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career</span> </div> </a> <button aria-controls="toc-Studies_and_university_career-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Studies and university career subsection</span> </button> <ul id="toc-Studies_and_university_career-sublist" class="vector-toc-list"> <li id="toc-University_career" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#University_career"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>University career</span> </div> </a> <ul id="toc-University_career-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Doctoral_students" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Doctoral_students"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Doctoral students</span> </div> </a> <ul id="toc-Doctoral_students-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Academic_contacts_in_Germany" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Academic_contacts_in_Germany"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Academic contacts in Germany</span> </div> </a> <ul id="toc-Academic_contacts_in_Germany-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Academic_contacts_in_Greece" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Academic_contacts_in_Greece"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Academic contacts in Greece</span> </div> </a> <ul id="toc-Academic_contacts_in_Greece-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Works" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Works"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Works</span> </div> </a> <button aria-controls="toc-Works-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Works subsection</span> </button> <ul id="toc-Works-sublist" class="vector-toc-list"> <li id="toc-Calculus_of_variations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Calculus_of_variations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Calculus of variations</span> </div> </a> <ul id="toc-Calculus_of_variations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Convex_geometry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Convex_geometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Convex geometry</span> </div> </a> <ul id="toc-Convex_geometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Real_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Real_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Real analysis</span> </div> </a> <ul id="toc-Real_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complex_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complex_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Complex analysis</span> </div> </a> <ul id="toc-Complex_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theory_of_measure" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Theory_of_measure"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Theory of measure</span> </div> </a> <ul id="toc-Theory_of_measure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Thermodynamics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Thermodynamics</span> </div> </a> <ul id="toc-Thermodynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Optics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Optics</span> </div> </a> <ul id="toc-Optics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historical" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Historical"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Historical</span> </div> </a> <ul id="toc-Historical-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-The_University_of_Smyrna" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#The_University_of_Smyrna"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>The University of Smyrna</span> </div> </a> <ul id="toc-The_University_of_Smyrna-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Linguistic_and_oratorical_talents" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Linguistic_and_oratorical_talents"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Linguistic and oratorical talents</span> </div> </a> <ul id="toc-Linguistic_and_oratorical_talents-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legacy" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Legacy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Legacy</span> </div> </a> <ul id="toc-Legacy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Publications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Publications"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Publications</span> </div> </a> <button aria-controls="toc-Publications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Publications subsection</span> </button> <ul id="toc-Publications-sublist" class="vector-toc-list"> <li id="toc-Journal_articles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Journal_articles"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Journal articles</span> </div> </a> <ul id="toc-Journal_articles-sublist" class="vector-toc-list"> </ul> </li> <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"> <span class="vector-toc-numb">7.2</span> <span>Books</span> </div> </a> <ul id="toc-Books-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Books_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Books_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Books</span> </div> </a> <ul id="toc-Books_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Biographical_articles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Biographical_articles"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.2</span> <span>Biographical articles</span> </div> </a> <ul id="toc-Biographical_articles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Encyclopaedias_and_reference_works" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Encyclopaedias_and_reference_works"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.3</span> <span>Encyclopaedias and reference works</span> </div> </a> <ul id="toc-Encyclopaedias_and_reference_works-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conferences" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Conferences"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.4</span> <span>Conferences</span> </div> </a> <ul id="toc-Conferences-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Constantin Carathéodory</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 36 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-36" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">36 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%B3%D8%B7%D9%86%D8%B7%D9%8A%D9%86_%D9%83%D8%A7%D8%B1%D8%A7%D8%AB%D9%8A%D9%88%D8%AF%D9%88%D8%B1%D9%8A" title="قسطنطين كاراثيودوري – Arabic" lang="ar" hreflang="ar" data-title="قسطنطين كاراثيودوري" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Konstantin_Karatodori" title="Konstantin Karatodori – Azerbaijani" lang="az" hreflang="az" data-title="Konstantin Karatodori" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%A9%D9%86%D8%B3%D8%AA%D8%A7%D9%86%D8%AA%DB%8C%D9%86_%DA%A9%D8%A7%D8%B1%D8%A7%D8%AA%D8%A6%D9%88%D8%AF%D9%88%D8%B1%DB%8C" title="کنستانتین کاراتئودوری – South Azerbaijani" lang="azb" hreflang="azb" data-title="کنستانتین کاراتئودوری" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A6%A8%E0%A7%8D%E0%A6%B8%E0%A6%A4%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A6%BF%E0%A6%A8_%E0%A6%95%E0%A6%BE%E0%A6%B0%E0%A6%BE%E0%A6%A4%E0%A7%87%E0%A6%93%E0%A6%A6%E0%A7%8B%E0%A6%B0%E0%A6%BF" title="কন্সতান্তিন কারাতেওদোরি – Bangla" lang="bn" hreflang="bn" data-title="কন্সতান্তিন কারাতেওদোরি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%86%D1%96%D0%BD_%D0%9A%D0%B0%D1%80%D0%B0%D1%82%D1%8D%D0%B0%D0%B4%D0%BE%D1%80%D1%8B" title="Канстанцін Каратэадоры – Belarusian" lang="be" hreflang="be" data-title="Канстанцін Каратэадоры" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B8%D0%BD_%D0%9A%D0%B0%D1%80%D0%B0%D1%82%D0%B5%D0%BE%D0%B4%D0%BE%D1%80%D0%B8" title="Константин Каратеодори – Bulgarian" lang="bg" hreflang="bg" data-title="Константин Каратеодори" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Catalan" lang="ca" hreflang="ca" data-title="Constantin Carathéodory" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Czech" lang="cs" hreflang="cs" data-title="Constantin Carathéodory" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – German" lang="de" hreflang="de" data-title="Constantin Carathéodory" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CF%89%CE%BD%CF%83%CF%84%CE%B1%CE%BD%CF%84%CE%AF%CE%BD%CE%BF%CF%82_%CE%9A%CE%B1%CF%81%CE%B1%CE%B8%CE%B5%CE%BF%CE%B4%CF%89%CF%81%CE%AE" title="Κωνσταντίνος Καραθεοδωρή – Greek" lang="el" hreflang="el" data-title="Κωνσταντίνος Καραθεοδωρή" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Spanish" lang="es" hreflang="es" data-title="Constantin Carathéodory" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Konstantino_Karateodori" title="Konstantino Karateodori – Esperanto" lang="eo" hreflang="eo" data-title="Konstantino Karateodori" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D9%86%D8%B3%D8%AA%D8%A7%D9%86%D8%AA%DB%8C%D9%86_%DA%A9%D8%A7%D8%B1%D8%A7%D8%AA%D8%A6%D9%88%D8%AF%D9%88%D8%B1%DB%8C" title="کنستانتین کاراتئودوری – Persian" lang="fa" hreflang="fa" data-title="کنستانتین کاراتئودوری" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – French" lang="fr" hreflang="fr" data-title="Constantin Carathéodory" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%BD%98%EC%8A%A4%ED%83%84%ED%8B%B0%EB%85%B8%EC%8A%A4_%EC%B9%B4%EB%9D%BC%ED%85%8C%EC%98%A4%EB%8F%84%EB%A6%AC" title="콘스탄티노스 카라테오도리 – Korean" lang="ko" hreflang="ko" data-title="콘스탄티노스 카라테오도리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%B6%D5%BD%D5%BF%D5%A1%D5%B6%D5%BF%D5%AB%D5%B6_%D4%BF%D5%A1%D6%80%D5%A1%D5%BF%D5%A5%D5%B8%D5%A4%D5%B8%D6%80%D5%AB" title="Կոնստանտին Կարատեոդորի – Armenian" lang="hy" hreflang="hy" data-title="Կոնստանտին Կարատեոդորի" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Italian" lang="it" hreflang="it" data-title="Constantin Carathéodory" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%95%D7%A0%D7%A1%D7%98%D7%A0%D7%98%D7%99%D7%9F_%D7%A7%D7%A8%D7%AA%D7%99%D7%90%D7%95%D7%93%D7%95%D7%A8%D7%99" title="קונסטנטין קרתיאודורי – Hebrew" lang="he" hreflang="he" data-title="קונסטנטין קרתיאודורי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%B0%D1%80%D0%B0%D1%82%D0%B5%D0%BE%D0%B4%D0%BE%D1%80%D0%B8_%D0%9A%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B8%D0%BD" title="Каратеодори Константин – Kazakh" lang="kk" hreflang="kk" data-title="Каратеодори Константин" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Haitian Creole" lang="ht" hreflang="ht" data-title="Constantin Carathéodory" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Constantinus_Caratheodores_(mathematicus)" title="Constantinus Caratheodores (mathematicus) – Latin" lang="la" hreflang="la" data-title="Constantinus Caratheodores (mathematicus)" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Hungarian" lang="hu" hreflang="hu" data-title="Constantin Carathéodory" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%83%D9%88%D9%86%D8%B3%D8%AA%D8%A7%D9%86%D8%AA%D9%8A%D9%86_%D9%83%D8%A7%D8%B1%D8%A7%D8%AB%D9%8A%D9%88%D8%AF%D9%88%D8%B1%D9%89" title="كونستانتين كاراثيودورى – Egyptian Arabic" lang="arz" hreflang="arz" data-title="كونستانتين كاراثيودورى" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B3%E3%83%B3%E3%82%B9%E3%82%BF%E3%83%B3%E3%83%86%E3%82%A3%E3%83%B3%E3%83%BB%E3%82%AB%E3%83%A9%E3%83%86%E3%82%AA%E3%83%89%E3%83%AA" title="コンスタンティン・カラテオドリ – Japanese" lang="ja" hreflang="ja" data-title="コンスタンティン・カラテオドリ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Constantin Carathéodory" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Piedmontese" lang="pms" hreflang="pms" data-title="Constantin Carathéodory" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Polish" lang="pl" hreflang="pl" data-title="Constantin Carathéodory" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li 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lang="ru" hreflang="ru" data-title="Каратеодори, Константин" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Slovak" lang="sk" hreflang="sk" data-title="Constantin Carathéodory" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Slovenian" lang="sl" hreflang="sl" data-title="Constantin Carathéodory" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory – Swedish" lang="sv" hreflang="sv" data-title="Constantin Carathéodory" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Konstantin_Karatodori" title="Konstantin Karatodori – Turkish" lang="tr" hreflang="tr" data-title="Konstantin Karatodori" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D1%81%D1%82%D1%8F%D0%BD%D1%82%D0%B8%D0%BD_%D0%9A%D0%B0%D1%80%D0%B0%D1%82%D0%B5%D0%BE%D0%B4%D0%BE%D1%80%D1%96" title="Костянтин Каратеодорі – Ukrainian" lang="uk" hreflang="uk" data-title="Костянтин Каратеодорі" data-language-autonym="Українська" 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searchaux" style="display:none">Greek mathematician (1873–1950)</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">For the Ottoman Greek doctor, see <a href="/wiki/Constantine_Caratheodory_(1802-1879)" class="mw-redirect" title="Constantine Caratheodory (1802-1879)">Constantine Caratheodory (1802-1879)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Constantin Carathéodory</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Caratheodory_(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Caratheodory_%28cropped%29.jpg/220px-Caratheodory_%28cropped%29.jpg" decoding="async" width="220" height="276" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Caratheodory_%28cropped%29.jpg/330px-Caratheodory_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Caratheodory_%28cropped%29.jpg/440px-Caratheodory_%28cropped%29.jpg 2x" data-file-width="804" data-file-height="1010" /></a></span><div class="infobox-caption">Constantin Carathéodory</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1873-09-13</span>)</span>13 September 1873<br /><div style="display:inline" class="birthplace"><a href="/wiki/Berlin" title="Berlin">Berlin</a>, <a href="/wiki/German_Empire" title="German Empire">German Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">2 February 1950<span style="display:none">(1950-02-02)</span> (aged 76)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Munich" title="Munich">Munich</a>, <a href="/wiki/West_Germany" title="West Germany">West Germany</a></div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><a href="/wiki/Greece" title="Greece">Greek</a></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a><br /><a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Carath%C3%A9odory_conjecture" title="Carathéodory conjecture">Carathéodory conjecture</a><br /><a href="/wiki/Carath%C3%A9odory_function" title="Carathéodory function">Carathéodory function</a><br /><a href="/wiki/Carath%C3%A9odory_metric" title="Carathéodory metric">Carathéodory metric</a><br /><a href="/wiki/Carath%C3%A9odory%27s_theorem_(disambiguation)" class="mw-redirect mw-disambig" title="Carathéodory's theorem (disambiguation)">Carathéodory theorems</a><br /><a href="/wiki/Carath%C3%A9odory%27s_criterion" title="Carathéodory's criterion">Carathéodory's criterion</a><br /><a href="/wiki/Carath%C3%A9odory%27s_lemma" class="mw-redirect" title="Carathéodory's lemma">Carathéodory's lemma</a><br /><a href="/wiki/Positive_harmonic_function#Carathéodory's_positivity_criterion_for_holomorphic_functions" title="Positive harmonic function">Carathéodory's positivity criterion for holomorphic functions</a><br /><a href="/wiki/Second_law_of_thermodynamics#Principle_of_Carathéodory" title="Second law of thermodynamics">Carathéodory's principle</a><br /><a href="/wiki/Sub-Riemannian_manifold" title="Sub-Riemannian manifold">Carnot–Carathéodory metric</a><br /><a href="/wiki/Adiabatic_accessibility" title="Adiabatic accessibility">Adiabatic accessibility</a><br /><a href="/wiki/Cyclic_polytope" title="Cyclic polytope">Cyclic polytope</a><br /><a href="/wiki/Prime_end" title="Prime end">Prime end</a><br /> General theory of <a href="/wiki/Outer_measure" title="Outer measure">outer measures</a><br />Axiomatic formulation of <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Calculus_of_variations" title="Calculus of variations">Calculus of variations</a> <br /> <a href="/wiki/Real_analysis" title="Real analysis">Real analysis</a> <br /> <a href="/wiki/Complex_analysis" title="Complex analysis">Complex analysis</a> <br /> <a href="/wiki/Measure_theory" class="mw-redirect" title="Measure theory">Measure theory</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"> <ul><li><a href="/wiki/University_of_Bonn" title="University of Bonn">University of Bonn</a></li> <li><a href="/wiki/University_of_Hannover" class="mw-redirect" title="University of Hannover">Hannover Technical High School</a></li> <li><a href="/wiki/Wroc%C5%82aw_University_of_Technology" class="mw-redirect" title="Wrocław University of Technology">Breslau Technical High School</a></li> <li><a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a></li> <li><a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a></li> <li><a href="/wiki/University_of_Munich" class="mw-redirect" title="University of Munich">University of Munich</a></li> <li><a href="/wiki/National_Technical_University_of_Athens" title="National Technical University of Athens">National Technical University of Athens</a></li> <li><a href="/wiki/Ionian_University_of_Smyrna" title="Ionian University of Smyrna">Ionian University of Smyrna</a></li></ul> </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/Hermann_Minkowski" title="Hermann Minkowski">Hermann Minkowski</a><sup id="cite_ref-mathgen1_1-0" class="reference"><a href="#cite_note-mathgen1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/Paul_Finsler" title="Paul Finsler">Paul Finsler</a><br /><a href="/wiki/Hans_Rademacher" title="Hans Rademacher">Hans Rademacher</a><br /><a href="/wiki/Georg_Aumann" title="Georg Aumann">Georg Aumann</a><br /><a href="/wiki/Hermann_Boerner" title="Hermann Boerner">Hermann Boerner</a><br /><a href="/wiki/Ernst_Peschl" title="Ernst Peschl">Ernst Peschl</a><br /><a href="/wiki/Wladimir_Seidel" title="Wladimir Seidel">Wladimir Seidel</a><br /><a href="/wiki/Nazim_Terzioglu" class="mw-redirect" title="Nazim Terzioglu">Nazım Terzioğlu</a><sup id="cite_ref-mathgen2_2-0" class="reference"><a href="#cite_note-mathgen2-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><br /><a href="/wiki/Xu_Ruiyun" title="Xu Ruiyun">Xu Ruiyun</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th colspan="2" class="infobox-header">Signature</th></tr><tr><td colspan="2" class="infobox-full-data"><span class="infobox-signature skin-invert" typeof="mw:File"><a href="/wiki/File:Caratheodory_signature.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Caratheodory_signature.png/150px-Caratheodory_signature.png" decoding="async" width="150" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Caratheodory_signature.png/225px-Caratheodory_signature.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Caratheodory_signature.png/300px-Caratheodory_signature.png 2x" data-file-width="463" data-file-height="77" /></a></span></td></tr></tbody></table> <p><b>Constantin Carathéodory</b> (<a href="/wiki/Greek_language" title="Greek language">Greek</a>: <span lang="el">Κωνσταντίνος Καραθεοδωρή</span>, <small><a href="/wiki/Romanization_of_Greek" title="Romanization of Greek">romanized</a>: </small><span title="Greek-language romanization"><i lang="el-Latn">Konstantinos Karatheodori</i></span>; 13 September 1873 – 2 February 1950) was a <a href="/wiki/Greeks" title="Greeks">Greek</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> who spent most of his professional career in Germany. He made significant contributions to real and complex analysis, the calculus of variations, and measure theory. He also created an axiomatic formulation of thermodynamics. Carathéodory is considered one of the greatest mathematicians of his era<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and the most renowned <a href="/wiki/Greek_mathematics" title="Greek mathematics">Greek mathematician</a> since <a href="/wiki/Ancient_history" title="Ancient history">antiquity</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Origins">Origins</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=1" title="Edit section: Origins"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tleft"><div class="thumbinner multiimageinner" style="width:204px;max-width:204px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Caratheodory_Constantin_and_Stephanos.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Caratheodory_Constantin_and_Stephanos.JPG/200px-Caratheodory_Constantin_and_Stephanos.JPG" decoding="async" width="200" height="322" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Caratheodory_Constantin_and_Stephanos.JPG/300px-Caratheodory_Constantin_and_Stephanos.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Caratheodory_Constantin_and_Stephanos.JPG/400px-Caratheodory_Constantin_and_Stephanos.JPG 2x" data-file-width="580" data-file-height="934" /></a></span></div><div class="thumbcaption">Carathéodory with his father, Stephanos, in 1900.</div></div></div><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Caratheodory_family.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Caratheodory_family.JPG/200px-Caratheodory_family.JPG" decoding="async" width="200" height="146" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Caratheodory_family.JPG/300px-Caratheodory_family.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Caratheodory_family.JPG/400px-Caratheodory_family.JPG 2x" data-file-width="840" data-file-height="615" /></a></span></div><div class="thumbcaption">Carathéodory (left) pictured sitting with his father, brother in law and sister, Carlsbad 1898</div></div></div></div></div> <p>Constantin Carathéodory was born in 1873 in <a href="/wiki/Berlin" title="Berlin">Berlin</a> to <a href="/wiki/Greeks" title="Greeks">Greek</a> parents and grew up in <a href="/wiki/Brussels" title="Brussels">Brussels</a>. His father <a href="/w/index.php?title=Stephanos_Karatheodori&action=edit&redlink=1" class="new" title="Stephanos Karatheodori (page does not exist)">Stephanos</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://tr.wikipedia.org/wiki/%C4%B0stefanaki_Karatodori_(diplomat)" class="extiw" title="tr:İstefanaki Karatodori (diplomat)">tr</a>]</span>, a lawyer, served as the <a href="/wiki/Ottoman_Empire" title="Ottoman Empire">Ottoman</a> ambassador to <a href="/wiki/Belgium" title="Belgium">Belgium</a>, <a href="/wiki/St._Petersburg" class="mw-redirect" title="St. Petersburg">St. Petersburg</a> and Berlin. His mother, Despina, née Petrokokkinos, was from the island of <a href="/wiki/Chios" title="Chios">Chios</a>. The Carathéodory family, originally from <a href="/w/index.php?title=Bosnochori&action=edit&redlink=1" class="new" title="Bosnochori (page does not exist)">Bosnochori</a> or <a href="/wiki/Vyssa" title="Vyssa">Vyssa</a>, was well established and respected in <a href="/wiki/Istanbul" title="Istanbul">Constantinople</a>, and its members held many important governmental positions. </p><p>The Carathéodory family spent 1874–75 in Constantinople, where Constantin's paternal grandfather lived, while his father Stephanos was on leave. Then in 1875 they went to Brussels when Stephanos was appointed there as Ottoman Ambassador. In Brussels, Constantin's younger sister Julia was born. The year 1879 was a tragic one for the family since Constantin's paternal grandfather died in that year, but much more tragically, Constantin's mother Despina died of <a href="/wiki/Pneumonia" title="Pneumonia">pneumonia</a> in <a href="/wiki/Cannes" title="Cannes">Cannes</a>. Constantin's maternal grandmother took on the task of bringing up Constantin and Julia in his father's home in Belgium. They employed a German maid who taught the children to speak German. Constantin was already bilingual in French and Greek by this time. </p><p>Constantin began his formal schooling at a private school in Vanderstock in 1881. He left after two years and then spent time with his father on a visit to Berlin, and also spent the winters of 1883–84 and 1884–85 on the <a href="/wiki/Italian_Riviera" title="Italian Riviera">Italian Riviera</a>. Back in Brussels in 1885 he attended a grammar school for a year where he first began to become interested in mathematics. In 1886, he entered the high school Athénée Royal d'Ixelles and studied there until his graduation in 1891. Twice during his time at this school Constantin won a prize as the best mathematics student in Belgium. </p><p>At this stage Carathéodory began training as a military engineer. He attended the École Militaire de Belgique from October 1891 to May 1895 and he also studied at the École d'Application from 1893 to 1896. In 1897 <a href="/wiki/Greco-Turkish_War_(1897)" title="Greco-Turkish War (1897)">a war broke out</a> between the Ottoman Empire and Greece. This put Carathéodory in a difficult position since he sided with the Greeks, yet his father served the government of the Ottoman Empire. Since he was a trained engineer he was offered a job in the British colonial service. This job took him to Egypt where he worked on the construction of the <a href="/wiki/Assiut" class="mw-redirect" title="Assiut">Assiut</a> dam until April 1900. During periods when construction work had to stop due to floods, he studied mathematics from some textbooks he had with him, such as <a href="/wiki/Camille_Jordan" title="Camille Jordan">Jordan's</a> <i>Cours d'Analyse</i> and <a href="/wiki/George_Salmon" title="George Salmon">Salmon's</a> text on the analytic geometry of <a href="/wiki/Conic_sections" class="mw-redirect" title="Conic sections">conic sections</a>. He also visited the <a href="/wiki/Pyramid_of_Cheops" class="mw-redirect" title="Pyramid of Cheops">Cheops pyramid</a> and made measurements which he wrote up and published in 1901.