "Erratum", Invent. Math., 54 (2): 189–192, <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/1979InMat..54..189A">1979InMat..54..189A</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%2FBF01408936">10.1007/BF01408936</a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0550183">0550183</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Invent.+Math.&rft.atitle=Erratum&rft.volume=54&rft.issue=2&rft.pages=189-192&rft.date=1979&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0550183%23id-name%3DMR&rft_id=info%3Adoi%2F10.1007%2FBF01408936&rft_id=info%3Abibcode%2F1979InMat..54..189A&rft.au=Atiyah%2C+Michael+F.&rft.au=Schmid%2C+Wilfried&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted in (<a href="#CITEREFAtiyah1988d">Atiyah 1988d</a>, paper 90).</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah2010" class="citation cs2">Atiyah, Michael (2010), Edinburgh Lectures on Geometry, Analysis and Physics, <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1009.4827v1">1009.4827v1</a>, <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/2010arXiv1009.4827A">2010arXiv1009.4827A</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Edinburgh+Lectures+on+Geometry%2C+Analysis+and+Physics&rft.date=2010&rft_id=info%3Aarxiv%2F1009.4827v1&rft_id=info%3Abibcode%2F2010arXiv1009.4827A&rft.aulast=Atiyah&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Awards_and_honours">Awards and honours</h2>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=12" title="Edit section: Awards and honours">edit</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Royal_Society_20040420.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Royal_Society_20040420.jpg/220px-Royal_Society_20040420.jpg" decoding="async" width="220" height="153" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Royal_Society_20040420.jpg/330px-Royal_Society_20040420.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Royal_Society_20040420.jpg/440px-Royal_Society_20040420.jpg 2x" data-file-width="1437" data-file-height="998" /></a><figcaption>The premises of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a>, where Atiyah was president from 1990 to 1995</figcaption></figure> In 1966, when he was thirty-seven years old, he was awarded the <a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medal</a>,<a href="#cite_note-123">[123]</a> for his work in developing K-theory, a generalized <a href="/wiki/Lefschetz_fixed-point_theorem" title="Lefschetz fixed-point theorem">Lefschetz fixed-point theorem</a> and the Atiyah–Singer theorem, for which he also won the <a href="/wiki/Abel_Prize" title="Abel Prize">Abel Prize</a> jointly with <a href="/wiki/Isadore_Singer" title="Isadore Singer">Isadore Singer</a> in 2004.<a href="#cite_note-124">[124]</a> Among other prizes he has received are the <a href="/wiki/Royal_Medal" title="Royal Medal">Royal Medal</a> of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> in 1968,<a href="#cite_note-125">[125]</a> the <a href="/wiki/De_Morgan_Medal" title="De Morgan Medal">De Morgan Medal</a> of the <a href="/wiki/London_Mathematical_Society" title="London Mathematical Society">London Mathematical Society</a> in 1980, the <a href="/wiki/Antonio_Feltrinelli_Prize" class="mw-redirect" title="Antonio Feltrinelli Prize">Antonio Feltrinelli Prize</a> from the <a href="/wiki/Accademia_Nazionale_dei_Lincei" class="mw-redirect" title="Accademia Nazionale dei Lincei">Accademia Nazionale dei Lincei</a> in 1981, the <a href="/wiki/King_Faisal_International_Prize_for_Science" class="mw-redirect" title="King Faisal International Prize for Science">King Faisal International Prize for Science</a> in 1987,<a href="#cite_note-126">[126]</a> the <a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a> of the Royal Society in 1988,<a href="#cite_note-127">[127]</a> the <a href="/wiki/Benjamin_Franklin_Medal_for_Distinguished_Achievement_in_the_Sciences" class="mw-redirect" title="Benjamin Franklin Medal for Distinguished Achievement in the Sciences">Benjamin Franklin Medal for Distinguished Achievement in the Sciences</a> of the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a> in 1993,<a href="#cite_note-franklinscience_recipients-128">[128]</a> the Jawaharlal Nehru Birth Centenary Medal of the <a href="/wiki/Indian_National_Science_Academy" title="Indian National Science Academy">Indian National Science Academy</a> in 1993,<a href="#cite_note-129">[129]</a> the <a href="/wiki/President%27s_Medal_of_the_IOP" title="President's Medal of the IOP">President's Medal</a> from the <a href="/wiki/Institute_of_Physics" title="Institute of Physics">Institute of Physics</a> in 2008,<a href="#cite_note-130">[130]</a> the <a href="/wiki/Grande_M%C3%A9daille" title="Grande Médaille">Grande Médaille</a> of the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a> in 2010<a href="#cite_note-131">[131]</a> and the Grand Officier of the <a href="/wiki/Legion_of_Honour" title="Legion of Honour">French Légion d'honneur</a> in 2011.<a href="#cite_note-132">[132]</a> He was elected a foreign member of the <a href="/wiki/United_States_National_Academy_of_Sciences" class="mw-redirect" title="United States National Academy of Sciences">National Academy of Sciences</a>, the <a href="/wiki/American_Academy_of_Arts_and_Sciences" title="American Academy of Arts and Sciences">American Academy of Arts and Sciences</a> (1969),<a href="#cite_note-AAAS-133">[133]</a> the <a href="/wiki/Acad%C3%A9mie_des_Sciences" class="mw-redirect" title="Académie des Sciences">Académie des Sciences</a>, the <a href="/wiki/Akademie_Leopoldina" class="mw-redirect" title="Akademie Leopoldina">Akademie Leopoldina</a>, the <a href="/wiki/Royal_Swedish_Academy" class="mw-redirect" title="Royal Swedish Academy">Royal Swedish Academy</a>, the <a href="/wiki/Royal_Irish_Academy" title="Royal Irish Academy">Royal Irish Academy</a>, the <a href="/wiki/Royal_Society_of_Edinburgh" title="Royal Society of Edinburgh">Royal Society of Edinburgh</a>, the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a>, the <a href="/wiki/Indian_National_Science_Academy" title="Indian National Science Academy">Indian National Science Academy</a>, the <a href="/wiki/Chinese_Academy_of_Science" class="mw-redirect" title="Chinese Academy of Science">Chinese Academy of Science</a>, the <a href="/wiki/Australian_Academy_of_Science" title="Australian Academy of Science">Australian Academy of Science</a>, the <a href="/wiki/Russian_Academy_of_Science" class="mw-redirect" title="Russian Academy of Science">Russian Academy of Science</a>, the <a href="/wiki/Ukrainian_Academy_of_Science" class="mw-redirect" title="Ukrainian Academy of Science">Ukrainian Academy of Science</a>, the <a href="/wiki/Georgian_Academy_of_Science" class="mw-redirect" title="Georgian Academy of Science">Georgian Academy of Science</a>, the <a href="/w/index.php?title=Venezuela_Academy_of_Science&action=edit&redlink=1" class="new" title="Venezuela Academy of Science (page does not exist)">Venezuela Academy of Science</a>, the <a href="/wiki/Norwegian_Academy_of_Science_and_Letters" title="Norwegian Academy of Science and Letters">Norwegian Academy of Science and Letters</a>, the <a href="/wiki/Royal_Spanish_Academy_of_Science" class="mw-redirect" title="Royal Spanish Academy of Science">Royal Spanish Academy of Science</a>, the <a href="/wiki/Accademia_dei_Lincei" title="Accademia dei Lincei">Accademia dei Lincei</a> and the <a href="/wiki/Moscow_Mathematical_Society" title="Moscow Mathematical Society">Moscow Mathematical Society</a>.<a href="#cite_note-cv1-8">[8]</a><a href="#cite_note-cv2-12">[12]</a> In 2012, he became a fellow of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>.<a href="#cite_note-134">[134]</a> He was also appointed as a Honorary <a href="/wiki/Fellow" title="Fellow">Fellow</a><a href="#cite_note-List_of_Fellows-135">[135]</a> of the <a href="/wiki/Royal_Academy_of_Engineering" title="Royal Academy of Engineering">Royal Academy of Engineering</a><a href="#cite_note-List_of_Fellows-135">[135]</a> in 1993. Atiyah was awarded honorary degrees by the universities of Birmingham, Bonn, Chicago, Cambridge, Dublin, Durham, Edinburgh, Essex, Ghent, Helsinki, Lebanon, Leicester, London, Mexico, Montreal, Oxford, Reading, Salamanca, St. Andrews, Sussex, Wales, Warwick, the American University of Beirut, Brown University, Charles University in Prague, Harvard University, Heriot–Watt University, Hong Kong (Chinese University), Keele University, Queen's University (Canada), The Open University, University of Waterloo, Wilfrid Laurier University, Technical University of Catalonia, and UMIST.<a href="#cite_note-cv1-8">[8]</a><a href="#cite_note-cv2-12">[12]</a><a href="#cite_note-136">[136]</a><a href="#cite_note-drhccuni-137">[137]</a> Atiyah was made a <a href="/wiki/Knight_Bachelor" title="Knight Bachelor">Knight Bachelor</a> in 1983<a href="#cite_note-cv1-8">[8]</a> and made a member of the <a href="/wiki/Order_of_Merit_(Commonwealth)" class="mw-redirect" title="Order of Merit (Commonwealth)">Order of Merit</a> in 1992.<a href="#cite_note-cv2-12">[12]</a> The Michael Atiyah building<a href="#cite_note-138">[138]</a> at the <a href="/wiki/University_of_Leicester" title="University of Leicester">University of Leicester</a> and the Michael Atiyah Chair in Mathematical Sciences<a href="#cite_note-139">[139]</a> at the <a href="/wiki/American_University_of_Beirut" title="American University of Beirut">American University of Beirut</a> were named after him. <div class="mw-heading mw-heading2"><h2 id="Personal_life">Personal life</h2>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=13" title="Edit section: Personal life">edit</a>]</div> Atiyah married Lily Brown on 30 July 1955, with whom he had three sons, John, David and Robin. Atiyah's eldest son John died on 24 June 2002 while on a walking holiday in the <a href="/wiki/Pyrenees" title="Pyrenees">Pyrenees</a> with his wife Maj-Lis. Lily Atiyah died on 13 March 2018 at the age of 90<a href="#cite_note-mactutor-4">[4]</a><a href="#cite_note-ja-6">[6]</a><a href="#cite_note-cv1-8">[8]</a> while Sir Michael Atiyah died less than a year later on 11 January 2019, aged 89.