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</li> <li id="toc-Zurich_lecture" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zurich_lecture"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Zurich lecture</span> </div> </a> <ul id="toc-Zurich_lecture-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Significant_students" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Significant_students"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Significant students</span> </div> </a> <ul id="toc-Significant_students-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legacy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legacy"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Legacy</span> </div> </a> <button aria-controls="toc-Legacy-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 Legacy subsection</span> </button> <ul id="toc-Legacy-sublist" class="vector-toc-list"> <li id="toc-Concepts_named_after_Schur" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Concepts_named_after_Schur"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Concepts named after Schur</span> </div> </a> <ul id="toc-Concepts_named_after_Schur-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quotes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Quotes</span> </div> </a> <ul id="toc-Quotes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Publications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Publications"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Publications</span> </div> </a> <ul id="toc-Publications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">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 " 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Available in 29 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-29" 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">29 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/%D8%A5%D9%8A%D8%B3%D8%A7%D9%8A_%D8%B4%D9%88%D8%B1" title="إيساي شور – Arabic" lang="ar" hreflang="ar" data-title="إيساي شور" 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/%C4%B0ssay_%C5%9Eur" title="İssay Şur – Azerbaijani" lang="az" hreflang="az" data-title="İssay Şur" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%DB%8C%D8%B3%D8%A7%DB%8C_%D8%B4%D9%88%D8%B1" title="ایسای شور – South Azerbaijani" lang="azb" hreflang="azb" data-title="ایسای شور" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%86%D1%81%D0%B0%D0%B9_%D0%A8%D1%83%D1%80" title="Ісай Шур – Belarusian" lang="be" hreflang="be" data-title="Ісай Шур" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%86%D1%81%D0%B0%D0%B9_%D0%A8%D1%83%D1%80" title="Ісай Шур – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Ісай Шур" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Catalan" lang="ca" hreflang="ca" data-title="Issai Schur" 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/Issai_Schur" title="Issai Schur – Czech" lang="cs" hreflang="cs" data-title="Issai Schur" 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/Issai_Schur" title="Issai Schur – German" lang="de" hreflang="de" data-title="Issai Schur" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Spanish" lang="es" hreflang="es" data-title="Issai Schur" 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/Issai_Schur" title="Issai Schur – Esperanto" lang="eo" hreflang="eo" data-title="Issai Schur" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Basque" lang="eu" hreflang="eu" data-title="Issai Schur" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%DB%8C%D8%B3%D8%A7%DB%8C_%D8%B4%D9%88%D8%B1" title="ایسای شور – Persian" lang="fa" hreflang="fa" data-title="ایسای شور" 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/Issai_Schur" title="Issai Schur – French" lang="fr" hreflang="fr" data-title="Issai Schur" 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%9D%B4%EC%82%AC%EC%9D%B4_%EC%8A%88%EC%96%B4" title="이사이 슈어 – Korean" lang="ko" hreflang="ko" data-title="이사이 슈어" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Indonesian" lang="id" hreflang="id" data-title="Issai Schur" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Italian" lang="it" hreflang="it" data-title="Issai Schur" 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%99%D7%A9%D7%99_%D7%A9%D7%95%D7%A8" title="ישי שור – Hebrew" lang="he" hreflang="he" data-title="ישי שור" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Haitian Creole" lang="ht" hreflang="ht" data-title="Issai Schur" 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-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Isajs_%C5%A0urs" title="Isajs Šurs – Latvian" lang="lv" hreflang="lv" data-title="Isajs Šurs" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Hungarian" lang="hu" hreflang="hu" data-title="Issai Schur" 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/%D8%A7%D9%8A%D8%B3%D8%A7%D9%89_%D8%B4%D9%88%D8%B1" title="ايساى شور – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ايساى شور" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Dutch" lang="nl" hreflang="nl" data-title="Issai