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> He also published a book on Egypt in the same year which contained a wealth of information on the history and geography of the country.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Studies_and_university_career">Studies and university career</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=2" title="Edit section: Studies and university career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Caratheodory_Constantine.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Caratheodory_Constantine.JPG/220px-Caratheodory_Constantine.JPG" decoding="async" width="220" height="333" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Caratheodory_Constantine.JPG/330px-Caratheodory_Constantine.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Caratheodory_Constantine.JPG/440px-Caratheodory_Constantine.JPG 2x" data-file-width="582" data-file-height="882" /></a><figcaption>Young Carathéodory</figcaption></figure> <p>Carathéodory studied engineering in <a href="/wiki/Belgium" title="Belgium">Belgium</a> at the <a href="/wiki/Royal_Military_Academy_(Belgium)" title="Royal Military Academy (Belgium)">Royal Military Academy</a>, where he was considered a charismatic and brilliant student. </p> <div class="mw-heading mw-heading3"><h3 id="University_career">University career</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=3" title="Edit section: University career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>1900 Studies at <a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a>.</li> <li>1902 Completed graduation at <a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a> (1904 Ph.D, 1905 Habilitation)</li> <li>1908 Dozent at <a href="/wiki/University_of_Bonn" title="University of Bonn">Bonn</a></li> <li>1909 Ordinary Professor at <a href="/wiki/University_of_Hannover" class="mw-redirect" title="University of Hannover">Hannover Technical High School</a>.</li> <li>1910 Ordinary Professor at <a href="/wiki/Wroc%C5%82aw_University_of_Technology" class="mw-redirect" title="Wrocław University of Technology">Breslau Technical High School</a>.</li> <li>1913 Professor following Klein at <a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a>.</li> <li>1919 Professor at <a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a></li> <li>1919 Elected to <a href="/wiki/Prussian_Academy_of_Science" class="mw-redirect" title="Prussian Academy of Science">Prussian Academy of Science</a>.</li> <li>1920 University Dean at <a href="/wiki/Ionian_University_of_Smyrna" title="Ionian University of Smyrna">Ionian University of Smyrna</a> (later, <a href="/wiki/University_of_the_Aegean" title="University of the Aegean">University of the Aegean</a>).</li> <li>1922 Professor at <a href="/wiki/University_of_Athens" class="mw-redirect" title="University of Athens">University of Athens</a>.</li> <li>1922 Professor at <a href="/wiki/Athens_Polytechnic" class="mw-redirect" title="Athens Polytechnic">Athens Polytechnic</a>.</li> <li>1924 Professor following Lindemann at <a href="/wiki/University_of_Munich" class="mw-redirect" title="University of Munich">University of Munich</a>.</li> <li>1938 Retirement from professorship. Continued working at Bavarian Academy of Science</li></ul> <div class="mw-heading mw-heading3"><h3 id="Doctoral_students">Doctoral students</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=4" title="Edit section: Doctoral students"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Carathéodory had about 20 doctoral students among these being <a href="/wiki/Hans_Rademacher" title="Hans Rademacher">Hans Rademacher</a>, known for his work on analysis and number theory, and <a href="/wiki/Paul_Finsler" title="Paul Finsler">Paul Finsler</a> known for his creation of <a href="/wiki/Finsler_space" class="mw-redirect" title="Finsler space">Finsler space</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Academic_contacts_in_Germany">Academic contacts in Germany</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=5" title="Edit section: Academic contacts in Germany"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Caratheodory_and_Fej%C3%A9r.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Caratheodory_and_Fej%C3%A9r.JPG/200px-Caratheodory_and_Fej%C3%A9r.JPG" decoding="async" width="200" height="262" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Caratheodory_and_Fej%C3%A9r.JPG/300px-Caratheodory_and_Fej%C3%A9r.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Caratheodory_and_Fej%C3%A9r.JPG/400px-Caratheodory_and_Fej%C3%A9r.JPG 2x" data-file-width="648" data-file-height="850" /></a><figcaption>Carathéodory (left) with Hungarian mathematician Lipót Fejér (1880–1959) (standing to the right).</figcaption></figure><p>Carathéodory had numerous contacts in Germany. They included such famous names as: <a href="/wiki/Hermann_Minkowski" title="Hermann Minkowski">Hermann Minkowski</a>, <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a>, <a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a>, <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>, <a href="/wiki/Edmund_Landau" title="Edmund Landau">Edmund Landau</a>, <a href="/wiki/Hermann_Amandus_Schwarz" class="mw-redirect" title="Hermann Amandus Schwarz">Hermann Amandus Schwarz</a>, and <a href="/wiki/Lip%C3%B3t_Fej%C3%A9r" title="Lipót Fejér">Lipót Fejér</a>. During the difficult period of World War II, his close associates at the Bavarian Academy of Sciences were Perron and Tietze. </p><p>Einstein, then a member of the Prussian Academy of Sciences in Berlin, was working on his general theory of relativity when he contacted Carathéodory for clarifications on the <a href="/wiki/Hamilton%E2%80%93Jacobi_equation" title="Hamilton–Jacobi equation">Hamilton-Jacobi equation</a> and <a href="/wiki/Canonical_transformation" title="Canonical transformation">canonical transformations</a>. He wanted to see a satisfactory derivation of the former and the origins of the latter. Einstein told Carathéodory his derivation was "beautiful" and recommended its publication in the <i>Annalen der Physik.</i> Einstein employed the former in a 1917 paper titled <i>Zum Quantensatz von Sommerfeld und Epstein</i> (On the Quantum Theorem of Sommerfeld and Epstein). Carathéodory explained some fundamental details of the canonical transformations and referred Einstein to <a href="/wiki/E._T._Whittaker" title="E. T. Whittaker">E.T. Whittaker's</a> <i><a href="/wiki/Analytical_Dynamics_of_Particles_and_Rigid_Bodies" title="Analytical Dynamics of Particles and Rigid Bodies">Analytical Dynamics</a></i>. Einstein was trying to solve the problem of "closed time-lines" or the geodesics corresponding to the closed trajectory of light and free particles in a static universe, which he introduced in 1917.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Landau and Schwarz stimulated his interest in the study of complex analysis.<sup id="cite_ref-:0_8-0" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Academic_contacts_in_Greece">Academic contacts in Greece</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=6" title="Edit section: Academic contacts in Greece"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While in Germany, Carathéodory retained numerous links with the Greek academic world, details of which can be found in Georgiadou's book. He was directly involved with the reorganization of Greek universities. An especially close friend and colleague in Athens was Nicolaos Kritikos who had attended his lectures at Göttingen, later going with him to Smyrna, then becoming professor at Athens Polytechnic. Kritikos and Carathéodory helped the Greek topologist <a href="/wiki/Christos_Papakyriakopoulos" title="Christos Papakyriakopoulos">Christos Papakyriakopoulos</a> take a doctorate in topology at Athens University in 1943 under very difficult circumstances. While teaching at Athens University, Carathéodory had Evangelos Stamatis as an undergraduate student, who subsequently achieved considerable distinction as a scholar of ancient Greek mathematical classics.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=7" title="Edit section: Works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Calculus_of_variations">Calculus of variations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=8" title="Edit section: Calculus of variations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In his doctoral dissertation, Carathéodory showed how to extend solutions to discontinuous cases and studied isoperimetric problems.<sup id="cite_ref-:0_8-1" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Previously, between the mid-1700s to the mid-1800s, <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>, <a href="/wiki/Adrien-Marie_Legendre" title="Adrien-Marie Legendre">Adrien-Marie Legendre</a>, and <a href="/wiki/Carl_Gustav_Jacob_Jacobi" title="Carl Gustav Jacob Jacobi">Carl Gustav Jacob Jacobi</a> were able to establish necessary but insufficient conditions for the existence of a strong relative minimum. In 1879, <a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a> added a fourth that does indeed guarantee such a quantity exists.<sup id="cite_ref-:2_10-0" class="reference"><a href="#cite_note-:2-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Carathéodory constructed his method for deriving sufficient conditions based on the use of the Hamilton–Jacobi equation to construct a field of extremals. The ideas are closely related to light propagation in optics. The method became known as <i>Carathéodory's method of equivalent variational problems</i> or <i>the royal road to the calculus of variations</i>.<sup id="cite_ref-:2_10-1" class="reference"><a href="#cite_note-:2-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> A key advantage of Carathéodory's work on this topic is that it illuminates the relation between the calculus of variations and partial differential equations.<sup id="cite_ref-:0_8-2" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> It allows for quick and elegant derivations of conditions of sufficiency in the calculus of variations and leads directly to the <a href="/wiki/Euler%E2%80%93Lagrange_equation" title="Euler–Lagrange equation">Euler-Lagrange equation</a> and the Weierstrass condition. He published his <i>Variationsrechnung und Partielle Differentialgleichungen Erster Ordnung</i> (Calculus of Variations and First-order Partial Differential Equations) in 1935.<sup id="cite_ref-:2_10-2" class="reference"><a href="#cite_note-:2-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>More recently, Carathéodory's work on the calculus of variations and the Hamilton-Jacobi equation has been taken into the theory of <a href="/wiki/Optimal_control" title="Optimal control">optimal control</a> and dynamic programming.<sup id="cite_ref-:2_10-3" class="reference"><a href="#cite_note-:2-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Convex_geometry">Convex geometry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=9" title="Edit section: Convex geometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Caratheodorys_theorem_example.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Caratheodorys_theorem_example.png/200px-Caratheodorys_theorem_example.png" decoding="async" width="200" height="185" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Caratheodorys_theorem_example.png/300px-Caratheodorys_theorem_example.