<a href="#cite_note-oxford-death-140">[140]</a><a href="#cite_note-royal-society-death-141">[141]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=14" title="Edit section: See also">edit</a>]</div> <ul><li><a href="/wiki/List_of_presidents_of_the_Royal_Society" title="List of presidents of the Royal Society">List of presidents of the Royal Society</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=15" title="Edit section: References">edit</a>]</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-aphd-1">^ <a href="#cite_ref-aphd_1-0">a</a> <a href="#cite_ref-aphd_1-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah1955" class="citation thesis cs1">Atiyah, Michael Francis (1955). <a rel="nofollow" class="external text" href="https://www.repository.cam.ac.uk/handle/1810/251002">Some applications of topological methods in algebraic geometry</a>. repository.cam.ac.uk (PhD thesis). 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Retrieved 4 April 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www1.hw.ac.uk&rft.atitle=Heriot-Watt+University+Edinburgh%3A+Honorary+Graduates&rft_id=http%3A%2F%2Fwww1.hw.ac.uk%2Fgraduation%2Fhonorary-graduates.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> </li> <li id="cite_note-drhccuni-137"><a href="#cite_ref-drhccuni_137-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.cuni.cz/UKEN-139.html">Honorary Doctorates</a>, Charles University in Prague, retrieved 4 May 2018</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Honorary+Doctorates&rft.pub=Charles+University+in+Prague&rft_id=https%3A%2F%2Fwww.cuni.cz%2FUKEN-139.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> </li> <li id="cite_note-138"><a href="#cite_ref-138">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090209061649/http://www.engg.le.ac.uk/Research_Groups/Mechanics_of_Materials_Research_Group/The_Michael_Atiyah_Building/">The Michael Atiyah building</a>, archived from <a rel="nofollow" class="external text" href="http://www.engg.le.ac.uk/Research_Groups/Mechanics_of_Materials_Research_Group/The_Michael_Atiyah_Building">the original</a> on 9 February 2009, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Michael+Atiyah+building&rft_id=http%3A%2F%2Fwww.engg.le.ac.uk%2FResearch_Groups%2FMechanics_of_Materials_Research_Group%2FThe_Michael_Atiyah_Building&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> </li> <li id="cite_note-139"><a href="#cite_ref-139">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080403090555/http://www.ameinfo.com/142298.html">American University of Beirut establishes the Michael Atiyah Chair in Mathematical Sciences</a>, archived from <a rel="nofollow" class="external text" href="http://www.ameinfo.com/142298.html">the original</a> on 3 April 2008, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=American+University+of+Beirut+establishes+the+Michael+Atiyah+Chair+in+Mathematical+Sciences&rft_id=http%3A%2F%2Fwww.ameinfo.com%2F142298.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> </li> <li id="cite_note-oxford-death-140"><a href="#cite_ref-oxford-death_140-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.maths.ox.ac.uk/node/31190">"Michael Atiyah 1929-2019"</a>. University of Oxford Mathematical Institute. 11 January 2019. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190111193302/https://www.maths.ox.ac.uk/node/31190">Archived</a> from the original on 11 January 2019. Retrieved 11 January 2019.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Michael+Atiyah+1929-2019&rft.pub=University+of+Oxford+Mathematical+Institute&rft.date=2019-01-11&rft_id=https%3A%2F%2Fwww.maths.ox.ac.uk%2Fnode%2F31190&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> </li> <li id="cite_note-royal-society-death-141"><a href="#cite_ref-royal-society-death_141-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://royalsociety.org/news/2019/01/tribute-to-former-president-of-the-royal-society-sir-michael-atiyah/">"A tribute to former President of the Royal Society Sir Michael Atiyah OM FRS (1929 - 2019)"</a>. The Royal Society. 11 January 2019. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190111173233/https://royalsociety.org/news/2019/01/tribute-to-former-president-of-the-royal-society-sir-michael-atiyah/">Archived</a> from the original on 11 January 2019. Retrieved 11 January 2019.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+tribute+to+former+President+of+the+Royal+Society+Sir+Michael+Atiyah+OM+FRS+%281929+-+2019%29&rft.pub=The+Royal+Society&rft.date=2019-01-11&rft_id=https%3A%2F%2Froyalsociety.org%2Fnews%2F2019%2F01%2Ftribute-to-former-president-of-the-royal-society-sir-michael-atiyah%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=16" title="Edit section: Sources">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-hanging-indents refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoyerHurtubiseMannMilgram1993" class="citation cs2">Boyer, Charles P.; <a href="/wiki/Jacques_Hurtubise_(mathematician)" title="Jacques Hurtubise (mathematician)">Hurtubise, J. C.</a>; Mann, B. M.; Milgram, R. J. (1993), "The topology of instanton moduli spaces. I. The Atiyah–Jones conjecture", <a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a>, Second Series, 137 (3): 561–609, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2946532">10.2307/2946532</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/0003-486X">0003-486X</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/2946532">2946532</a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1217348">1217348</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=The+topology+of+instanton+moduli+spaces.+I.+The+Atiyah%E2%80%93Jones+conjecture&rft.volume=137&rft.issue=3&rft.pages=561-609&rft.date=1993&rft.issn=0003-486X&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1217348%23id-name%3DMR&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2946532%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F2946532&rft.aulast=Boyer&rft.aufirst=Charles+P.&rft.au=Hurtubise%2C+J.+C.&rft.au=Mann%2C+B.+M.&rft.au=Milgram%2C+R.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarthHulekPetersVan_de_Ven2004" class="citation cs2">Barth, Wolf P.; Hulek, Klaus; Peters, Chris A.M.; Van de Ven, Antonius (2004), Compact Complex Surfaces, Berlin: Springer, p. 334, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-00832-3" title="Special:BookSources/978-3-540-00832-3"><bdi>978-3-540-00832-3</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Compact+Complex+Surfaces&rft.place=Berlin&rft.pages=334&rft.pub=Springer&rft.date=2004&rft.isbn=978-3-540-00832-3&rft.aulast=Barth&rft.aufirst=Wolf+P.&rft.au=Hulek%2C+Klaus&rft.au=Peters%2C+Chris+A.M.&rft.au=Van+de+Ven%2C+Antonius&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGel'fand1960" class="citation cs2">Gel'fand, Israel M. (1960), "On elliptic equations", Russ. Math. Surv., 15 (3): 113–123, <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/1960RuMaS..15..113G">1960RuMaS..15..113G</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%2Frm1960v015n03ABEH004094">10.1070/rm1960v015n03ABEH004094</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Russ.+Math.+Surv.&rft.atitle=On+elliptic+equations&rft.volume=15&rft.issue=3&rft.pages=113-123&rft.date=1960&rft_id=info%3Adoi%2F10.1070%2Frm1960v015n03ABEH004094&rft_id=info%3Abibcode%2F1960RuMaS..15..113G&rft.aulast=Gel%27fand&rft.aufirst=Israel+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. Reprinted in volume 1 of his collected works, p. 65–75, <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/0-387-13619-3" title="Special:BookSources/0-387-13619-3">0-387-13619-3</a>. On page 120 Gel'fand suggests that the index of an elliptic operator should be expressible in terms of topological data.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarderNarasimhan1975" class="citation cs2">Harder, G.; Narasimhan, M. S. 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(1965), Seminar on the Atiyah–Singer Index Theorem, Annals of Mathematics Studies, vol. 57, S.l.: Princeton Univ Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-08031-4" title="Special:BookSources/978-0-691-08031-4"><bdi>978-0-691-08031-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Seminar+on+the+Atiyah%E2%80%93Singer+Index+Theorem&rft.place=S.l.&rft.series=Annals+of+Mathematics+Studies&rft.pub=Princeton+Univ+Press&rft.date=1965&rft.isbn=978-0-691-08031-4&rft.aulast=Palais&rft.aufirst=Richard+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">. This describes the original proof of the index theorem. (Atiyah and Singer never published their original proof themselves, but only improved versions of it.)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSegal1968" class="citation cs2"><a href="/wiki/Graeme_Segal" title="Graeme Segal">Segal, Graeme B.</a> (1968), <a rel="nofollow" class="external text" href="http://www.numdam.org/item?id=PMIHES_1968__34__113_0">"The representation ring of a compact Lie group"</a>, Inst. Hautes Études Sci. Publ. Math., 34: 113–128, <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%2FBF02684592">10.1007/BF02684592</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:55847918">55847918</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Inst.+Hautes+%C3%89tudes+Sci.+Publ.+Math.