Schur" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A4%E3%82%B5%E3%82%A4%E3%83%BB%E3%82%B7%E3%83%A5%E3%83%BC%E3%82%A2" title="イサイ・シューア – Japanese" lang="ja" hreflang="ja" data-title="イサイ・シューア" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Polish" lang="pl" hreflang="pl" data-title="Issai Schur" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Portuguese" lang="pt" hreflang="pt" data-title="Issai Schur" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A8%D1%83%D1%80,_%D0%98%D1%81%D0%B0%D0%B9" title="Шур, Исай – Russian" lang="ru" hreflang="ru" data-title="Шур, Исай" 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/Issai_Schur" title="Issai Schur – Slovak" lang="sk" hreflang="sk" data-title="Issai Schur" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%8C%D8%B3%D8%A7%DB%8C_%D8%B4%D9%88%D8%B1" title="ئیسای شور – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئیسای شور" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Issai_Schur" title="Issai Schur – Swedish" lang="sv" hreflang="sv" data-title="Issai Schur" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q72599#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" 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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">Not to be confused with <a href="/wiki/Friedrich_Schur" title="Friedrich Schur">Friedrich Schur</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Issai Schur</div></th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Schur.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Schur.jpg/200px-Schur.jpg" decoding="async" width="200" height="335" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/1/1f/Schur.jpg 1.5x" data-file-width="239" data-file-height="400" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1875-01-10</span>)</span>10 January 1875<br /><div style="display:inline" class="birthplace"><a href="/wiki/Mogilev" title="Mogilev">Mogilev</a>, <a href="/wiki/Russian_Empire" title="Russian Empire">Russian Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">10 January 1941<span style="display:none">(1941-01-10)</span> (aged 66)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Tel_Aviv" title="Tel Aviv">Tel Aviv</a>, <a href="/wiki/Mandatory_Palestine" title="Mandatory Palestine">Mandatory Palestine</a></div></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li><a href="/wiki/Schur_decomposition" title="Schur decomposition">Schur decomposition</a></li> <li><a href="/wiki/Schur%27s_lemma" title="Schur's lemma">Schur's lemma</a></li> <li><a href="/wiki/Schur_complement" title="Schur complement">Schur complement</a></li></ul> </div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Georg_Frobenius" class="mw-redirect" title="Georg Frobenius">Georg Frobenius</a></li> <li><a href="/wiki/Lazarus_Fuchs" title="Lazarus Fuchs">Lazarus Fuchs</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Richard_Brauer" title="Richard Brauer">Richard Brauer</a></li> <li><a href="/wiki/Robert_Frucht" title="Robert Frucht">Robert Frucht</a></li> <li><a href="/wiki/Maximilian_Herzberger" title="Maximilian Herzberger">Maximilian Herzberger</a></li> <li><a href="/wiki/Eberhard_Hopf" title="Eberhard Hopf">Eberhard Hopf</a></li> <li><a href="/wiki/Bernhard_Neumann" title="Bernhard Neumann">Bernhard Neumann</a></li> <li><a href="/wiki/Rose_Peltesohn" title="Rose Peltesohn">Rose Peltesohn</a></li> <li><a href="/wiki/Heinz_Pr%C3%BCfer" title="Heinz Prüfer">Heinz Prüfer</a></li> <li><a href="/wiki/Richard_Rado" title="Richard Rado">Richard Rado</a></li> <li><a href="/wiki/Isaac_Jacob_Schoenberg" title="Isaac Jacob Schoenberg">Isaac Jacob Schoenberg</a></li> <li><a href="/wiki/Arnold_Scholz" title="Arnold Scholz">Arnold Scholz</a></li> <li><a href="/wiki/Wilhelm_Specht" title="Wilhelm Specht">Wilhelm Specht</a></li> <li>Karl Dörge</li> <li><a href="/wiki/Wolfgang_Hahn" title="Wolfgang Hahn">Wolfgang Hahn</a></li></ul> </div></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Issai Schur</b> (10 January 1875 – 10 January 1941<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>) was a Russian <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> who worked in <a href="/wiki/Germany" title="Germany">Germany</a> for most of his life. He studied at the <a href="/wiki/Humboldt_University_of_Berlin" title="Humboldt University of Berlin">University of Berlin</a>. He obtained his <a href="/wiki/Doctorate" title="Doctorate">doctorate</a> in 1901, became <a href="/wiki/Lecturer" title="Lecturer">lecturer</a> in 1903 and, after a stay at the <a href="/wiki/University_of_Bonn" title="University of Bonn">University of Bonn</a>, <a href="/wiki/Professor" title="Professor">professor</a> in 1919. </p><p>As a student of <a href="/wiki/Ferdinand_Georg_Frobenius" title="Ferdinand Georg Frobenius">Ferdinand Georg Frobenius</a>, he worked on <a href="/wiki/Group_representation" title="Group representation">group representations</a> (the subject with which he is most closely associated), but