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Caratheodorys_theorem_example.png/400px-Caratheodorys_theorem_example.png 2x" data-file-width="475" data-file-height="439" /></a><figcaption>An illustration of <a href="/wiki/Carath%C3%A9odory%27s_theorem_(convex_hull)" title="Carathéodory's theorem (convex hull)">Carathéodory's theorem (convex hull)</a> for a square in <b>R</b><sup>2</sup>.</figcaption></figure><p><a href="/wiki/Carath%C3%A9odory%27s_theorem_(convex_hull)" title="Carathéodory's theorem (convex hull)">Carathéodory's theorem</a> in convex geometry states that if a point <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a713426956296f1668fce772df3c60b9dde8a685" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.77ex; height:2.676ex;" alt="{\displaystyle \mathbb {R} ^{d}}"></span> lies in the <a href="/wiki/Convex_hull" title="Convex hull">convex hull</a> of a set <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>, then <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> can be written as the convex combination of at most <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/056e0c06c828dbe71a0f9021b2828ff176a3d337" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.219ex; height:2.343ex;" alt="{\displaystyle d+1}"></span> points in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>. Namely, there is a subset <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>P</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef4efa52c8f47f06136f6ebfd1d68c1249aaca39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.506ex; height:2.509ex;" alt="{\displaystyle P'}"></span> of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> consisting of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/056e0c06c828dbe71a0f9021b2828ff176a3d337" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.219ex; height:2.343ex;" alt="{\displaystyle d+1}"></span> or fewer points such that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> lies in the convex hull of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>P</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef4efa52c8f47f06136f6ebfd1d68c1249aaca39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.506ex; height:2.509ex;" alt="{\displaystyle P'}"></span>. Equivalently, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> lies in an <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>-<a href="/wiki/Simplex" title="Simplex">simplex</a> with vertices in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\leq d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>≤</mo> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\leq d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ab44f2a3044ef07ab2fd7c24439961bc8643d0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.363ex; height:2.343ex;" alt="{\displaystyle r\leq d}"></span>. The smallest <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> that makes the last statement valid for each <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> in the convex hull of <i>P</i> is defined as the <i>Carathéodory's number</i> of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>. Depending on the properties of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>, upper bounds lower than the one provided by Carathéodory's theorem can be obtained.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>He is credited with the authorship of the <a href="/wiki/Carath%C3%A9odory_conjecture" title="Carathéodory conjecture">Carathéodory conjecture</a> claiming that a closed convex surface admits at least two <a href="/wiki/Umbilic_point" class="mw-redirect" title="Umbilic point">umbilic points</a>. As of 2021, this conjecture remained unproven despite having attracted a large amount of research. </p> <div class="mw-heading mw-heading3"><h3 id="Real_analysis">Real analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=10" title="Edit section: Real analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>He proved an <a href="/wiki/Carath%C3%A9odory%27s_existence_theorem" title="Carathéodory's existence theorem">existence theorem</a> for the solution to ordinary differential equations under mild regularity conditions. </p><p>Another theorem of his on the derivative of a function at a point could be used to prove the <a href="/wiki/Chain_rule" title="Chain rule">Chain Rule</a> and the formula for the <a href="/wiki/Inverse_functions_and_differentiation" class="mw-redirect" title="Inverse functions and differentiation">derivative of inverse functions</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Complex_analysis">Complex analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=11" title="Edit section: Complex analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>He greatly extended the theory of <a href="/wiki/Conformal_transformation" class="mw-redirect" title="Conformal transformation">conformal transformation</a><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> proving his <a href="/wiki/Carath%C3%A9odory%27s_theorem_(conformal_mapping)" title="Carathéodory's theorem (conformal mapping)">theorem</a> about the extension of conformal mapping to the boundary of Jordan domains. In studying boundary correspondence he originated the theory of <a href="/wiki/Prime_end" title="Prime end">prime ends</a>.<sup id="cite_ref-:0_8-3" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> He exhibited an elementary proof of the <a href="/wiki/Schwarz_lemma" title="Schwarz lemma">Schwarz lemma</a>.<sup id="cite_ref-:0_8-4" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Carathéodory was also interested in the theory of functions of multiple complex variables. In his investigations on this subject he sought analogs of classical results from the single-variable case. He proved that a ball in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {C} ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f43d6ec8a1e1fe5a85aec0dd9bdcd45ae09b06b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.732ex; height:2.676ex;" alt="{\displaystyle \mathbb {C} ^{2}}"></span> is not holomorphically equivalent to the bidisc.<sup id="cite_ref-:0_8-5" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Theory_of_measure">Theory of measure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=12" title="Edit section: Theory of measure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>He is credited with the <a href="/wiki/Carath%C3%A9odory_extension_theorem" class="mw-redirect" title="Carathéodory extension theorem">Carathéodory extension theorem</a> which is fundamental to modern measure theory. Later Carathéodory extended the theory from sets to <a href="/wiki/Boolean_algebra_(structure)" title="Boolean algebra (structure)">Boolean algebras</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Thermodynamics">Thermodynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=13" title="Edit section: Thermodynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Thermodynamics had been a subject dear to Carathéodory since his time in Belgium.<sup id="cite_ref-:1_16-0" class="reference"><a href="#cite_note-:1-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> In 1909, he published a pioneering work "Investigations on the Foundations of Thermodynamics"<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> in which he formulated the second law of thermodynamics axiomatically, that is, without the use of Carnot engines and refrigerators and only by mathematical reasoning. This is yet another version of the second law, alongside the statements of <a href="/wiki/Clausius_theorem" title="Clausius theorem">Clausius</a>, and of <a href="/wiki/Kelvin%E2%80%93Planck_statement" class="mw-redirect" title="Kelvin–Planck statement">Kelvin and Planck</a>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Carathéodory's version attracted the attention of some of the top physicists of the time, including Max Planck, Max Born, and Arnold Sommerfeld.<sup id="cite_ref-:0_8-6" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> According to Bailyn's survey of thermodynamics, Carathéodory's approach is called "mechanical," rather than "thermodynamic."<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Max Born acclaimed this "first axiomatically rigid foundation of thermodynamics" and he expressed his enthusiasm in his letters to Einstein.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_16-1" class="reference"><a href="#cite_note-:1-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> However, Max Planck had some misgivings<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> in that while he was impressed by Carathéodory's mathematical prowess, he did not accept that this was a fundamental formulation, given the statistical nature of the second law.<sup id="cite_ref-:1_16-2" class="reference"><a href="#cite_note-:1-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>In his theory he simplified the basic concepts, for instance <i>heat</i> is not an essential concept but a derived one.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> He formulated the axiomatic principle of irreversibility in thermodynamics stating that inaccessibility of states is related to the existence of entropy, where temperature is the integration function. The <a href="/wiki/Second_Law_of_Thermodynamics" class="mw-redirect" title="Second Law of Thermodynamics">Second Law of Thermodynamics</a> was expressed via the following axiom: "In the neighbourhood of any initial state, there are states which cannot be approached arbitrarily close through adiabatic changes of state." In this connexion he coined the term <a href="/wiki/Adiabatic_accessibility" title="Adiabatic accessibility">adiabatic accessibility</a>.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Optics">Optics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=14" title="Edit section: Optics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Carathéodory's work in <a href="/wiki/Optics" title="Optics">optics</a> is closely related to his method in the calculus of variations. In 1926 he gave a strict and general proof that no system of lenses and mirrors can avoid <a href="/wiki/Aberration_in_optical_systems" class="mw-redirect" title="Aberration in optical systems">aberration</a>, except for the trivial case of plane mirrors. In his later work he gave the theory of the <a href="/wiki/Schmidt_telescope" class="mw-redirect" title="Schmidt telescope">Schmidt telescope</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> In his <i>Geometrische Optik</i> (1937), Carathéodory demonstrated the equivalence of Huygens' principle and Fermat's principle starting from the former using Cauchy's theory of characteristics. He argued that an important advantage of his approach was that it covers the integral invariants of <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> and <a href="/wiki/%C3%89lie_Cartan" title="Élie Cartan">Élie Cartan</a> and completes the <a href="/wiki/Malus%27_law" class="mw-redirect" title="Malus' law">Malus law</a>. He explained that in his investigations in optics, <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a> conceived a minimum principle similar to that enunciated by <a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Hero of Alexandria</a> to study reflection.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Historical">Historical</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=15" title="Edit section: Historical"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>During the Second World War Carathéodory edited two volumes of <a href="/wiki/Euler" class="mw-redirect" title="Euler">Euler</a>'s Complete Works dealing with the Calculus of Variations which were submitted for publication in 1946.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="The_University_of_Smyrna">The University of Smyrna</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=16" title="Edit section: The University of Smyrna"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ionian_University_of_Smyrna.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Ionian_University_of_Smyrna.jpg/220px-Ionian_University_of_Smyrna.jpg" decoding="async" width="220" height="127" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Ionian_University_of_Smyrna.jpg/330px-Ionian_University_of_Smyrna.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Ionian_University_of_Smyrna.jpg/440px-Ionian_University_of_Smyrna.jpg 2x" data-file-width="945" data-file-height="547" /></a><figcaption>Photo of the <a href="/wiki/Ionian_University_of_Smyrna" title="Ionian University of Smyrna">Ionian University of Smyrna</a>.