&rft.atitle=The+representation+ring+of+a+compact+Lie+group&rft.volume=34&rft.pages=113-128&rft.date=1968&rft_id=info%3Adoi%2F10.1007%2FBF02684592&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A55847918%23id-name%3DS2CID&rft.aulast=Segal&rft.aufirst=Graeme+B.&rft_id=http%3A%2F%2Fwww.numdam.org%2Fitem%3Fid%3DPMIHES_1968__34__113_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYauChan1999" class="citation cs2">Yau, Shing-Tung; Chan, Raymond H., eds. (1999), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080808140555/http://www.intlpress.com/AJM/AJM-v03.php">"Sir Michael Atiyah: a great mathematician of the twentieth century"</a>, Asian J. Math., 3 (1), International Press: 1–332, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-57146-080-6" title="Special:BookSources/978-1-57146-080-6"><bdi>978-1-57146-080-6</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1701915">1701915</a>, archived from <a rel="nofollow" class="external text" href="http://www.intlpress.com/AJM/AJM-v03.php">the original</a> on 8 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Asian+J.+Math.&rft.atitle=Sir+Michael+Atiyah%3A+a+great+mathematician+of+the+twentieth+century&rft.volume=3&rft.issue=1&rft.pages=1-332&rft.date=1999&rft.isbn=978-1-57146-080-6&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1701915%23id-name%3DMR&rft_id=http%3A%2F%2Fwww.intlpress.com%2FAJM%2FAJM-v03.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYau2005" class="citation cs2">Yau, Shing-Tung, ed. (2005), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060207181013/http://www.intlpress.com/books/FoundersIndexTheory.php">The Founders of Index Theory: Reminiscences of Atiyah, Bott, Hirzebruch, and Singer</a>, International Press, p. 358, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-57146-120-9" title="Special:BookSources/978-1-57146-120-9"><bdi>978-1-57146-120-9</bdi></a>, archived from <a rel="nofollow" class="external text" href="http://www.intlpress.com/books/FoundersIndexTheory.php">the original</a> on 7 February 2006</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Founders+of+Index+Theory%3A+Reminiscences+of+Atiyah%2C+Bott%2C+Hirzebruch%2C+and+Singer&rft.pages=358&rft.pub=International+Press&rft.date=2005&rft.isbn=978-1-57146-120-9&rft_id=http%3A%2F%2Fwww.intlpress.com%2Fbooks%2FFoundersIndexTheory.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988">.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Michael_Atiyah&action=edit&section=17" title="Edit section: External links">edit</a>]</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 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.sister-logo{display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center}.mw-parser-output .sister-link{display:inline-block;margin-left:4px;width:182px;vertical-align:middle}@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-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-v2.svg"]{background-color:white}}</style><div role="navigation" 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"><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" /></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <a href="https://en.wikiquote.org/wiki/Michael_Atiyah" class="extiw" title="q:Michael Atiyah">Michael Atiyah</a>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://webofstories.com/gl/michael.atiyah">Michael Atiyah tells his life story</a> at <a href="/wiki/Web_of_Stories" title="Web of Stories">Web of Stories</a></li> <li><a rel="nofollow" class="external text" href="http://www.maths.ed.ac.uk/~aar/atiyah80.htm">The celebrations of Michael Atiyah's 80th birthday in Edinburgh, 20-24 April 2009</a></li> <li><a rel="nofollow" class="external text" href="http://www.maths.ed.ac.uk/~aar/confer/atiyahd.pdf">Mathematical descendants of Michael Atiyah</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080914135040/http://www.superstringtheory.com/people/atiyah.html">"Sir Michael Atiyah on math, physics and fun"</a>, superstringtheory.com, Official Superstring theory web site], archived from <a rel="nofollow" class="external text" href="http://www.superstringtheory.com/people/atiyah.html">the original</a> on 14 September 2008, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=superstringtheory.com&rft.atitle=Sir+Michael+Atiyah+on+math%2C+physics+and+fun&rft_id=http%3A%2F%2Fwww.superstringtheory.com%2Fpeople%2Fatiyah.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah" class="citation cs2">Atiyah, Michael, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110526211540/http://video.google.com/videoplay?docid=-5911099858813393554">Beauty in Mathematics (video, 3m14s)</a>, archived from <a rel="nofollow" class="external text" href="http://video.google.com/videoplay?docid=-5911099858813393554">the original</a> on 26 May 2011, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Beauty+in+Mathematics+%28video%2C+3m14s%29&rft.aulast=Atiyah&rft.aufirst=Michael&rft_id=http%3A%2F%2Fvideo.google.com%2Fvideoplay%3Fdocid%3D-5911099858813393554&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtiyah" class="citation cs2">Atiyah, Michael, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200803215854/http://online.itp.ucsb.edu/plecture/atiyah/">The nature of space (Online lecture)</a>, archived from <a rel="nofollow" class="external text" href="http://online.itp.ucsb.edu/plecture/atiyah/">the original</a> on 3 August 2020, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+nature+of+space+%28Online+lecture%29&rft.aulast=Atiyah&rft.aufirst=Michael&rft_id=http%3A%2F%2Fonline.itp.ucsb.edu%2Fplecture%2Fatiyah%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBatra2003" class="citation cs2">Batra, Amba (8 November 2003), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090208121300/http://cities.expressindia.com/fullstory.php?newsid=67555">Maths guru with Einstein's dream prefers chalk to mouse. (Interview with Atiyah.)</a>, Delhi newsline, archived from <a rel="nofollow" class="external text" href="http://cities.expressindia.com/fullstory.php?newsid=67555">the original</a> on 8 February 2009, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Maths+guru+with+Einstein%27s+dream+prefers+chalk+to+mouse.+%28Interview+with+Atiyah.%29&rft.pub=Delhi+newsline&rft.date=2003-11-08&rft.aulast=Batra&rft.aufirst=Amba&rft_id=http%3A%2F%2Fcities.expressindia.com%2Ffullstory.php%3Fnewsid%3D67555&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=30949">Michael Atiyah</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHalim1998" class="citation cs2">Halim, Hala (1998), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20040816122817/http://weekly.ahram.org.eg/1998/391/people.htm">"Michael Atiyah:Euclid and Victoria"</a>, Al-Ahram Weekly On-line, no. 391, archived from <a rel="nofollow" class="external text" href="http://weekly.ahram.org.eg/1998/391/people.htm">the original</a> on 16 August 2004, retrieved 26 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Al-Ahram+Weekly+On-line&rft.atitle=Michael+Atiyah%3AEuclid+and+Victoria&rft.issue=391&rft.date=1998&rft.aulast=Halim&rft.aufirst=Hala&rft_id=http%3A%2F%2Fweekly.ahram.org.eg%2F1998%2F391%2Fpeople.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMeek2004" class="citation cs2">Meek, James (21 April 2004), <a rel="nofollow" class="external text" href="https://www.theguardian.com/education/2004/apr/21/highereducation.uk">"Interview with Michael Atiyah"</a>, The Guardian, London, retrieved 14 August 2008</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=Interview+with+Michael+Atiyah&rft.date=2004-04-21&rft.aulast=Meek&rft.aufirst=James&rft_id=https%3A%2F%2Fwww.theguardian.com%2Feducation%2F2004%2Fapr%2F21%2Fhighereducation.uk&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080531085252/http://www.newton.ac.uk/history/atiyah.html">Sir Michael Atiyah FRS</a>, <a href="/wiki/Isaac_Newton_Institute" title="Isaac Newton Institute">Isaac Newton Institute</a>, archived from <a rel="nofollow" class="external text" href="http://www.newton.ac.uk/history/atiyah.html">the original</a> on 31 May 2008, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sir+Michael+Atiyah+FRS&rft.pub=Isaac+Newton+Institute&rft_id=http%3A%2F%2Fwww.newton.ac.uk%2Fhistory%2Fatiyah.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><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/notices/200406/comm-abel.pdf">"Atiyah and Singer receive 2004 Abel prize"</a> (PDF), <a href="/wiki/Notices_of_the_American_Mathematical_Society" title="Notices of the American Mathematical Society">Notices of the American Mathematical Society</a>, 51 (6): 650–651, 2006, retrieved 14 August 2008</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+American+Mathematical+Society&rft.atitle=Atiyah+and+Singer+receive+2004+Abel+prize&rft.volume=51&rft.issue=6&rft.pages=650-651&rft.date=2006&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F200406%2Fcomm-abel.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRaussenSkau2004" class="citation cs2">Raussen, Martin; Skau, Christian (24 May 2004), <a rel="nofollow" class="external text" href="http://www.abelprisen.no/en/prisvinnere/2004/interview_2004_1.html">Interview with Michael Atiyah and Isadore Singer</a>, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Interview+with+Michael+Atiyah+and+Isadore+Singer&rft.date=2004-05-24&rft.aulast=Raussen&rft.aufirst=Martin&rft.au=Skau%2C+Christian&rft_id=http%3A%2F%2Fwww.abelprisen.no%2Fen%2Fprisvinnere%2F2004%2Finterview_2004_1.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="http://owpdb.mfo.de/person_detail?id=124">Photos of Michael Francis Atiyah</a>, Oberwolfach photo collection, retrieved 14 August 2008</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Photos+of+Michael+Francis+Atiyah&rft.pub=Oberwolfach+photo+collection&rft_id=http%3A%2F%2Fowpdb.mfo.de%2Fperson_detail%3Fid%3D124&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWade2009" class="citation cs2">Wade, Mike (21 April 2009), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090507224829/http://www.timesonline.co.uk/tol/news/uk/scotland/article6143896.ece">"Maths and the bomb: Sir Michael Atiyah at 80"</a>, Physics Today (5), London: Timesonline: 13725, <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/2009PhT..2009e3725.">2009PhT..2009e3725.</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%2Fpt.5.023354">10.1063/pt.5.023354</a>, archived from <a rel="nofollow" class="external text" href="http://www.timesonline.co.uk/tol/news/uk/scotland/article6143896.ece">the original</a> on 7 May 2009, retrieved 12 May 2010</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=Maths+and+the+bomb%3A+Sir+Michael+Atiyah+at+80&rft.issue=5&rft.pages=13725&rft.date=2009-04-21&rft_id=info%3Adoi%2F10.1063%2Fpt.5.023354&rft_id=info%3Abibcode%2F2009PhT..2009e3725.&rft.aulast=Wade&rft.aufirst=Mike&rft_id=http%3A%2F%2Fwww.timesonline.co.uk%2Ftol%2Fnews%2Fuk%2Fscotland%2Farticle6143896.ece&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><a rel="nofollow" class="external text" href="http://celebratio.org/Atiyah_MF/article/36/">List of works of Michael Atiyah</a> from <a href="/wiki/Celebratio_Mathematica" class="mw-redirect" title="Celebratio Mathematica">Celebratio Mathematica</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFConnesKouneiher2019" class="citation journal cs1">Connes, Alain; Kouneiher, Joseph (2019). "Sir Michael Atiyah, a Knight Mathematician: A tribute to Michael Atiyah, an inspiration and a friend". Notices of the American Mathematical Society. 66 (10): 1660–1685. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1910.07851">1910.07851</a>. <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/2019arXiv191007851C">2019arXiv191007851C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fnoti1981">10.1090/noti1981</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:204743755">204743755</a>.</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+American+Mathematical+Society&rft.atitle=Sir+Michael+Atiyah%2C+a+Knight+Mathematician%3A+A+tribute+to+Michael+Atiyah%2C+an+inspiration+and+a+friend&rft.volume=66&rft.issue=10&rft.pages=1660-1685&rft.date=2019&rft_id=info%3Aarxiv%2F1910.07851&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A204743755%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1090%2Fnoti1981&rft_id=info%3Abibcode%2F2019arXiv191007851C&rft.aulast=Connes&rft.aufirst=Alain&rft.au=Kouneiher%2C+Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMichael+Atiyah" class="Z3988"></li> <li><a rel="nofollow" class="external text" href="https://www.npg.org.uk/collections/search/person.php?LinkID=mp6509">Portraits of Michael Atiyah</a> at the <a href="/wiki/National_Portrait_Gallery,_London" title="National Portrait Gallery, London">National Portrait Gallery, London</a></li></ul> <table class="wikitable succession-box noprint" style="margin:0.5em auto; font-size:small;clear:both;"> <tbody><tr> <th colspan="3" style="border-top: 5px solid lightgreen">Professional and academic associations </th></tr> <tr style="text-align:center;"> <td style="width:30%;" rowspan="1">Preceded by<div style="font-weight: bold"><a href="/wiki/George_Porter" title="George Porter">George Porter</a></div> </td> <td style="width: 40%; text-align: center;" rowspan="1">57th <a href="/wiki/Royal_Society" title="Royal Society">President of the Royal Society</a> 1990–1995 </td> <td style="width: 30%; text-align: center;" rowspan="1">Succeeded by<div style="font-weight: bold"><a href="/wiki/Aaron_Klug" title="Aaron Klug">Sir Aaron Klug</a></div> </td></tr> <tr style="text-align:center;"> <td style="width:30%;" rowspan="1">Preceded by<div style="font-weight: bold"><a href="/wiki/Lord_Sutherland_of_Houndwood" class="mw-redirect" title="Lord Sutherland of Houndwood">Lord Sutherland of Houndwood</a></div> </td> <td style="width: 40%; text-align: center;" rowspan="1">42nd <a href="/wiki/Royal_Society_of_Edinburgh" title="Royal Society of Edinburgh">President of the Royal Society of Edinburgh</a> 2005–2008 </td> <td style="width: 30%; text-align: center;" rowspan="1">Succeeded by<div style="font-weight: bold"><a href="/wiki/David_Wilson,_Baron_Wilson_of_Tillyorn" title="David Wilson, Baron Wilson of Tillyorn">David Wilson, Baron Wilson of Tillyorn</a></div> </td></tr> <tr> <th colspan="3" style="border-top: 5px solid #DAA520;">Academic offices </th></tr> <tr style="text-align:center;"> <td style="width:30%;" rowspan="1">Preceded by<div style="font-weight: bold"><a href="/wiki/Andrew_Huxley" title="Andrew Huxley">Sir Andrew Huxley</a></div> </td> <td style="width: 40%; text-align: center;" rowspan="1">35th <a href="/wiki/List_of_masters_of_Trinity_College,_Cambridge" title="List of masters of Trinity College, Cambridge">Master of Trinity College, Cambridge</a> 1990–1997 </td> <td style="width: 30%; text-align: center;" rowspan="1">Succeeded by<div style="font-weight: bold"><a href="/wiki/Amartya_Sen" title="Amartya Sen">Amartya Sen</a></div> </td></tr> <tr style="text-align:center;"> <td style="width:30%;" rowspan="1">Preceded by<div style="font-weight: bold"><a href="/wiki/George_Porter" title="George Porter">The Lord Porter of Luddenham</a></div> </td> <td style="width: 40%; text-align: center;" rowspan="1">4th <a href="/wiki/Chancellor_(education)" title="Chancellor (education)">Chancellor</a> of the <a href="/wiki/University_of_Leicester" title="University of Leicester">University of Leicester</a> 1995–2005 </td> <td style="width: 30%; text-align: center;" rowspan="1">Succeeded by<div style="font-weight: bold"><a href="/wiki/Peter_Williams_(physicist)" title="Peter Williams (physicist)">Sir Peter Williams</a></div> </td></tr> <tr> <th colspan="3" style="border-top: 5px solid #FFF179;">Awards and achievements </th></tr> <tr style="text-align:center;"> <td style="width:30%;" 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title="Isadore Singer">Isadore Singer</a></li></ul></div></li> <li><div class="hlist"><ul><li>2005  <a href="/wiki/Peter_Lax" title="Peter Lax">Peter Lax</a></li></ul></div></li> <li><div class="hlist"><ul><li>2006  <a href="/wiki/Lennart_Carleson" title="Lennart Carleson">Lennart Carleson</a></li></ul></div></li> <li><div class="hlist"><ul><li>2007  <a href="/wiki/S._R._Srinivasa_Varadhan" title="S. R. Srinivasa Varadhan">S. R. Srinivasa Varadhan</a></li></ul></div></li> <li><div class="hlist"><ul><li>2008  <a href="/wiki/John_G._Thompson" title="John G. Thompson">John G. Thompson</a></li><li><a href="/wiki/Jacques_Tits" title="Jacques Tits">Jacques Tits</a></li></ul></div></li> <li><div class="hlist"><ul><li>2009  <a href="/wiki/Mikhael_Gromov_(mathematician)" title="Mikhael Gromov (mathematician)">Mikhail Gromov</a></li></ul></div></li> <li><div class="hlist"><ul><li>2010  <a href="/wiki/John_Tate_(mathematician)" title="John Tate (mathematician)">John Tate</a></li></ul></div></li> <li><div class="hlist"><ul><li>2011  <a href="/wiki/John_Milnor" title="John Milnor">John Milnor</a></li></ul></div></li> <li><div class="hlist"><ul><li>2012  <a href="/wiki/Endre_Szemer%C3%A9di" title="Endre Szemerédi">Endre Szemerédi</a></li></ul></div></li> <li><div class="hlist"><ul><li>2013  <a href="/wiki/Pierre_Deligne" title="Pierre Deligne">Pierre Deligne</a></li></ul></div></li> <li><div class="hlist"><ul><li>2014  <a href="/wiki/Yakov_Sinai" title="Yakov Sinai">Yakov Sinai</a></li></ul></div></li> <li><div class="hlist"><ul><li>2015  <a href="/wiki/John_Forbes_Nash_Jr." title="John Forbes Nash Jr.">John Forbes Nash Jr.</a></li><li><a href="/wiki/Louis_Nirenberg" title="Louis Nirenberg">Louis Nirenberg</a></li></ul></div></li> <li><div class="hlist"><ul><li>2016  <a href="/wiki/Andrew_Wiles" title="Andrew Wiles">Andrew Wiles</a></li></ul></div></li> <li><div class="hlist"><ul><li>2017  <a href="/wiki/Yves_Meyer" title="Yves Meyer">Yves Meyer</a></li></ul></div></li> <li><div class="hlist"><ul><li>2018  <a href="/wiki/Robert_Langlands" title="Robert Langlands">Robert Langlands</a></li></ul></div></li> <li><div class="hlist"><ul><li>2019  <a href="/wiki/Karen_Uhlenbeck" title="Karen Uhlenbeck">Karen Uhlenbeck</a></li></ul></div></li> <li><div class="hlist"><ul><li>2020  <a href="/wiki/Hillel_Furstenberg" title="Hillel Furstenberg">Hillel Furstenberg</a></li><li><a href="/wiki/Grigory_Margulis" title="Grigory Margulis">Grigory Margulis</a></li></ul></div></li> <li><div class="hlist"><ul><li>2021  <a href="/wiki/L%C3%A1szl%C3%B3_Lov%C3%A1sz" title="László Lovász">László Lovász</a></li><li><a href="/wiki/Avi_Wigderson" title="Avi Wigderson">Avi Wigderson</a></li></ul></div></li> <li><div class="hlist"><ul><li>2022  <a href="/wiki/Dennis_Sullivan" title="Dennis Sullivan">Dennis Sullivan</a></li></ul></div></li> <li><div class="hlist"><ul><li>2023  <a href="/wiki/Luis_Caffarelli" title="Luis Caffarelli">Luis Caffarelli</a></li></ul></div></li> <li><div class="hlist"><ul><li>2024  <a href="/wiki/Michel_Talagrand" title="Michel Talagrand">Michel Talagrand</a></li></ul></div></li></ul> </div></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:r1126788409"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><link 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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:Fields_medalists" title="Template:Fields medalists"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Fields_medalists" title="Template talk:Fields medalists"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Fields_medalists" title="Special:EditPage/Template:Fields