</figcaption></figure> <p>At the time, Athens was the only major educational centre in the wider area and had limited capacity to sufficiently satisfy the growing educational needs of the eastern part of the Aegean Sea and the <a href="/wiki/Balkans" title="Balkans">Balkans</a>. Carathéodory, who was a professor at the <a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a> at the time, proposed the establishment of a new university <sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> - the difficulties regarding the establishment of a Greek university in <a href="/wiki/Constantinople" title="Constantinople">Constantinople</a> led him to consider three other cities: <a href="/wiki/Thessaloniki" title="Thessaloniki">Thessaloniki</a>, <a href="/wiki/Chios" title="Chios">Chios</a> and <a href="/wiki/Smyrna" title="Smyrna">Smyrna</a>.<sup id="cite_ref-The_importance_of_the_foundation_of_the_University_of_Smyrni_28-0" class="reference"><a href="#cite_note-The_importance_of_the_foundation_of_the_University_of_Smyrni-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>At the invitation of the Greek Prime Minister <a href="/wiki/Eleftherios_Venizelos" title="Eleftherios Venizelos">Eleftherios Venizelos</a>, he submitted a plan on 20 October 1919 for the creation of a new university at <a href="/wiki/Smyrna" title="Smyrna">Smyrna</a> in Asia Minor, to be named <a href="/wiki/Ionian_University_of_Smyrna" title="Ionian University of Smyrna">Ionian University of Smyrna</a>. In 1920 Carathéodory was appointed dean of the university and took a major part in establishing the institution, touring Europe to buy books and equipment. The university however never actually admitted students, due to the <a href="/wiki/Greco-Turkish_War_(1919%E2%80%931922)" title="Greco-Turkish War (1919–1922)">War in Asia Minor</a> which ended in the <a href="/wiki/Great_Fire_of_Smyrna" class="mw-redirect" title="Great Fire of Smyrna">Great Fire of Smyrna</a>. Carathéodory managed to save books from the library and was only rescued at the last moment by a journalist who took him by rowboat to the battleship Naxos which was standing by.<sup id="cite_ref-Constantin_Carathéodory:_His_life_and_work_29-0" class="reference"><a href="#cite_note-Constantin_Carathéodory:_His_life_and_work-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Carathéodory brought to Athens some of the university library and stayed there, teaching at the university and technical school until 1924. </p><p>In 1924 Carathéodory was appointed professor of mathematics at the University of Munich, and held this position until retirement in 1938. He later worked at the Bavarian Academy of Sciences until his death in 1950. </p><p>The new Greek university in the broader area of the Southeast Mediterranean region, as originally envisioned by Carathéodory, finally materialised with the establishment of the <a href="/wiki/Aristotle_University_of_Thessaloniki" title="Aristotle University of Thessaloniki">Aristotle University of Thessaloniki</a> in 1925.<sup id="cite_ref-Brief_History_of_Aristotle_University_of_Thessaloniki_30-0" class="reference"><a href="#cite_note-Brief_History_of_Aristotle_University_of_Thessaloniki-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Linguistic_and_oratorical_talents">Linguistic and oratorical talents</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=17" title="Edit section: Linguistic and oratorical talents"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Caratheodory_constantin.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Caratheodory_constantin.jpg/200px-Caratheodory_constantin.jpg" decoding="async" width="200" height="301" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Caratheodory_constantin.jpg/300px-Caratheodory_constantin.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Caratheodory_constantin.jpg/400px-Caratheodory_constantin.jpg 2x" data-file-width="510" data-file-height="768" /></a><figcaption>Caratheodory at a mature age.</figcaption></figure><p>Carathéodory excelled at languages, much like many members of his family. <a href="/wiki/Greek_language" title="Greek language">Greek</a> and <a href="/wiki/French_language" title="French language">French</a> were his first languages, and he mastered <a href="/wiki/German_language" title="German language">German</a> with such perfection, that his writings composed in the German language are stylistic masterworks.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Carathéodory also spoke and wrote <a href="/wiki/English_language" title="English language">English</a>, <a href="/wiki/Italian_language" title="Italian language">Italian</a>, <a href="/wiki/Turkish_language" title="Turkish language">Turkish</a>, and the <a href="/wiki/Ancient_languages" class="mw-redirect" title="Ancient languages">ancient languages</a> without any effort. Such an impressive linguistic arsenal enabled him to communicate and exchange ideas directly with other mathematicians during his numerous travels, and greatly extended his fields of knowledge. </p><p>Much more than that, Carathéodory was a treasured conversation partner for his fellow professors in the Munich Department of Philosophy. The well-respected German <a href="/wiki/Philology" title="Philology">philologist</a> and professor of ancient languages, <a href="/wiki/Kurt_von_Fritz" title="Kurt von Fritz">Kurt von Fritz</a>, praised Carathéodory on the grounds that from him one could learn an endless amount about the old and new Greece, the old Greek language, and Hellenic mathematics. Von Fritz conducted numerous philosophical discussions with Carathéodory. </p><p>The mathematician sent his son Stephanos and daughter Despina to a German high school, but they also obtained daily additional instruction in Greek language and culture from a Greek priest, and at home he allowed them to speak Greek only. </p><p>Carathéodory was a talented public speaker, and was often invited to give speeches. In 1936, it was he who handed out the first ever <a href="/wiki/Fields_Medal" title="Fields Medal">Fields Medals</a> at the meeting of the International Congress of Mathematicians in Oslo, Norway.<sup id="cite_ref-:0_8-7" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Legacy">Legacy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=18" title="Edit section: Legacy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Grave_Caratheodory_2019b.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Grave_Caratheodory_2019b.jpg/200px-Grave_Caratheodory_2019b.jpg" decoding="async" width="200" height="253" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Grave_Caratheodory_2019b.jpg/300px-Grave_Caratheodory_2019b.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Grave_Caratheodory_2019b.jpg/400px-Grave_Caratheodory_2019b.jpg 2x" data-file-width="2612" data-file-height="3304" /></a><figcaption>Grave of Carathéodory in Munich.</figcaption></figure> <p>In 2002, in recognition of his achievements, the University of Munich named one of the largest lecture rooms in the mathematical institute the Constantin-Carathéodory Lecture Hall.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>In the town of Nea Vyssa, Caratheodory's ancestral home, a unique family museum is to be found. The museum is located in the central square of the town near to its church, and includes a number of Karatheodory's personal items, as well as letters he exchanged with Albert Einstein. More information is provided at the original website of the club, <a rel="nofollow" class="external free" href="http://www.s-karatheodoris.gr">http://www.s-karatheodoris.gr</a>. </p><p>At the same time, Greek authorities had long since intended to create a museum honoring Karatheodoris in <a href="/wiki/Komotini" title="Komotini">Komotini</a>, a major town of the northeastern Greek region, more than 200 km away from his home town above. On 21 March 2009, the "Karatheodoris" Museum (Καραθεοδωρής) opened its gates to the public in Komotini.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p><p>The coordinator of the Museum, Athanasios Lipordezis (Αθανάσιος Λιπορδέζης), has noted that the museum provides a home for original manuscripts of the mathematician running to about 10,000 pages, including correspondence with the German mathematician <a href="/wiki/Arthur_Rosenthal" title="Arthur Rosenthal">Arthur Rosenthal</a> for the algebraization of measure. At the showcase, visitors are also able to view the books <i>" Gesammelte mathematische Schriften Band 1,2,3,4 ", "Mass und ihre Algebraiserung", " Reelle Functionen Band 1", " Zahlen/Punktionen Funktionen "</i>, and a number of others. Handwritten letters by Carathéodory to <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> and <a href="/wiki/Hellmuth_Kneser" title="Hellmuth Kneser">Hellmuth Kneser</a>, as well as photographs of the Carathéodory family, are on display. </p><p>Efforts to furnish the museum with more exhibits are ongoing.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Publications">Publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=19" title="Edit section: Publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Journal_articles">Journal articles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=20" title="Edit section: Journal articles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A complete list of Carathéodory's journal article publications can be found in his <i>Collected Works</i>(<i>Ges. Math. Schr.</i>). Notable publications are: </p> <ul><li><i>Über die kanonischen Veränderlichen in der Variationsrechnung der mehrfachen Integrale</i><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup></li> <li><i>Über das Schwarzsche Lemma bei analytischen Funktionen von zwei komplexen Veränderlichen</i><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></li> <li><i>Über die diskontinuierlichen Lösungen in der Variationsrechnung.</i> Diss. Göttingen Univ. 1904; Ges. Math. Schr. I 3–79.</li> <li><i>Über die starken Maxima und Minima bei einfachen Integralen.</i> Habilitationsschrift Göttingen 1905; Math. Annalen 62 1906 449–503; Ges. Math. Schr. I 80–142.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup></li> <li><i>Untersuchungen über die Grundlagen der Thermodynamik</i>, Math. Ann. 67 (1909) pp. 355–386; Ges. Math. Schr. II 131–166.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup></li> <li><i>Über das lineare Mass von Punktmengen – eine Verallgemeinerung des Längenbegriffs.</i>, Gött. Nachr. (1914) 404–406; Ges. Math. Schr. IV 249–275.</li> <li><i>Elementarer Beweis für den Fundamentalsatz der konformen Abbildungen</i>. Schwarzsche Festschrift, Berlin 1914; Ges. Math. Schr.IV 249–275.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup></li> <li><i>Zur Axiomatic der speziellen Relativitätstheorie</i>. Sitzb. Preuss. Akad. Wiss. (1924) 12–27; Ges. Math. Schr. II 353–373.</li> <li><i>Variationsrechnung</i> in Frank P. & von Mises (eds): <i>Die Differential= und Integralgleichungen der Mechanik und Physik</i>, Braunschweig 1930 (Vieweg); New York 1961 (Dover) 227–279; Ges. Math. Schr. I 312–370.</li> <li><i>Entwurf für eine Algebraisierung des Integralbegriffs</i>, Sitzber. Bayer. Akad. Wiss. (1938) 27–69; Ges. Math. Schr. IV 302–342.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Books">Books</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=21" title="Edit section: Books"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFCarathéodory1918" class="citation cs2">Carathéodory, Constantin (1918), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=9rJXAAAAYAAJ"><i>Vorlesungen über reelle Funktionen</i></a> (3rd ed.), Leipzig: Teubner, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8284-0038-1" title="Special:BookSources/978-0-8284-0038-1"><bdi>978-0-8284-0038-1</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=0225940">0225940</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vorlesungen+%C3%BCber+reelle+Funktionen&rft.place=Leipzig&rft.edition=3rd&rft.pub=Teubner&rft.date=1918&rft.isbn=978-0-8284-0038-1&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0225940%23id-name%3DMR&rft.aulast=Carath%C3%A9odory&rft.aufirst=Constantin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D9rJXAAAAYAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span> Reprinted 1968 (Chelsea)</li> <li><i>Conformal Representation</i>, Cambridge 1932 (Cambridge Tracts in Mathematics and Physics)</li> <li><i>Geometrische Optik</i>, Berlin, 1937</li> <li><i>Elementare Theorie des Spiegelteleskops von B. Schmidt</i> (Elementary Theory of B. Schmidt's Reflecting Telescope), Leipzig Teubner, 1940 36 pp.; Ges. math. Schr. II 234–279</li> <li><i>Funktionentheorie I, II</i>, Basel 1950,<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> 1961 (Birkhäuser). English translation: <i>Theory of Functions of a Complex Variable</i>, 2 vols, New York, Chelsea Publishing Company, 3rd ed 1958</li> <li><i>Mass und Integral und ihre Algebraisierung</i>, Basel 1956. English translation, <i>Measure and Integral and Their Algebraisation</i>, New York, Chelsea Publishing Company, 1963</li> <li><i>Variationsrechnung und partielle Differentialgleichungen erster Ordnung</i>, Leipzig, 1935. English translation next reference</li> <li><i>Calculus of Variations and Partial Differential Equations of the First Order</i>, 2 vols. vol. I 1965, vol. II 1967 Holden-Day.