medalists"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Fields_Medalists" style="font-size:114%;margin:0 4em"><a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medalists</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd plainlist" style="width:100%;padding:0"><div style="padding:0 0.25em"><div class="div-col" style="column-width: 25.0em;text-align:left;"> <ul><li><div class="hlist"><ul><li>1936  <a href="/wiki/Lars_Ahlfors" title="Lars Ahlfors">Ahlfors</a></li><li><a href="/wiki/Jesse_Douglas" title="Jesse Douglas">Douglas</a></li></ul></div></li> <li><div class="hlist"><ul><li>1950  <a href="/wiki/Laurent_Schwartz" title="Laurent Schwartz">Schwartz</a></li><li><a href="/wiki/Atle_Selberg" title="Atle Selberg">Selberg</a></li></ul></div></li> <li><div class="hlist"><ul><li>1954  <a href="/wiki/Kunihiko_Kodaira" title="Kunihiko Kodaira">Kodaira</a></li><li><a href="/wiki/Jean-Pierre_Serre" title="Jean-Pierre Serre">Serre</a></li></ul></div></li> <li><div class="hlist"><ul><li>1958  <a href="/wiki/Klaus_Roth" title="Klaus Roth">Roth</a></li><li><a href="/wiki/Ren%C3%A9_Thom" title="René Thom">Thom</a></li></ul></div></li> <li><div class="hlist"><ul><li>1962  <a href="/wiki/Lars_H%C3%B6rmander" title="Lars Hörmander">Hörmander</a></li><li><a href="/wiki/John_Milnor" title="John Milnor">Milnor</a></li></ul></div></li> <li><div class="hlist"><ul><li>1966  <a class="mw-selflink selflink">Atiyah</a></li><li><a href="/wiki/Paul_Cohen" title="Paul Cohen">Cohen</a></li><li><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck</a></li><li><a href="/wiki/Stephen_Smale" title="Stephen Smale">Smale</a></li></ul></div></li> <li><div class="hlist"><ul><li>1970  <a href="/wiki/Alan_Baker_(mathematician)" title="Alan Baker (mathematician)">Baker</a></li><li><a href="/wiki/Heisuke_Hironaka" title="Heisuke Hironaka">Hironaka</a></li><li><a href="/wiki/Sergei_Novikov_(mathematician)" title="Sergei Novikov (mathematician)">Novikov</a></li><li><a href="/wiki/John_G._Thompson" title="John G. Thompson">Thompson</a></li></ul></div></li> <li><div class="hlist"><ul><li>1974  <a href="/wiki/Enrico_Bombieri" title="Enrico Bombieri">Bombieri</a></li><li><a href="/wiki/David_Mumford" title="David Mumford">Mumford</a></li></ul></div></li> <li><div class="hlist"><ul><li>1978  <a href="/wiki/Pierre_Deligne" title="Pierre Deligne">Deligne</a></li><li><a href="/wiki/Charles_Fefferman" title="Charles Fefferman">Fefferman</a></li><li><a href="/wiki/Grigory_Margulis" title="Grigory Margulis">Margulis</a></li><li><a href="/wiki/Daniel_Quillen" title="Daniel Quillen">Quillen</a></li></ul></div></li> <li><div class="hlist"><ul><li>1982  <a href="/wiki/Alain_Connes" title="Alain Connes">Connes</a></li><li><a href="/wiki/William_Thurston" title="William Thurston">Thurston</a></li><li><a href="/wiki/Shing-Tung_Yau" title="Shing-Tung Yau">Yau</a></li></ul></div></li> <li><div class="hlist"><ul><li>1986  <a href="/wiki/Simon_Donaldson" title="Simon Donaldson">Donaldson</a></li><li><a href="/wiki/Gerd_Faltings" title="Gerd Faltings">Faltings</a></li><li><a href="/wiki/Michael_Freedman" title="Michael Freedman">Freedman</a></li></ul></div></li> <li><div class="hlist"><ul><li>1990  <a href="/wiki/Vladimir_Drinfeld" title="Vladimir Drinfeld">Drinfeld</a></li><li><a href="/wiki/Vaughan_Jones" title="Vaughan Jones">Jones</a></li><li><a href="/wiki/Shigefumi_Mori" title="Shigefumi Mori">Mori</a></li><li><a href="/wiki/Edward_Witten" title="Edward Witten">Witten</a></li></ul></div></li> <li><div class="hlist"><ul><li>1994  <a href="/wiki/Jean_Bourgain" title="Jean Bourgain">Bourgain</a></li><li><a href="/wiki/Pierre-Louis_Lions" title="Pierre-Louis Lions">Lions</a></li><li><a href="/wiki/Jean-Christophe_Yoccoz" title="Jean-Christophe Yoccoz">Yoccoz</a></li><li><a href="/wiki/Efim_Zelmanov" title="Efim Zelmanov">Zelmanov</a></li></ul></div></li> <li><div class="hlist"><ul><li>1998  <a href="/wiki/Richard_Borcherds" title="Richard Borcherds">Borcherds</a></li><li><a href="/wiki/Timothy_Gowers" title="Timothy Gowers">Gowers</a></li><li><a href="/wiki/Maxim_Kontsevich" title="Maxim Kontsevich">Kontsevich</a></li><li><a href="/wiki/Curtis_T._McMullen" title="Curtis T. McMullen">McMullen</a></li></ul></div></li> <li><div class="hlist"><ul><li>2002  <a href="/wiki/Laurent_Lafforgue" title="Laurent Lafforgue">Lafforgue</a></li><li><a href="/wiki/Vladimir_Voevodsky" title="Vladimir Voevodsky">Voevodsky</a></li></ul></div></li> <li><div class="hlist"><ul><li>2006  <a href="/wiki/Andrei_Okounkov" title="Andrei Okounkov">Okounkov</a></li><li><a href="/wiki/Grigori_Perelman" title="Grigori Perelman">Perelman</a></li><li><a href="/wiki/Terence_Tao" title="Terence Tao">Tao</a></li><li><a href="/wiki/Wendelin_Werner" title="Wendelin Werner">Werner</a></li></ul></div></li> <li><div class="hlist"><ul><li>2010  <a href="/wiki/Elon_Lindenstrauss" title="Elon Lindenstrauss">Lindenstrauss</a></li><li><a href="/wiki/Ng%C3%B4_B%E1%BA%A3o_Ch%C3%A2u" title="Ngô Bảo Châu">Ngô</a></li><li><a href="/wiki/Stanislav_Smirnov" title="Stanislav Smirnov">Smirnov</a></li><li><a href="/wiki/C%C3%A9dric_Villani" title="Cédric Villani">Villani</a></li></ul></div></li> <li><div class="hlist"><ul><li>2014  <a href="/wiki/Artur_Avila" title="Artur Avila">Avila</a></li><li><a href="/wiki/Manjul_Bhargava" title="Manjul Bhargava">Bhargava</a></li><li><a href="/wiki/Martin_Hairer" title="Martin Hairer">Hairer</a></li><li><a href="/wiki/Maryam_Mirzakhani" title="Maryam Mirzakhani">Mirzakhani</a></li></ul></div></li> <li><div class="hlist"><ul><li>2018  <a href="/wiki/Caucher_Birkar" title="Caucher Birkar">Birkar</a></li><li><a href="/wiki/Alessio_Figalli" title="Alessio Figalli">Figalli</a></li><li><a href="/wiki/Peter_Scholze" title="Peter Scholze">Scholze</a></li><li><a href="/wiki/Akshay_Venkatesh" title="Akshay Venkatesh">Venkatesh</a></li></ul></div></li> <li><div class="hlist"><ul><li>2022  <a href="/wiki/Hugo_Duminil-Copin" title="Hugo Duminil-Copin">Duminil-Copin</a></li><li><a href="/wiki/June_Huh" title="June Huh">Huh</a></li><li><a href="/wiki/James_Maynard_(mathematician)" class="mw-redirect" title="James Maynard (mathematician)">Maynard</a></li><li><a href="/wiki/Maryna_Viazovska" title="Maryna Viazovska">Viazovska</a></li></ul></div></li></ul> </div></div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2" style="background:#d3d3d3;;font-weight:bold;"><div> <ul><li><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:Fields_Medalists" title="Category:Fields Medalists">Category</a></li> <li><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a> <a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Savilian_Professors" 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"><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:Savilian_Professors" title="Template:Savilian Professors"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Savilian_Professors" title="Template talk:Savilian Professors"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Savilian_Professors" title="Special:EditPage/Template:Savilian Professors"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Savilian_Professors" style="font-size:114%;margin:0 4em">Savilian Professors</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>Chairs established by <a href="/wiki/Henry_Savile_(Bible_translator)" title="Henry Savile (Bible translator)">Sir Henry Savile</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Savilian_Professor_of_Astronomy" title="Savilian Professor of Astronomy">Savilian Professors of Astronomy</a></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/John_Bainbridge_(astronomer)" title="John Bainbridge (astronomer)">John Bainbridge</a> (1620)</li> <li><a href="/wiki/John_Greaves" title="John Greaves">John Greaves</a> (1642)</li> <li><a href="/wiki/Seth_Ward_(bishop_of_Salisbury)" title="Seth Ward (bishop of Salisbury)">Seth Ward</a> (1649)</li> <li><a href="/wiki/Christopher_Wren" title="Christopher Wren">Christopher Wren</a> (1661)</li> <li><a href="/wiki/Edward_Bernard" title="Edward Bernard">Edward Bernard</a> (1673)</li> <li><a href="/wiki/David_Gregory_(mathematician)" title="David Gregory (mathematician)">David Gregory</a> (1691)</li> <li><a href="/wiki/John_Caswell" title="John Caswell">John Caswell</a> (1709)</li> <li><a href="/wiki/John_Keill" title="John Keill">John Keill</a> (1712)</li> <li><a href="/wiki/James_Bradley" title="James Bradley">James Bradley</a> (1721)</li> <li><a href="/wiki/Thomas_Hornsby" title="Thomas Hornsby">Thomas Hornsby</a> (1763)</li> <li><a href="/wiki/Abraham_Robertson" title="Abraham Robertson">Abraham Robertson</a> (1810)</li> <li><a href="/wiki/Stephen_Peter_Rigaud" title="Stephen Peter Rigaud">Stephen Rigaud</a> (1827)</li> <li><a href="/wiki/George_Johnson_(priest)" title="George Johnson (priest)">George Johnson</a> (1839)</li> <li><a href="/wiki/William_Fishburn_Donkin" title="William Fishburn Donkin">William Donkin</a> (1842)</li> <li><a href="/wiki/Charles_Pritchard" title="Charles Pritchard">Charles Pritchard</a> (1870)</li> <li><a href="/wiki/Herbert_Hall_Turner" title="Herbert Hall Turner">Herbert Turner</a> (1893)</li> <li><a href="/wiki/Harry_Hemley_Plaskett" title="Harry Hemley Plaskett">Harry Plaskett</a> (1932)</li> <li><a href="/wiki/Donald_Blackwell" title="Donald Blackwell">Donald Blackwell</a> (1960)</li> <li><a href="/wiki/George_Efstathiou" title="George Efstathiou">George Efstathiou</a> (1994)</li> <li><a href="/wiki/Joseph_Silk" title="Joseph Silk">Joseph Silk</a> (1999)</li> <li><a href="/wiki/Steven_Balbus" title="Steven Balbus">Steven Balbus</a> (2012)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Savilian_Professor_of_Geometry" title="Savilian Professor of Geometry">Savilian Professors of