</li> <li><i>Gesammelte mathematische Schriften</i> München 1954–7 (Beck) I–V.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=22" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1259569809">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output 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.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-mathgen1-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-mathgen1_1-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20180713153220/https://www.genealogy.math.ndsu.nodak.edu/id.php?id=7517">"The Mathematics Genealogy Project - Constantin Carathéodory"</a>. <i>Mathematics Genealogy Project</i>. North Dakota State University Department of Mathematics. Archived from <a rel="nofollow" class="external text" href="http://genealogy.math.ndsu.nodak.edu/id.php?id=7517">the original</a> on 13 July 2018<span class="reference-accessdate">. Retrieved <span class="nowrap">27 August</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Mathematics+Genealogy+Project&rft.atitle=The+Mathematics+Genealogy+Project+-+Constantin+Carath%C3%A9odory&rft_id=http%3A%2F%2Fgenealogy.math.ndsu.nodak.edu%2Fid.php%3Fid%3D7517&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-mathgen2-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-mathgen2_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://genealogy.math.ndsu.nodak.edu/id.php?id=148430">"The Mathematics Genealogy Project - Nazım Terzioğlu"</a>. <i>Mathematics Genealogy Project</i>. North Dakota State University Department of Mathematics<span class="reference-accessdate">. Retrieved <span class="nowrap">27 August</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Mathematics+Genealogy+Project&rft.atitle=The+Mathematics+Genealogy+Project+-+Naz%C4%B1m+Terzio%C4%9Flu&rft_id=http%3A%2F%2Fgenealogy.math.ndsu.nodak.edu%2Fid.php%3Fid%3D148430&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHallettMajer2004" class="citation book cs1">Hallett, Michael; Majer, Ulrich (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NxENTTHJCz4C"><i>David Hilbert's Lectures on the Foundations of Geometry 1891–1902</i></a>. Springer Science & Business Media. p. 11. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-64373-9" title="Special:BookSources/978-3-540-64373-9"><bdi>978-3-540-64373-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=David+Hilbert%27s+Lectures+on+the+Foundations+of+Geometry+1891%E2%80%931902&rft.pages=11&rft.pub=Springer+Science+%26+Business+Media&rft.date=2004&rft.isbn=978-3-540-64373-9&rft.aulast=Hallett&rft.aufirst=Michael&rft.au=Majer%2C+Ulrich&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DNxENTTHJCz4C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSzpiro2008" class="citation book cs1">Szpiro, George G. (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=iEBOce-4S2EC"><i>Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles</i></a>. Penguin. p. 104. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4406-3428-4" title="Special:BookSources/978-1-4406-3428-4"><bdi>978-1-4406-3428-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Poincare%27s+Prize%3A+The+Hundred-Year+Quest+to+Solve+One+of+Math%27s+Greatest+Puzzles&rft.pages=104&rft.pub=Penguin&rft.date=2008&rft.isbn=978-1-4406-3428-4&rft.aulast=Szpiro&rft.aufirst=George+G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DiEBOce-4S2EC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Brussells 1901 (Hayez);Ges. math. Schr. V. 273-281</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">H Aigyptos, Syllogos Ophelimon Biblion, no 14, 118 pp Athens 1901, 1928, New York 1920</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGeorgiadou2004" class="citation book cs1">Georgiadou, Maria (2004). "2.15: Einstein Contacts Carathéodory". <i>Constantin Carathéodory: Mathematics and Politics in Turbulent Times</i>. Germany: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-20352-4" title="Special:BookSources/3-540-20352-4"><bdi>3-540-20352-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=2.15%3A+Einstein+Contacts+Carath%C3%A9odory&rft.btitle=Constantin+Carath%C3%A9odory%3A+Mathematics+and+Politics+in+Turbulent+Times&rft.place=Germany&rft.pub=Springer&rft.date=2004&rft.isbn=3-540-20352-4&rft.aulast=Georgiadou&rft.aufirst=Maria&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-:0-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_8-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:0_8-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:0_8-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:0_8-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-:0_8-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-:0_8-7"><sup><i><b>h</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBegehr1998" class="citation book cs1">Begehr, H. G. W. (1998). "Constantin Carathéodory (1873-1950)". In Begehr, H. G. W.; Koch, H; Krammer, J; Schappacher, N; Thiele, E.-J (eds.). <i>Mathematics in Berlin</i>. Germany: Birkhäuser Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-7643-5943-9" title="Special:BookSources/3-7643-5943-9"><bdi>3-7643-5943-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Constantin+Carath%C3%A9odory+%281873-1950%29&rft.btitle=Mathematics+in+Berlin&rft.place=Germany&rft.pub=Birkh%C3%A4user+Verlag&rft.date=1998&rft.isbn=3-7643-5943-9&rft.aulast=Begehr&rft.aufirst=H.+G.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">J P Christianidis & N Kastanis: <i>In memoriam Evangelos S Stamatis (1898–1990) Historia Mathematica 19 (1992) 99-105</i></span> </li> <li id="cite_note-:2-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:2_10-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:2_10-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKot2014" class="citation book cs1">Kot, Mark (2014). "Chapter 12: Sufficient Conditions". <i>A First Course in the Calculus of Variations</i>. American Mathematical Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4704-1495-5" title="Special:BookSources/978-1-4704-1495-5"><bdi>978-1-4704-1495-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+12%3A+Sufficient+Conditions&rft.btitle=A+First+Course+in+the+Calculus+of+Variations&rft.pub=American+Mathematical+Society&rft.date=2014&rft.isbn=978-1-4704-1495-5&rft.aulast=Kot&rft.aufirst=Mark&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">H. Boerner, <i>Carathéodory und die Variationsrechnung</i>, in A Panayotopolos (ed.), Proceedings of C. Carathéodory International Symposium, September 1973, Athens (Athens, 1974), 80–90.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><a href="/wiki/Richard_Bellman" class="mw-redirect" title="Richard Bellman">Bellman</a> for his <i>Dynamic programming</i> in its continuous-time form used Carathéodory's work in the form of the <a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Bellman_equation" title="Hamilton–Jacobi–Bellman equation">Hamilton–Jacobi–Bellman equation</a>. <a href="/wiki/Rudolf_E._K%C3%A1lm%C3%A1n" title="Rudolf E. Kálmán">Kálmán</a> also explicitly used Carathéodory's formulation in his initial papers on optimal control. See e.g. R. E. Kalman: <i>Contributions to the theory of optimal control</i>. Boletin de la Sociedad Matematica Mexicana 1960</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBárányKarasev2012" class="citation journal cs1">Bárány, Imre; Karasev, Roman (2012-07-20). "Notes About the Carathéodory Number". <i>Discrete & Computational Geometry</i>. <b>48</b> (3): 783–792. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1112.5942">1112.5942</a></span>. <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%2Fs00454-012-9439-z">10.1007/s00454-012-9439-z</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/0179-5376">0179-5376</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:9090617">9090617</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Discrete+%26+Computational+Geometry&rft.atitle=Notes+About+the+Carath%C3%A9odory+Number&rft.volume=48&rft.issue=3&rft.pages=783-792&rft.date=2012-07-20&rft_id=info%3Aarxiv%2F1112.5942&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9090617%23id-name%3DS2CID&rft.issn=0179-5376&rft_id=info%3Adoi%2F10.1007%2Fs00454-012-9439-z&rft.aulast=B%C3%A1r%C3%A1ny&rft.aufirst=Imre&rft.au=Karasev%2C+Roman&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBartleSherbert2011" class="citation book cs1">Bartle, Robert G.; Sherbert, Donald R. (2011). "6.1: The Derivative". <i>Introduction to Real Analysis</i>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-43331-6" title="Special:BookSources/978-0-471-43331-6"><bdi>978-0-471-43331-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=6.1%3A+The+Derivative&rft.btitle=Introduction+to+Real+Analysis&rft.pub=John+Wiley+%26+Sons&rft.date=2011&rft.isbn=978-0-471-43331-6&rft.aulast=Bartle&rft.aufirst=Robert+G.&rft.au=Sherbert%2C+Donald+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">A. Shields: <i>Carathéodory and Conformal Mapping</i> Math. Intelligencer vol.10(1), 1988</span> </li> <li id="cite_note-:1-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_16-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_16-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGeorgiadou2004" class="citation book cs1">Georgiadou, Maria (2004). "2.2 Axiomatic Foundation of Thermodynamics". <i>Constantin Carathéodory: Mathematics and Politics in Turbulent Times</i>. Germany: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-20352-4" title="Special:BookSources/3-540-20352-4"><bdi>3-540-20352-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=2.2+Axiomatic+Foundation+of+Thermodynamics&rft.btitle=Constantin+Carath%C3%A9odory%3A+Mathematics+and+Politics+in+Turbulent+Times&rft.place=Germany&rft.pub=Springer&rft.date=2004&rft.isbn=3-540-20352-4&rft.aulast=Georgiadou&rft.aufirst=Maria&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarathéodory1909" class="citation journal cs1">Carathéodory, Constantin (1909). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20191012152205/http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf">"Untersuchungen ueber die Grundlagen der Thermodynamik"</a> [Examination of the foundations of Thermodynamics] <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Mathematische_Annalen" title="Mathematische Annalen">Mathematische Annalen</a></i>. <b>67</b> (3). Translated by Delphinich, D. H.: 355–386. <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%2Fbf01450409">10.1007/bf01450409</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:118230148">118230148</a>. Archived from <a rel="nofollow" class="external text" href="http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2019-10-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-07-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Annalen&rft.atitle=Untersuchungen+ueber+die+Grundlagen+der+Thermodynamik&rft.volume=67&rft.issue=3&rft.pages=355-386&rft.date=1909&rft_id=info%3Adoi%2F10.1007%2Fbf01450409&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118230148%23id-name%3DS2CID&rft.aulast=Carath%C3%A9odory&rft.aufirst=Constantin&rft_id=http%3A%2F%2Fneo-classical-physics.info%2Fuploads%2F3%2F0%2F6%2F5%2F3065888%2Fcaratheodory_-_thermodynamics.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLewis2007" class="citation book cs1">Lewis, Christopher J. T. (2007). "Chapter 5. Energy and Entropy: The Birth of Thermodynamics.". <i>Heat and Thermodynamics: A Historical Perspective</i>. Westport, Connecticut: Greenwood Press. p. 110. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-313-33332-3" title="Special:BookSources/978-0-313-33332-3"><bdi>978-0-313-33332-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+5.+Energy+and+Entropy%3A+The+Birth+of+Thermodynamics.&rft.btitle=Heat+and+Thermodynamics%3A+A+Historical+Perspective&rft.place=Westport%2C+Connecticut&rft.pages=110&rft.pub=Greenwood+Press&rft.date=2007&rft.isbn=978-0-313-33332-3&rft.aulast=Lewis&rft.aufirst=Christopher+J.