Geometry</a></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/Henry_Briggs_(mathematician)" title="Henry Briggs (mathematician)">Henry Briggs</a> (1619)</li> <li><a href="/wiki/Peter_Turner_(mathematician)" title="Peter Turner (mathematician)">Peter Turner</a> (1631)</li> <li><a href="/wiki/John_Wallis" title="John Wallis">John Wallis</a> (1649)</li> <li><a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a> (1704)</li> <li><a href="/wiki/Nathaniel_Bliss" title="Nathaniel Bliss">Nathaniel Bliss</a> (1742)</li> <li><a href="/wiki/Joseph_Betts" title="Joseph Betts">Joseph Betts</a> (1765)</li> <li><a href="/wiki/John_Smith_(anatomist_and_chemist)" title="John Smith (anatomist and chemist)">John Smith</a> (1766)</li> <li><a href="/wiki/Abraham_Robertson" title="Abraham Robertson">Abraham Robertson</a> (1797)</li> <li><a href="/wiki/Stephen_Peter_Rigaud" title="Stephen Peter Rigaud">Stephen Rigaud</a> (1810)</li> <li><a href="/wiki/Baden_Powell_(mathematician)" title="Baden Powell (mathematician)">Baden Powell</a> (1827)</li> <li><a href="/wiki/Henry_John_Stephen_Smith" title="Henry John Stephen Smith">Henry John Stephen Smith</a> (1861)</li> <li><a href="/wiki/James_Joseph_Sylvester" title="James Joseph Sylvester">James Joseph Sylvester</a> (1883)</li> <li><a href="/wiki/William_Esson" title="William Esson">William Esson</a> (1897)</li> <li><a href="/wiki/G._H._Hardy" title="G. H. Hardy">Godfrey Harold Hardy</a> (1919)</li> <li><a href="/wiki/Edward_Charles_Titchmarsh" title="Edward Charles Titchmarsh">Edward Charles Titchmarsh</a> (1931)</li> <li><a class="mw-selflink selflink">Michael Atiyah</a> (1963)</li> <li><a href="/wiki/Ioan_James" title="Ioan James">Ioan James</a> (1969)</li> <li><a href="/wiki/Richard_Taylor_(mathematician)" title="Richard Taylor (mathematician)">Richard Taylor</a> (1995)</li> <li><a href="/wiki/Nigel_Hitchin" title="Nigel Hitchin">Nigel Hitchin</a> (1997)</li> <li><a href="/wiki/Frances_Kirwan" title="Frances Kirwan">Frances Kirwan</a> (2017)</li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a> <a href="/wiki/Portal:University_of_Oxford" title="Portal:University of Oxford">University of Oxford portal</a></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="Presidents_of_the_Royal_Society" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Royal_Society_presidents" title="Template:Royal Society presidents"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Royal_Society_presidents" title="Template talk:Royal Society presidents"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Royal_Society_presidents" title="Special:EditPage/Template:Royal Society presidents"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Presidents_of_the_Royal_Society" style="font-size:114%;margin:0 4em"><a href="/wiki/List_of_presidents_of_the_Royal_Society" title="List of presidents of the Royal Society">Presidents</a> of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">17th century</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/William_Brouncker,_2nd_Viscount_Brouncker" title="William Brouncker, 2nd Viscount Brouncker">Viscount Brouncker</a> (1662)</li> <li><a href="/wiki/Joseph_Williamson_(English_politician)" title="Joseph Williamson (English politician)">Joseph Williamson</a> (1677)</li> <li><a href="/wiki/Christopher_Wren" title="Christopher Wren">Christopher Wren</a> (1680)</li> <li><a href="/wiki/Sir_John_Hoskyns,_2nd_Baronet" title="Sir John Hoskyns, 2nd Baronet">John Hoskyns</a> (1682)</li> <li><a href="/wiki/Cyril_Wyche" title="Cyril Wyche">Cyril Wyche</a> (1683)</li> <li><a href="/wiki/Samuel_Pepys" title="Samuel Pepys">Samuel Pepys</a> (1684)</li> <li><a href="/wiki/John_Vaughan,_3rd_Earl_of_Carbery" title="John Vaughan, 3rd Earl of Carbery">Earl of Carbery</a> (1686)</li> <li><a href="/wiki/Thomas_Herbert,_8th_Earl_of_Pembroke" title="Thomas Herbert, 8th Earl of Pembroke">Earl of Pembroke</a> (1689)</li> <li><a href="/wiki/Sir_Robert_Southwell_(diplomat)" class="mw-redirect" title="Sir Robert Southwell (diplomat)">Robert Southwell</a> (1690)</li> <li><a href="/wiki/Charles_Montagu,_1st_Earl_of_Halifax" title="Charles Montagu, 1st Earl of Halifax">Charles Montagu</a> (1695)</li> <li><a href="/wiki/John_Somers,_1st_Baron_Somers" title="John Somers, 1st Baron Somers">Lord Somers</a> (1698)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">18th century</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/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> (1703)</li> <li><a href="/wiki/Hans_Sloane" title="Hans Sloane">Hans Sloane</a> (1727)</li> <li><a href="/wiki/Martin_Folkes" title="Martin Folkes">Martin Folkes</a> (1741)</li> <li><a href="/wiki/George_Parker,_2nd_Earl_of_Macclesfield" title="George Parker, 2nd Earl of Macclesfield">Earl of Macclesfield</a> (1752)</li> <li><a href="/wiki/James_Douglas,_14th_Earl_of_Morton" title="James Douglas, 14th Earl of Morton">Earl of Morton</a> (1764)</li> <li><a href="/wiki/James_Burrow" title="James Burrow">James Burrow</a> (1768)</li> <li><a href="/wiki/James_West_(antiquary)" title="James West (antiquary)">James West</a> (1768)</li> <li><a href="/wiki/James_Burrow" title="James Burrow">James Burrow</a> (1772)</li> <li><a href="/wiki/John_Pringle_(physician)" class="mw-redirect" title="John Pringle (physician)">John Pringle</a> (1772)</li> <li><a href="/wiki/Joseph_Banks" title="Joseph Banks">Joseph Banks</a> (1778)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">19th century</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/William_Hyde_Wollaston" title="William Hyde Wollaston">William Hyde Wollaston</a> (1820)</li> <li><a href="/wiki/Humphry_Davy" title="Humphry Davy">Humphry Davy</a> (1820)</li> <li><a href="/wiki/Davies_Gilbert" title="Davies Gilbert">Davies Gilbert</a> (1827)</li> <li><a href="/wiki/Prince_Augustus_Frederick,_Duke_of_Sussex" title="Prince Augustus Frederick, Duke of Sussex">Duke of Sussex</a> (1830)</li> <li><a href="/wiki/Spencer_Compton,_2nd_Marquess_of_Northampton" title="Spencer Compton, 2nd Marquess of Northampton">Marquess of Northampton</a> (1838)</li> <li><a href="/wiki/William_Parsons,_3rd_Earl_of_Rosse" title="William Parsons, 3rd Earl of Rosse">Earl of Rosse</a> (1848)</li> <li><a href="/wiki/John_Wrottesley,_2nd_Baron_Wrottesley" title="John Wrottesley, 2nd Baron Wrottesley">Lord Wrottesley</a> (1854)</li> <li><a href="/wiki/Sir_Benjamin_Collins_Brodie,_1st_Baronet" title="Sir Benjamin Collins Brodie, 1st Baronet">Benjamin Collins Brodie</a> (1858)</li> <li><a href="/wiki/Edward_Sabine" title="Edward Sabine">Edward Sabine</a> (1861)</li> <li><a href="/wiki/George_Biddell_Airy" title="George Biddell Airy">George Biddell Airy</a> (1871)</li> <li><a href="/wiki/Joseph_Dalton_Hooker" title="Joseph Dalton Hooker">Joseph Dalton Hooker</a> (1873)</li> <li><a href="/wiki/William_Spottiswoode" title="William Spottiswoode">William Spottiswoode</a> (1878)</li> <li><a href="/wiki/Thomas_Henry_Huxley" title="Thomas Henry Huxley">Thomas Henry Huxley</a> (1883)</li> <li><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">George Gabriel Stokes</a> (1885)</li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Lord Kelvin</a> (1890)</li> <li><a href="/wiki/Joseph_Lister" title="Joseph Lister">Joseph Lister</a> (1895)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">20th century</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/William_Huggins" title="William Huggins">William Huggins</a> (1900)</li> <li><a href="/wiki/John_William_Strutt,_3rd_Baron_Rayleigh" title="John William Strutt, 3rd Baron Rayleigh">Lord Rayleigh</a> (1905)</li> <li><a href="/wiki/Archibald_Geikie" title="Archibald Geikie">Archibald Geikie</a> (1908)</li> <li><a href="/wiki/William_Crookes" title="William Crookes">William Crookes</a> (1913)</li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">J. J. Thomson</a> (1915)</li> <li><a href="/wiki/Charles_Scott_Sherrington" title="Charles Scott Sherrington">Charles Scott Sherrington</a> (1920)</li> <li><a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> (1925)</li> <li><a href="/wiki/Frederick_Gowland_Hopkins" title="Frederick Gowland Hopkins">Frederick Gowland Hopkins</a> (1930)</li> <li><a href="/wiki/William_Henry_Bragg" title="William Henry Bragg">William Henry Bragg</a> (1935)</li> <li><a href="/wiki/Henry_Hallett_Dale" title="Henry Hallett Dale">Henry Hallett Dale</a> (1940)</li> <li><a href="/wiki/Robert_Robinson_(organic_chemist)" class="mw-redirect" title="Robert Robinson (organic chemist)">Robert Robinson</a> (1945)</li> <li><a href="/wiki/Edgar_Adrian,_1st_Baron_Adrian" class="mw-redirect" title="Edgar Adrian, 1st Baron Adrian">Lord Adrian</a> (1950)</li> <li><a href="/wiki/Cyril_Norman_Hinshelwood" class="mw-redirect" title="Cyril Norman Hinshelwood">Cyril Norman Hinshelwood</a> (1955)</li> <li><a href="/wiki/Howard_Florey" title="Howard Florey">Howard Florey</a> (1960)</li> <li><a href="/wiki/Patrick_Blackett" title="Patrick Blackett">Patrick Blackett</a> (1965)</li> <li><a href="/wiki/Alan_Lloyd_Hodgkin" class="mw-redirect" title="Alan Lloyd Hodgkin">Alan Lloyd Hodgkin</a> (1970)</li> <li><a href="/wiki/Alexander_R._Todd" class="mw-redirect" title="Alexander R. Todd">Lord Todd</a> (1975)</li> <li><a href="/wiki/Andrew_Huxley" title="Andrew Huxley">Andrew Huxley</a> (1980)</li> <li><a href="/wiki/George_Porter" title="George Porter">George Porter</a> (1985)</li> <li><a class="mw-selflink selflink">Sir Michael Atiyah</a> (1990)</li> <li><a href="/wiki/Aaron_Klug" title="Aaron Klug">Sir Aaron Klug</a> (1995)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">21st century</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/Robert_May,_Baron_May_of_Oxford" title="Robert May, Baron May of Oxford">Lord May</a> (2000)</li> <li><a href="/wiki/Martin_Rees,_Baron_Rees_of_Ludlow" class="mw-redirect" title="Martin Rees, Baron Rees of Ludlow">Lord Rees</a> (2005)</li> <li><a href="/wiki/Paul_Nurse" title="Paul Nurse">Sir Paul Nurse</a> (2010)</li> <li><a href="/wiki/Venki_Ramakrishnan" title="Venki Ramakrishnan">Venki Ramakrishnan</a> (2015)</li> <li><a href="/wiki/Adrian_Smith_(statistician)" title="Adrian Smith (statistician)">Adrian Smith</a> (2020)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Copley_Medallists_(1951–2000)" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Copley_Medallists_1951%E2%80%932000" title="Template:Copley Medallists 1951–2000"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Copley_Medallists_1951%E2%80%932000" title="Template talk:Copley Medallists 1951–2000"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Copley_Medallists_1951%E2%80%932000" title="Special:EditPage/Template:Copley Medallists 1951–2000"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Copley_Medallists_(1951–2000)" style="font-size:114%;margin:0 4em"><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medallists</a> (1951–2000)</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/David_Keilin" title="David Keilin">David Keilin</a> (1951)</li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> (1952)</li> <li><a href="/wiki/Albert_Kluyver" title="Albert Kluyver">Albert Kluyver</a> (1953)</li> <li><a href="/wiki/E._T._Whittaker" title="E. T. Whittaker">E. T. Whittaker</a> (1954)</li> <li><a href="/wiki/Ronald_Fisher" title="Ronald Fisher">Ronald Fisher</a> (1955)</li> <li><a href="/wiki/Patrick_Blackett" title="Patrick Blackett">Patrick Blackett</a> (1956)</li> <li><a href="/wiki/Howard_Florey" title="Howard Florey">Howard Florey</a> (1957)</li> <li><a href="/wiki/John_Edensor_Littlewood" title="John Edensor Littlewood">John Edensor Littlewood</a> (1958)</li> <li><a href="/wiki/Macfarlane_Burnet" title="Macfarlane Burnet">Macfarlane Burnet</a> (1959)</li> <li><a href="/wiki/Harold_Jeffreys" title="Harold Jeffreys">Harold Jeffreys</a> (1960)</li> <li><a href="/wiki/Hans_Krebs_(biochemist)" title="Hans Krebs (biochemist)">Hans Krebs</a> (1961)</li> <li><a href="/wiki/Cyril_Norman_Hinshelwood" class="mw-redirect" title="Cyril Norman Hinshelwood">Cyril Norman Hinshelwood</a> (1962)</li> <li><a href="/wiki/Paul_Fildes" title="Paul Fildes">Paul Fildes</a> (1963)</li> <li><a href="/wiki/Sydney_Chapman_(mathematician)" title="Sydney Chapman (mathematician)">Sydney Chapman</a> (1964)</li> <li><a href="/wiki/Alan_Hodgkin" title="Alan Hodgkin">Alan Hodgkin</a> (1965)</li> <li><a href="/wiki/Lawrence_Bragg" title="Lawrence Bragg">Lawrence Bragg</a> (1966)</li> <li><a href="/wiki/Bernard_Katz" title="Bernard Katz">Bernard Katz</a> (1967)</li> <li><a href="/wiki/Tadeusz_Reichstein" title="Tadeusz Reichstein">Tadeusz Reichstein</a> (1968)</li> <li><a href="/wiki/Peter_Medawar" title="Peter Medawar">Peter Medawar</a> (1969)</li> <li><a href="/wiki/Alexander_R._Todd" class="mw-redirect" title="Alexander R. Todd">Alexander R. Todd</a> (1970)</li> <li><a href="/wiki/Norman_Pirie" title="Norman Pirie">Norman Pirie</a> (1971)</li> <li><a href="/wiki/Nevill_Francis_Mott" title="Nevill Francis Mott">Nevill Francis Mott</a> (1972)</li> <li><a href="/wiki/Andrew_Huxley" title="Andrew Huxley">Andrew Huxley</a> (1973)</li> <li><a href="/wiki/W._V._D._Hodge" title="W. V. D. Hodge">W. V. D. Hodge</a> (1974)</li> <li><a href="/wiki/Francis_Crick" title="Francis Crick">Francis Crick</a> (1975)</li> <li><a href="/wiki/Dorothy_Hodgkin" title="Dorothy Hodgkin">Dorothy Hodgkin</a> (1976)</li> <li><a href="/wiki/Frederick_Sanger" title="Frederick Sanger">Frederick Sanger</a> (1977)</li> <li><a href="/wiki/Robert_Burns_Woodward" title="Robert Burns Woodward">Robert Burns Woodward</a> (1978)</li> <li><a href="/wiki/Max_Perutz" title="Max Perutz">Max Perutz</a> (1979)</li> <li><a href="/wiki/Derek_Barton" title="Derek Barton">Derek Barton</a> (1980)</li> <li><a href="/wiki/Peter_D._Mitchell" title="Peter D. Mitchell">Peter D. Mitchell</a> (1981)</li> <li><a href="/wiki/John_Cornforth" title="John Cornforth">John Cornforth</a> (1982)</li> <li><a href="/wiki/Rodney_Robert_Porter" class="mw-redirect" title="Rodney Robert Porter">Rodney Robert Porter</a> (1983)</li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Subrahmanyan Chandrasekhar</a> (1984)</li> <li><a href="/wiki/Aaron_Klug" title="Aaron Klug">Aaron Klug</a> (1985)</li> <li><a href="/wiki/Rudolf_Peierls" title="Rudolf Peierls">Rudolf Peierls</a> (1986)</li> <li><a href="/wiki/Robin_Hill_(biochemist)" title="Robin Hill (biochemist)">Robin Hill</a> (1987)</li> <li><a class="mw-selflink selflink">Michael Atiyah</a> (1988)</li> <li><a href="/wiki/C%C3%A9sar_Milstein" title="César Milstein">César Milstein</a> (1989)</li> <li><a href="/wiki/Abdus_Salam" title="Abdus Salam">Abdus Salam</a> (1990)</li> <li><a href="/wiki/Sydney_Brenner" title="Sydney Brenner">Sydney Brenner</a> (1991)</li> <li><a href="/wiki/George_Porter" title="George Porter">George Porter</a> (1992)</li> <li><a href="/wiki/James_Watson" title="James Watson">James D. Watson</a> (1993)</li> <li><a href="/wiki/Frederick_Charles_Frank" title="Frederick Charles Frank">Frederick Charles Frank</a> (1994)</li> <li><a href="/wiki/Frank_Fenner" title="Frank Fenner">Frank Fenner</a> (1995)</li> <li><a href="/wiki/Alan_Cottrell" title="Alan Cottrell">Alan Cottrell</a> (1996)</li> <li><a href="/wiki/Hugh_Huxley" title="Hugh Huxley">Hugh Huxley</a> (1997)</li> <li><a href="/wiki/James_Lighthill" title="James Lighthill">James Lighthill</a> (1998)</li> <li><a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">John Maynard Smith</a> (1999)</li> <li><a href="/wiki/Alan_R._Battersby" title="Alan R. Battersby">Alan Battersby</a> (2000)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="De_Morgan_Medallists" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:De_Morgan_Medallists" title="Template:De Morgan Medallists"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:De_Morgan_Medallists" title="Template talk:De Morgan Medallists"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:De_Morgan_Medallists" title="Special:EditPage/Template:De Morgan Medallists"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="De_Morgan_Medallists" style="font-size:114%;margin:0 4em"><a href="/wiki/De_Morgan_Medal" title="De Morgan Medal">De Morgan Medallists</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arthur_Cayley" title="Arthur Cayley">Arthur Cayley</a> (1884)</li> <li><a href="/wiki/James_Joseph_Sylvester" title="James Joseph Sylvester">James Joseph Sylvester</a> (1887)</li> <li><a href="/wiki/John_William_Strutt,_3rd_Baron_Rayleigh" title="John William Strutt, 3rd Baron Rayleigh">Lord Rayleigh</a> (1890)</li> <li><a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a> (1893)</li> <li><a href="/wiki/Samuel_Roberts_(mathematician)" title="Samuel Roberts (mathematician)">S. Roberts</a> (1896)</li> <li><a href="/wiki/William_Burnside" title="William Burnside">William Burnside</a> (1899)</li> <li><a href="/wiki/A._G._Greenhill" class="mw-redirect" title="A. G. Greenhill">A. G. Greenhill</a> (1902)</li> <li><a href="/wiki/H._F._Baker" class="mw-redirect" title="H. F. Baker">H. F. Baker</a> (1905)</li> <li><a href="/wiki/J._W._L._Glaisher" class="mw-redirect" title="J. W. L. Glaisher">J. W. L. Glaisher</a> (1908)</li> <li><a href="/wiki/Horace_Lamb" title="Horace Lamb">Horace Lamb</a> (1911)</li> <li><a href="/wiki/J._Larmor" class="mw-redirect" title="J. Larmor">J. Larmor</a> (1914)</li> <li><a href="/wiki/W._H._Young" class="mw-redirect" title="W. H. Young">W. H. Young</a> (1917)</li> <li><a href="/wiki/E._W._Hobson" title="E. W. Hobson">E. W. Hobson</a> (1920)</li> <li><a href="/wiki/P._A._MacMahon" class="mw-redirect" title="P. A. MacMahon">P. A. MacMahon</a> (1923)</li> <li><a href="/wiki/Augustus_Edward_Hough_Love" title="Augustus Edward Hough Love">A. E. H. Love</a> (1926)</li> <li><a href="/wiki/Godfrey_Harold_Hardy" class="mw-redirect" title="Godfrey Harold Hardy">Godfrey Harold Hardy</a> (1929)</li> <li><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> (1932)</li> <li><a href="/wiki/E._T._Whittaker" title="E. T. Whittaker">E. T. Whittaker</a> (1935)</li> <li><a href="/wiki/John_Edensor_Littlewood" title="John Edensor Littlewood">J. E. Littlewood</a> (1938)</li> <li><a href="/wiki/Louis_Mordell" class="mw-redirect" title="Louis Mordell">Louis Mordell</a> (1941)</li> <li><a href="/wiki/Sydney_Chapman_(mathematician)" title="Sydney Chapman (mathematician)">Sydney Chapman</a> (1944)</li> <li><a href="/wiki/George_Neville_Watson" class="mw-redirect" title="George Neville Watson">George Neville Watson</a> (1947)</li> <li><a href="/wiki/A._S._Besicovitch" class="mw-redirect" title="A. S. Besicovitch">A. S. Besicovitch</a> (1950)</li> <li><a href="/wiki/Edward_Charles_Titchmarsh" title="Edward Charles Titchmarsh">E. C. Titchmarsh</a> (1953)</li> <li><a href="/wiki/G._I._Taylor" title="G. I. Taylor">G. I. Taylor</a> (1956)</li> <li><a href="/wiki/W._V._D._Hodge" title="W. V. D. Hodge">W. V. D. Hodge</a> (1959)</li> <li><a href="/wiki/Max_Newman" title="Max Newman">Max Newman</a> (1962)</li> <li><a href="/wiki/Philip_Hall" title="Philip Hall">Philip Hall</a> (1965)</li> <li><a href="/wiki/Mary_Cartwright" title="Mary Cartwright">Mary Cartwright</a> (1968)</li> <li><a href="/wiki/Kurt_Mahler" title="Kurt Mahler">Kurt Mahler</a> (1971)</li> <li><a href="/wiki/Graham_Higman" title="Graham Higman">Graham Higman</a> (1974)</li> <li><a href="/wiki/Claude_Ambrose_Rogers" title="Claude Ambrose Rogers">C. Ambrose Rogers</a> (1977)</li> <li><a class="mw-selflink selflink">Michael Atiyah</a> (1980)</li> <li><a href="/wiki/K._F._Roth" class="mw-redirect" title="K. F. Roth">K. F. Roth</a> (1983)</li> <li><a