+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">Bailyn, M. (1994). <i>A Survey of Thermodynamics</i>, American Institute of Physics, Woodbury NY, <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/0-88318-797-3" title="Special:BookSources/0-88318-797-3">0-88318-797-3</a>.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text">Max Born: <i>The Born–Einstein Letters</i>, MacMillan 1971</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><i><a rel="nofollow" class="external text" href="http://web.ist.utl.pt/ist12219/data/68.pdf">Constantin Carathéodory and the axiomatic thermodynamics</a></i> by Lionello Pogliani and Mario N. Berberan-Santos</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoglianiBerberan-Santos2000" class="citation journal cs1">Pogliani, Lionello; Berberan-Santos, Mario N. (2000). <a rel="nofollow" class="external text" href="http://link.springer.com/10.1023/A:1018834326958">"Constantin Carathéodory and the axiomatic thermodynamics"</a>. <i>Journal of Mathematical Chemistry</i>. <b>28</b> (1/3): 313–324. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FA%3A1018834326958">10.1023/A:1018834326958</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:17244147">17244147</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+Mathematical+Chemistry&rft.atitle=Constantin+Carath%C3%A9odory+and+the+axiomatic+thermodynamics&rft.volume=28&rft.issue=1%2F3&rft.pages=313-324&rft.date=2000&rft_id=info%3Adoi%2F10.1023%2FA%3A1018834326958&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A17244147%23id-name%3DS2CID&rft.aulast=Pogliani&rft.aufirst=Lionello&rft.au=Berberan-Santos%2C+Mario+N.&rft_id=http%3A%2F%2Flink.springer.com%2F10.1023%2FA%3A1018834326958&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">adiabatic accessibility = <a href="https://de.wikipedia.org/wiki/Adiabatische_Erreichbarkeit" class="extiw" title="de:Adiabatische Erreichbarkeit">adiabatische Erreichbarkeit</a>; see also Elliott H. Lieb, Jakob Yngvason: <a rel="nofollow" class="external text" href="http://www.arxiv.org/abs/cond-mat/9708200"><i>The Physics and Mathematics of the Second Law of Thermodynamics</i></a>, Phys. Rep. 310, 1–96 (1999) and Elliott H. Lieb, (editors: B. Nachtergaele, J.P. Solovej, J. Yngvason): <i>Statistical Mechanics: Selecta of Elliott H. Lieb</i>, 2005, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-22297-2" title="Special:BookSources/978-3-540-22297-2">978-3-540-22297-2</a></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><i>Über den Zusammenhang der Theorie der absoluten optischen Instrumente mit einem Satz der Variationsrechnung</i>, Münchener Sitzb. Math. -naturw Abteilung 1926 1–18; Ges. Math. Schr. II 181–197.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGeorgiadou2004" class="citation book cs1">Georgiadou, Maria (2004). "5.29: Geometric Optics". <i>Constantin Carathéodory: Mathematics and Politics in Turbulent Times</i>. Germany: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-20352-4" title="Special:BookSources/3-540-20352-4"><bdi>3-540-20352-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=5.29%3A+Geometric+Optics&rft.btitle=Constantin+Carath%C3%A9odory%3A+Mathematics+and+Politics+in+Turbulent+Times&rft.place=Germany&rft.pub=Springer&rft.date=2004&rft.isbn=3-540-20352-4&rft.aulast=Georgiadou&rft.aufirst=Maria&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">Euler Opera Omnia, Series 1 (a) vol.24: <i>Methodus inveniendi lineas curvas maximi minimive gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti</i>. Lausanne & Geneva 1744 (M. Bousquet) ed. C. Carathéodory Zürich 1952 (Fuesli). (b) vol.25 <i>Commentationes analyticae ad calculum variationum pertinentes</i>. ed C. Carathéodory Zürich 1952 (Fuesli).</span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.tovima.gr/books-ideas/article/?aid=127956">Constantin Carathéodory: A Biography, newspaper article, 2000 "<i>(...) Είχε γνωρίσει τον Ελευθέριο Βενιζέλο από το 1895, στην Κρήτη, και από το 1913 είχε προτείνει τη δημιουργία δεύτερου ελληνικού πανεπιστημίου στη Θεσσαλονίκη. Ο πόλεμος που ξεσπάει μεταθέτει τις αποφάσεις. Στην Ελλάδα θα επανέλθει το 1930-32, όταν θα αποδεχθεί τη θέση του κυβερνητικού επιτρόπου και θα οργανώσει τα πανεπιστήμια Αθήνας και Θεσσαλονίκης με τον νόμο 5343/32, ο οποίος ίσχυε μέχρι προσφάτως. Από τη θέση αυτή θα τον απολύσει η κυβέρνηση Παπαναστασίου που διαδέχεται τον Βενιζέλο το 1932 και εκεί θα σταματήσει η ενεργός ανάμειξή του στα κοινά της Ελλάδας.</i>" (Greek)</a></span> </li> <li id="cite_note-The_importance_of_the_foundation_of_the_University_of_Smyrni-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-The_importance_of_the_foundation_of_the_University_of_Smyrni_28-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120614082453/http://www.elemedu.upatras.gr/eriande/synedria/synedrio4/praktika1/pyrgiotakis.htm">"The importance of the foundation of the University of Smyrna(Essay)"</a>. Department of Primary Education, University of Patras. Archived from <a rel="nofollow" class="external text" href="http://www.elemedu.upatras.gr/eriande/synedria/synedrio4/praktika1/pyrgiotakis.htm">the original</a> on 14 June 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+importance+of+the+foundation+of+the+University+of+Smyrna%28Essay%29&rft.pub=Department+of+Primary+Education%2C+University+of+Patras&rft_id=http%3A%2F%2Fwww.elemedu.upatras.gr%2Feriande%2Fsynedria%2Fsynedrio4%2Fpraktika1%2Fpyrgiotakis.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-Constantin_Carathéodory:_His_life_and_work-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-Constantin_Carathéodory:_His_life_and_work_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20171222123424/http://www.24grammata.com/wp-content/uploads/2011/12/Caratheodori-24grammata.com_.pdf">"Constantin Carathéodory: His life and work(Essay)"</a> <span class="cs1-format">(PDF)</span>. National Technical University of Athens. Archived from <a rel="nofollow" class="external text" href="http://www.24grammata.com/wp-content/uploads/2011/12/Caratheodori-24grammata.com_.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2017-12-22.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Constantin+Carath%C3%A9odory%3A+His+life+and+work%28Essay%29&rft.pub=National+Technical+University+of+Athens&rft_id=http%3A%2F%2Fwww.24grammata.com%2Fwp-content%2Fuploads%2F2011%2F12%2FCaratheodori-24grammata.com_.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span>"<i>His daughter Mrs Despina Rodopoulou – Carathéodory referred to this period: "He stayed to save anything he could: library, machines etc which were shipped in different ships hoping that one day they will arrive in Athens. My father stayed until the last moment. George Horton, consul of U.S.A. in Smyrni wrote a book... which was translated in Greek. In this book Horton notes: "One of the last Greek I saw on the streets of Smyrna before the entry of the Turks was Professor Carathéodory, president of the doomed University. With him departed the incarnation of Greek genious [</i><a href="/wiki/Sic" title="Sic">sic</a><i>] of culture and civilization on Orient." </i>"</span> </li> <li id="cite_note-Brief_History_of_Aristotle_University_of_Thessaloniki-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-Brief_History_of_Aristotle_University_of_Thessaloniki_30-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.auth.gr/en/history">"Brief History"</a>. Aristotle University of Thessaloniki<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-12-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Brief+History&rft.pub=Aristotle+University+of+Thessaloniki&rft_id=https%3A%2F%2Fwww.auth.gr%2Fen%2Fhistory&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text">Denker, Forscher und Entdecker: eine Geschichte der Bayerischen Akademie By Dietmar Willoweit p.263</span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.mathematik.uni-muenchen.de/~fmwus/download/ausgabe07.pdf">Constantin Carathéodory-Hörsaal</a>, mathe-lmu, Nr. 7/2002, Hrsg. Förderverein Mathematik in Wirtschaft, Universität und Schule an der Ludwig-Maximilians-Universität München e.V., S. 9.</span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><span class="languageicon">(in Greek)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.karatheodori.gr/index.php?op=news&lop=viewNew&nid=20">"Caratheodory Museum Opening"</a>. Friends of C.Caratheodory.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Caratheodory+Museum+Opening&rft.pub=Friends+of+C.Caratheodory&rft_id=http%3A%2F%2Fwww.karatheodori.gr%2Findex.php%3Fop%3Dnews%26lop%3DviewNew%26nid%3D20&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100104215737/http://www.greekembassy.org.au/media_news.php?act=detail&id=267">"Caratheodory Museum Opens"</a>. Hellenic Republic Embassy at Australia, Press and Communication Office. Archived from <a rel="nofollow" class="external text" href="http://www.greekembassy.org.au/media_news.php?act=detail&id=267">the original</a> on 2010-01-04<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-12-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Caratheodory+Museum+Opens&rft.pub=Hellenic+Republic+Embassy+at+Australia%2C+Press+and+Communication+Office&rft_id=http%3A%2F%2Fwww.greekembassy.org.au%2Fmedia_news.php%3Fact%3Ddetail%26id%3D267&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.hri.org/news/greek/ana/2009/09-03-20.ana.html#36">"Caratheodory Museum enriched with new exhibits"</a>. Athens News Agency.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Caratheodory+Museum+enriched+with+new+exhibits&rft.pub=Athens+News+Agency&rft_id=http%3A%2F%2Fwww.hri.org%2Fnews%2Fgreek%2Fana%2F2009%2F09-03-20.ana.html%2336&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><span class="languageicon">(in Greek)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20111002122646/http://archive.enet.gr/online/online_text/c=112,dt=23.03.2009,id=53237924">"The museum of C.Carathéodory at Komotini"</a>. Eleftherotipia, major Greek newspaper. Archived from <a rel="nofollow" class="external text" href="http://archive.enet.gr/online/online_text/c=112,dt=23.03.2009,id=53237924">the original</a> on 2011-10-02.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+museum+of+C.Carath%C3%A9odory+at+Komotini&rft.pub=Eleftherotipia%2C+major+Greek+newspaper&rft_id=http%3A%2F%2Farchive.enet.gr%2Fonline%2Fonline_text%2Fc%3D112%2Cdt%3D23.03.2009%2Cid%3D53237924&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><span class="languageicon">(in Greek)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110716055345/http://portal.kathimerini.gr/4dcgi/_w_articles_kathextra_1_02/04/2009_273714">"Carathéodory Museum: attractor"</a>. Kathimerini, major Greek newspaper. Archived from <a rel="nofollow" class="external text" href="http://portal.kathimerini.gr/4dcgi/_w_articles_kathextra_1_02/04/2009_273714">the original</a> on 2011-07-16<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-12-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Carath%C3%A9odory+Museum%3A+attractor&rft.pub=Kathimerini%2C+major+Greek+newspaper&rft_id=http%3A%2F%2Fportal.kathimerini.gr%2F4dcgi%2F_w_articles_kathextra_1_02%2F04%2F2009_273714&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><span class="languageicon">(in Greek)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.makthes.gr/index.php?name=News&file=article&sid=35863">"The museum of Carathéodory opened its gates to the public"</a>. Macedonia, Greek major newspaper.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+museum+of+Carath%C3%A9odory+opened+its+gates+to+the+public&rft.pub=Macedonia%2C+Greek+major+newspaper&rft_id=http%3A%2F%2Fwww.makthes.gr%2Findex.php%3Fname%3DNews%26file%3Darticle%26sid%3D35863&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarathéodory1982" class="citation book cs1">Carathéodory, C. (1982). "Über die kanonischen Veränderlichen in der Variationsrechnung der mehrfachen Integrale". <i>Festschrift zu seinem sechzigsten Geburtstag am 23.Januar 1922</i>. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 78–88. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-61810-9_11">10.1007/978-3-642-61810-9_11</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-61810-9" title="Special:BookSources/978-3-642-61810-9"><bdi>978-3-642-61810-9</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:179177711">179177711</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%C3%9Cber+die+kanonischen+Ver%C3%A4nderlichen+in+der+Variationsrechnung+der+mehrfachen+Integrale&rft.btitle=Festschrift+zu+seinem+sechzigsten+Geburtstag+am+23.Januar+1922&rft.place=Berlin%2C+Heidelberg&rft.pages=78-88&rft.pub=Springer+Berlin+Heidelberg&rft.date=1982&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A179177711%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2F978-3-642-61810-9_11&rft.isbn=978-3-642-61810-9&rft.aulast=Carath%C3%A9odory&rft.aufirst=C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarathéodory1927" class="citation journal cs1">Carathéodory, C. (1927). "Über das Schwarzsche Lemma bei analytischen Funktionen von zwei komplexen Veränderlichen". <i>Mathematische Annalen</i>. <b>97</b> (1): 76–98. <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%2FBF01447861">10.1007/BF01447861</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:123411126">123411126</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Annalen&rft.atitle=%C3%9Cber+das+Schwarzsche+Lemma+bei+analytischen+Funktionen+von+zwei+komplexen+Ver%C3%A4nderlichen&rft.volume=97&rft.issue=1&rft.pages=76-98&rft.date=1927&rft_id=info%3Adoi%2F10.1007%2FBF01447861&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A123411126%23id-name%3DS2CID&rft.aulast=Carath%C3%A9odory&rft.aufirst=C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarathéodory1906" class="citation journal cs1">Carathéodory, C. (1906). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1585874">"Über die starken maxima und minima bei einfachen Integralen"</a>. <i>Mathematische Annalen</i>. <b>62</b> (4): 449–503. <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%2FBF01449816">10.1007/BF01449816</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:115532504">115532504</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Annalen&rft.atitle=%C3%9Cber+die+starken+maxima+und+minima+bei+einfachen+Integralen&rft.volume=62&rft.issue=4&rft.pages=449-503&rft.date=1906&rft_id=info%3Adoi%2F10.1007%2FBF01449816&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A115532504%23id-name%3DS2CID&rft.aulast=Carath%C3%A9odory&rft.aufirst=C.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1585874&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarathéodory1909" class="citation journal cs1">Carathéodory, C. (1909). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1428268">"Untersuchungen Über die Grundlagen der Thermodynamik"</a>. <i>Mathematische Annalen</i>. <b>67</b> (3): 355–386. <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%2FBF01450409">10.1007/BF01450409</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:118230148">118230148</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Annalen&rft.atitle=Untersuchungen+%C3%9Cber+die+Grundlagen+der+Thermodynamik&rft.volume=67&rft.issue=3&rft.pages=355-386&rft.date=1909&rft_id=info%3Adoi%2F10.1007%2FBF01450409&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118230148%23id-name%3DS2CID&rft.aulast=Carath%C3%A9odory&rft.aufirst=C.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1428268&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarathéodory1914" class="citation book cs1">Carathéodory, C. Carathéodory (1914). "Elementarer Beweis für den Fundamentalsatz der konformen Abbildungen". <i>Mathematische Abhandlungen Hermann Amandus Schwarz</i>. Springer Berlin Heidelberg. pp. 19–41. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-50735-9_2">10.1007/978-3-642-50735-9_2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-50735-9" title="Special:BookSources/978-3-642-50735-9"><bdi>978-3-642-50735-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Elementarer+Beweis+f%C3%BCr+den+Fundamentalsatz+der+konformen+Abbildungen&rft.btitle=Mathematische+Abhandlungen+Hermann+Amandus+Schwarz&rft.pages=19-41&rft.pub=Springer+Berlin+Heidelberg&rft.date=1914&rft_id=info%3Adoi%2F10.1007%2F978-3-642-50735-9_2&rft.isbn=978-3-642-50735-9&rft.aulast=Carath%C3%A9odory&rft.aufirst=C.+Carath%C3%A9odory&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeins,_Maurice1951" class="citation journal cs1"><a href="/wiki/Maurice_Heins" title="Maurice Heins">Heins, Maurice</a> (1951). <a rel="nofollow" class="external text" href="http://projecteuclid.org/download/pdf_1/euclid.bams/1183516047">"Review: <i>Funktionentheorie</i> by C. Carathéodory"</a>. <i>Bulletin of the American Mathematical Society</i>. <b>57</b> (3): 190–192. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1951-09486-0">10.1090/s0002-9904-1951-09486-0</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+American+Mathematical+Society&rft.atitle=Review%3A+Funktionentheorie+by+C.+Carath%C3%A9odory&rft.volume=57&rft.issue=3&rft.pages=190-192&rft.date=1951&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1951-09486-0&rft.au=Heins%2C+Maurice&rft_id=http%3A%2F%2Fprojecteuclid.org%2Fdownload%2Fpdf_1%2Feuclid.bams%2F1183516047&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=24" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Books_2">Books</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=25" title="Edit section: Books"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Maria Georgiadou, <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=IVIXBOFNty8C">Constantin Carathéodory: Mathematics and Politics in Turbulent Times</a>,</i> Berlin-Heidelberg: Springer Verlag, 2004. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-44258-8" title="Special:BookSources/3-540-44258-8">3-540-44258-8</a>.</li> <li><a href="/wiki/Themistocles_M._Rassias" title="Themistocles M. Rassias">Themistocles M. Rassias</a> (editor) (1991) <i>Constantin Caratheodory: An International Tribute</i>, Teaneck, NJ: World Scientific Publishing Co., <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/981-02-0544-9" title="Special:BookSources/981-02-0544-9">981-02-0544-9</a>.</li> <li>Nicolaos K. Artemiadis; translated by Nikolaos E. Sofronidis [2000](2004), <i>History of Mathematics: From a Mathematician's Vantage Point</i>, Rhode Island, USA: American Mathematical Society, pp. 270–4, 281, <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/0-8218-3403-7" title="Special:BookSources/0-8218-3403-7">0-8218-3403-7</a>.</li> <li><i>Constantin Carathéodory in his...origins</i>. International Congress at Vissa-Orestiada, Greece, 1–4 September 2000. Proceedings: T Vougiouklis (ed.), Hadronic Press, Palm Harbor FL 2001.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Biographical_articles">Biographical articles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=26" title="Edit section: Biographical articles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>C. Carathéodory, <i>Autobiographische Notizen</i>, (In German) Wiener Akad. Wiss. 1954–57, vol.V, pp. 389–408. Reprinted in Carathéodory's Collected Writings vol.V. English translation in A. Shields, <i>Carathéodory and conformal mapping</i>, The Mathematical Intelligencer 10 (1) (1988), 18–22.</li> <li><a href="/wiki/Oskar_Perron" title="Oskar Perron">O. Perron</a>, <i>Obituary: Constantin Carathéodory</i>, Jahresberichte der Deutschen Mathematiker Vereinigung 55 (1952), 39–51.</li> <li>N. Sakellariou, <i>Obituary: Constantin Carathéodory</i> (Greek), Bull. Soc. Math. Grèce 26 (1952), 1–13.</li> <li><a href="/wiki/Heinrich_Tietze" title="Heinrich Tietze">H Tietze</a>, <i>Obituary: Constantin Carathéodory</i>, Arch. Math. 2 (1950), 241–245.</li> <li>H. Behnke, <i>Carathéodorys Leben und Wirken</i>, in A. Panayotopolos (ed.), Proceedings of C .Carathéodory International Symposium, September 1973, Athens (Athens, 1974), 17–33.</li> <li>Bulirsch R., Hardt M., (2000): <i>Constantin Carathéodory: Life and Work</i>, International Congress: "Constantin Carathéodory", 1–4 September 2000, Vissa, Orestiada, Greece</li></ul> <div class="mw-heading mw-heading3"><h3 id="Encyclopaedias_and_reference_works">Encyclopaedias and reference works</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=27" title="Edit section: Encyclopaedias and reference works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Chambers Biographical Dictionary (1997), <i>Constantine Carathéodory</i>, 6th ed., Edinburgh: Chambers Harrap Publishers Ltd, pp 270–1, <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/0-550-10051-2" title="Special:BookSources/0-550-10051-2">0-550-10051-2</a> (also available <a rel="nofollow" class="external text" href="http://www.chambersharrap.co.uk/chambers/features/chref/chref.py/main?query=caratheodory&title=biog">online</a>).</li> <li><i>The New Encyclopædia Britannica</i> (1992), <i>Constantine Carathéodory</i>, 15th ed., vol. 2, USA: The University of Chicago, Encyclopædia Britannica, Inc., pp 842, <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/0-85229-553-7" title="Special:BookSources/0-85229-553-7">0-85229-553-7</a> * <a rel="nofollow" class="external text" href="http://www.britannica.com/eb/article-9020226/Constantin-Caratheodory">New edition Online entry</a></li> <li>H. Boerner, Biography of <i>Carathéodory</i> in Dictionary of Scientific Biography (New York 1970–1990).</li></ul> <div class="mw-heading mw-heading3"><h3 id="Conferences">Conferences</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=28" title="Edit section: Conferences"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>C. Carathéodory International Symposium</i>, Athens, Greece September 1973. Proceedings edited by A. Panayiotopoulos (Greek Mathematical Society) 1975. <a rel="nofollow" class="external text" href="http://www.hms.gr/apothema/?s=scf&i=29">Online</a></li> <li>Conference on <i>Advances in Convex Analysis and Global Optimization (Honoring the memory of C. Carathéodory)</i> June 5–9, 2000, Pythagorion, Samos, Greece. <a rel="nofollow" class="external text" href="http://www.samos.aegean.gr/math/acago">Online</a>.</li> <li>International Congress: <i>Carathéodory in his ... origins</i>, September 1–4, 2000, Vissa Orestiada, Greece. Proceedings edited by Thomas Vougiouklis (Democritus University of Thrace), Hadronic Press FL USA, 2001. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-57485-053-9" title="Special:BookSources/1-57485-053-9">1-57485-053-9</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Constantin_Carath%C3%A9odory&action=edit&section=29" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Constantin_Caratheodory" class="extiw" title="commons:Category:Constantin Caratheodory">Constantin Caratheodory</a> at Wikimedia Commons</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Caratheodory.html">"Constantin Carathéodory"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Constantin+Carath%C3%A9odory&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FCaratheodory.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AConstantin+Carath%C3%A9odory" class="Z3988"></span></li> <li><span class="languageicon">(in Greek)</span> <a rel="nofollow" class="external text" href="http://www.karatheodori.gr/">Web site dedicated to Carathéodory</a></li> <li><span class="languageicon">(in Greek)</span> <a rel="nofollow" class="external text" href="http://www.s-karatheodoris.gr">club www.s-karatheodoris.gr</a></li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=7517">Constantin Carathéodory</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output 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style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/000000010879777X">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/24679333">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/98138/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJfMgcyfwg66GmMbTKP84q">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Carathéodory, Constantin"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/118667076">Germany</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n82116586">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb123627598">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb123627598">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an36164774">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=jx20090826004&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX1339335">Spain</a></span></li><li><span 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href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007259588705171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA01181942?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=7517">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:caratheodory.constantin">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/45180">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" 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