href="/wiki/J._W._S._Cassels" title="J. W. S. Cassels">J. W. S. Cassels</a> (1986)</li> <li><a href="/wiki/D._G._Kendall" class="mw-redirect" title="D. G. Kendall">D. G. Kendall</a> (1989)</li> <li><a href="/wiki/Albrecht_Fr%C3%B6hlich" title="Albrecht Fröhlich">Albrecht Fröhlich</a> (1992)</li> <li><a href="/wiki/W._K._Hayman" class="mw-redirect" title="W. K. Hayman">W. K. Hayman</a> (1995)</li> <li><a href="/wiki/R._A._Rankin" class="mw-redirect" title="R. A. Rankin">R. A. Rankin</a> (1998)</li> <li><a href="/wiki/Sandy_Green_(mathematician)" title="Sandy Green (mathematician)">J. A. Green</a> (2001)</li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a> (2004)</li> <li><a href="/wiki/Bryan_John_Birch" title="Bryan John Birch">Bryan John Birch</a> (2007)</li> <li><a href="/wiki/Keith_William_Morton" title="Keith William Morton">Keith William Morton</a> (2010)</li> <li><a href="/wiki/John_Griggs_Thompson" class="mw-redirect" title="John Griggs Thompson">John Griggs Thompson</a> (2013)</li> <li><a href="/wiki/Timothy_Gowers" title="Timothy Gowers">Timothy Gowers</a> (2016)</li> <li><a href="/wiki/Andrew_Wiles" title="Andrew Wiles">Andrew Wiles</a> (2019)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Masters_of_Trinity_College,_Cambridge" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Masters_of_Trinity_College,_Cambridge" title="Template:Masters of Trinity College, Cambridge"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Masters_of_Trinity_College,_Cambridge" title="Template talk:Masters of Trinity College, Cambridge"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Masters_of_Trinity_College,_Cambridge" title="Special:EditPage/Template:Masters of Trinity College, Cambridge"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Masters_of_Trinity_College,_Cambridge" style="font-size:114%;margin:0 4em"><a href="/wiki/List_of_masters_of_Trinity_College,_Cambridge" title="List of masters of Trinity College, Cambridge">Masters of Trinity College, Cambridge</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/John_Redman_(Trinity_College)" title="John Redman (Trinity College)">John Redman</a></li> <li><a href="/wiki/William_Bill" title="William Bill">William Bill</a></li> <li><a href="/wiki/John_Christopherson" title="John Christopherson">John Christopherson</a></li> <li><a href="/wiki/Robert_Beaumont_(Master_of_Trinity_College)" title="Robert Beaumont (Master of Trinity College)">Robert Beaumont</a></li> <li><a href="/wiki/John_Whitgift" title="John Whitgift">John Whitgift</a></li> <li><a href="/wiki/John_Still" title="John Still">John Still</a></li> <li><a href="/wiki/Thomas_Nevile" title="Thomas Nevile">Thomas Nevile</a></li> <li><a href="/wiki/John_Richardson_(translator)" title="John Richardson (translator)">John Richardson</a></li> <li><a href="/wiki/Leonard_Mawe" title="Leonard Mawe">Leonard Mawe</a></li> <li><a href="/wiki/Samuel_Brooke" title="Samuel Brooke">Samuel Brooke</a></li> <li><a href="/wiki/Thomas_Comber_(dean_of_Carlisle)" title="Thomas Comber (dean of Carlisle)">Thomas Comber</a></li> <li><a href="/wiki/Thomas_Hill_(Cambridge)" title="Thomas Hill (Cambridge)">Thomas Hill</a></li> <li><a href="/wiki/John_Arrowsmith_(scholar)" title="John Arrowsmith (scholar)">John Arrowsmith</a></li> <li><a href="/wiki/John_Wilkins" title="John Wilkins">John Wilkins</a></li> <li><a href="/wiki/Henry_Ferne" title="Henry Ferne">Henry Ferne</a></li> <li><a href="/wiki/John_Pearson_(bishop)" title="John Pearson (bishop)">John Pearson</a></li> <li><a href="/wiki/Isaac_Barrow" title="Isaac Barrow">Isaac Barrow</a></li> <li><a href="/wiki/John_North_(Trinity)" title="John North (Trinity)">John North</a></li> <li><a href="/wiki/John_Montagu_(Trinity)" title="John Montagu (Trinity)">John Montagu</a></li> <li><a href="/wiki/Richard_Bentley" title="Richard Bentley">Richard Bentley</a></li> <li><a href="/wiki/Robert_Smith_(mathematician)" title="Robert Smith (mathematician)">Robert Smith</a></li> <li><a href="/wiki/John_Hinchliffe" title="John Hinchliffe">John Hinchliffe</a></li> <li><a href="/wiki/Thomas_Postlethwaite" title="Thomas Postlethwaite">Thomas Postlethwaite</a></li> <li><a href="/wiki/William_Lort_Mansel" title="William Lort Mansel">William Lort Mansel</a></li> <li><a href="/wiki/Christopher_Wordsworth_(divine)" title="Christopher Wordsworth (divine)">Christopher Wordsworth</a></li> <li><a href="/wiki/William_Whewell" title="William Whewell">William Whewell</a></li> <li><a href="/wiki/William_Hepworth_Thompson" title="William Hepworth Thompson">William Hepworth Thompson</a></li> <li><a href="/wiki/Henry_Montagu_Butler" title="Henry Montagu Butler">Henry Montagu Butler</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">J. J. Thomson</a></li> <li><a href="/wiki/G._M._Trevelyan" title="G. M. Trevelyan">G. M. Trevelyan</a></li> <li><a href="/wiki/Edgar_Adrian" title="Edgar Adrian">Edgar Adrian</a></li> <li><a href="/wiki/Rab_Butler" title="Rab Butler">Rab Butler</a></li> <li><a href="/wiki/Alan_Hodgkin" title="Alan Hodgkin">Alan Hodgkin</a></li> <li><a href="/wiki/Andrew_Huxley" title="Andrew Huxley">Andrew Huxley</a></li> <li><a class="mw-selflink selflink">Michael Atiyah</a></li> <li><a href="/wiki/Amartya_Sen" title="Amartya Sen">Amartya Sen</a></li> <li><a href="/wiki/Martin_Rees" title="Martin Rees">Martin Rees</a></li> <li><a href="/wiki/Gregory_Winter" title="Gregory Winter">Gregory Winter</a></li> <li><a href="/wiki/Sally_Davies_(doctor)" title="Sally Davies (doctor)">Sally Davies</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="1" style="width:1px;padding:0 0 0 2px"><div><a href="/wiki/File:Trinity_College_(Cambridge)_shield.svg" class="mw-file-description"><img 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Template:Abel_Prize_laureates"," 4.91% 85.287 1 Template:Short_description"," 4.85% 84.290 42 Template:Hlist"," 4.08% 70.884 58 Template:Main_other"," 3.76% 65.322 1 Template:Sfn"]},"scribunto":{"limitreport-timeusage":{"value":"1.004","limit":"10.000"},"limitreport-memusage":{"value":13035424,"limit":52428800},"limitreport-logs":"anchor_id_list = table#1 {\n [\"CITEREFAtiyah\"] = 2,\n [\"CITEREFAtiyah,_Michael_F.BottPatodi1975\"] = 1,\n [\"CITEREFAtiyah,_Michael_F.Schmid1979\"] = 1,\n [\"CITEREFAtiyah1955\"] = 1,\n [\"CITEREFAtiyah1961\"] = 1,\n [\"CITEREFAtiyah1970\"] = 1,\n [\"CITEREFAtiyah1974\"] = 1,\n [\"CITEREFAtiyah1976\"] = 1,\n [\"CITEREFAtiyah1979\"] = 1,\n [\"CITEREFAtiyah1988a\"] = 1,\n [\"CITEREFAtiyah1988b\"] = 1,\n [\"CITEREFAtiyah1988c\"] = 1,\n [\"CITEREFAtiyah1988d\"] = 1,\n [\"CITEREFAtiyah1988e\"] = 1,\n [\"CITEREFAtiyah1989\"] = 1,\n [\"CITEREFAtiyah1990\"] = 1,\n [\"CITEREFAtiyah2000\"] = 1,\n [\"CITEREFAtiyah2004\"] = 1,\n [\"CITEREFAtiyah2007\"] = 1,\n [\"CITEREFAtiyah2010\"] = 1,\n [\"CITEREFAtiyah2014\"] = 2,\n [\"CITEREFAtiyah2016\"] = 1,\n [\"CITEREFAtiyahBott1966\"] = 1,\n [\"CITEREFAtiyahBott1967\"] = 1,\n [\"CITEREFAtiyahBott1968\"] = 1,\n [\"CITEREFAtiyahBottPatodi1973\"] = 1,\n [\"CITEREFAtiyahHirzebruch1961\"] = 1,\n [\"CITEREFAtiyahHitchin1988\"] = 1,\n [\"CITEREFAtiyahIagolnitzerChong2015\"] = 1,\n [\"CITEREFAtiyahMacdonald1969\"] = 1,\n [\"CITEREFAtiyahSchmid1977\"] = 1,\n [\"CITEREFAtiyahSegal1968\"] = 1,\n [\"CITEREFAtiyahSegal1969\"] = 1,\n [\"CITEREFAtiyahSinger1963\"] = 1,\n [\"CITEREFAtiyahSinger1968a\"] = 1,\n [\"CITEREFAtiyahSinger1968b\"] = 1,\n [\"CITEREFAtiyahSinger1971\"] = 2,\n [\"CITEREFBarthHulekPetersVan_de_Ven2004\"] = 1,\n [\"CITEREFBatra2003\"] = 2,\n [\"CITEREFBoyerHurtubiseMannMilgram1993\"] = 1,\n [\"CITEREFCartan1968\"] = 1,\n [\"CITEREFConnesKouneiher2019\"] = 1,\n [\"CITEREFDeligne\"] = 1,\n [\"CITEREFGel\u0026#039;fand1960\"] = 1,\n [\"CITEREFHalim1998\"] = 1,\n [\"CITEREFHarderNarasimhan1975\"] = 1,\n [\"CITEREFHitchin1972\"] = 1,\n [\"CITEREFMatsuki2002\"] = 1,\n [\"CITEREFMeek2004\"] = 1,\n [\"CITEREFPalais1965\"] = 1,\n [\"CITEREFRaafat\"] = 1,\n [\"CITEREFRaussenSkau2004\"] = 1,\n [\"CITEREFSegal1968\"] = 1,\n [\"CITEREFWade2009\"] = 1,\n [\"CITEREFYau2005\"] = 1,\n [\"CITEREFYauChan1999\"] = 1,\n}\ntemplate_list = table#1 {\n [\"!\"] = 1,\n [\"Abel Prize laureates\"] = 1,\n [\"Authority control\"] = 1,\n [\"Birth date\"] = 1,\n [\"Citation\"] = 74,\n [\"Citation needed\"] = 2,\n [\"Cite arXiv\"] = 2,\n [\"Cite journal\"] = 2,\n [\"Cite news\"] = 2,\n [\"Cite thesis\"] = 2,\n [\"Cite web\"] = 11,\n [\"Colend\"] = 2,\n [\"Copley Medallists 1951–2000\"] = 1,\n [\"DEFAULTSORT:Atiyah, Michael\"] = 1,\n [\"De Morgan Medallists\"] = 1,\n [\"Dead link\"] = 1,\n [\"Death date and age\"] = 1,\n [\"Div col\"] = 2,\n [\"EThOS\"] = 1,\n [\"Fields medalists\"] = 1,\n [\"Harv\"] = 21,\n [\"Harvnb\"] = 95,\n [\"Harvs\"] = 1,\n [\"IPAc-en\"] = 1,\n [\"ISBN\"] = 1,\n [\"Infobox scientist\"] = 1,\n [\"MacTutor Biography\"] = 1,\n [\"Main\"] = 4,\n [\"Masters of Trinity College, Cambridge\"] = 1,\n [\"MathGenealogy\"] = 3,\n [\"NPG name\"] = 1,\n [\"Plainlist\"] = 4,\n [\"Postnominals\"] = 1,\n [\"Primary sources\"] = 1,\n [\"Quote box\"] = 6,\n [\"Refbegin\"] = 1,\n [\"Refend\"] = 1,\n [\"Reflist\"] = 1,\n [\"Royal Society presidents 1900s\"] = 1,\n [\"S-aca\"] = 1,\n [\"S-ach\"] = 1,\n [\"S-aft\"] = 5,\n [\"S-bef\"] = 5,\n [\"S-break\"] = 4,\n [\"S-end\"] = 1,\n [\"S-npo\"] = 1,\n [\"S-start\"] = 1,\n [\"S-ttl\"] = 5,\n [\"Savilian Professors of Geometry\"] = 1,\n [\"Sfn\"] = 1,\n [\"Short description\"] = 1,\n [\"Sister project links\"] = 1,\n [\"Use dmy dates\"] = 1,\n [\"Webarchive\"] = 1,\n [\"Who's Who\"] = 1,\n}\narticle_whitelist = table#1 {\n}\n","limitreport-profile":[["?","280","25.0"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::callParserFunction","200","17.9"],["recursiveClone 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