also in <a href="/wiki/Combinatorics" title="Combinatorics">combinatorics</a> and <a href="/wiki/Quadratic_residue#The_Pólya–Vinogradov_inequality" title="Quadratic residue">number theory</a> and even <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>. He is perhaps best known today for his result on the existence of the <a href="/wiki/Schur_decomposition" title="Schur decomposition">Schur decomposition</a> and for his work on group representations (<a href="/wiki/Schur%27s_lemma" title="Schur's lemma">Schur's lemma</a>). </p><p>Schur published under the name of both I. Schur, and J. Schur, the latter especially in <i><a href="/wiki/Journal_f%C3%BCr_die_reine_und_angewandte_Mathematik" class="mw-redirect" title="Journal für die reine und angewandte Mathematik">Journal für die reine und angewandte Mathematik</a></i>. This has led to some confusion.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Childhood">Childhood</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=1" title="Edit section: Childhood"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Issai Schur was born into a <a href="/wiki/Jewish" class="mw-redirect" title="Jewish">Jewish</a> family, the son of the businessman Moses Schur and his wife Golde Schur (née Landau). He was born in <a href="/wiki/Mogilev" title="Mogilev">Mogilev</a> on the <a href="/wiki/Dnieper_River" class="mw-redirect" title="Dnieper River">Dnieper River</a> in what was then the <a href="/wiki/Russian_Empire" title="Russian Empire">Russian Empire</a>. Schur used the name <i>Schaia </i> (<i>Isaiah</i> as the epitaph on his grave) rather than <i>Issai</i> up in his middle twenties.<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> Schur's father may have been a wholesale merchant.<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><p>In 1888, at the age of 13, Schur went to <a href="/wiki/Liep%C4%81ja" title="Liepāja">Liepāja</a> (<a href="/wiki/Courland" title="Courland">Courland</a>, now in <a href="/wiki/Latvia" title="Latvia">Latvia</a>), where his married sister and his brother lived, 640 km north-west of Mogilev. Kurland was one of the three <a href="/wiki/Baltic_governorates" class="mw-redirect" title="Baltic governorates">Baltic governorates</a> of Tsarist Russia, and since the Middle Ages the Baltic Germans were the upper social class.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The local Jewish community spoke mostly German and not Yiddish.<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>Schur attended the German-speaking <a href="/wiki/Nicolai_Gymnasium_in_Libau" class="mw-redirect" title="Nicolai Gymnasium in Libau">Nicolai Gymnasium in Libau</a> from 1888 to 1894 and reached the top grade in his final examination, and received a gold medal.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Here he became fluent in German. </p> <div class="mw-heading mw-heading2"><h2 id="Education">Education</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=2" title="Edit section: Education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In October 1894, Schur attended the <a href="/wiki/Humboldt_University_of_Berlin" title="Humboldt University of Berlin">University of Berlin</a>, with concentration in mathematics and physics. In 1901, he graduated summa cum laude under Frobenius and <a href="/wiki/Lazarus_Immanuel_Fuchs" class="mw-redirect" title="Lazarus Immanuel Fuchs">Lazarus Immanuel Fuchs</a> with his dissertation <i>On a class of matrices that can be assigned to a given matrix</i>,<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> which contains a general theory of the representation of <a href="/wiki/Linear_group" title="Linear group">linear groups</a>. According to Vogt,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> he began to use the name <i>Issai</i> at this time. Schur thought that his chance of success in the Russian Empire was rather poor,<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> and because he spoke German so perfectly, he remained in Berlin. He graduated in 1903 and was a lecturer at the University of Berlin. Schur held a position as professor at the Berlin University for the ten years from 1903 to 1913.<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><p>In 1913 he accepted an appointment as associate professor and successor of <a href="/wiki/Felix_Hausdorff" title="Felix Hausdorff">Felix Hausdorff</a> at the <a href="/wiki/University_of_Bonn" title="University of Bonn">University of Bonn</a>. In the following years Frobenius tried various ways to get Schur back to Berlin. Among other things, Schur's name was mentioned in a letter dated 27 June 1913<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> from Frobenius to Robert Gnehm (the School Board President of the <a href="/wiki/ETH" class="mw-redirect" title="ETH">ETH</a>) as a possible successor to <a href="/wiki/Carl_Friedrich_Geiser" title="Carl Friedrich Geiser">Carl Friedrich Geiser</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> Frobenius complained that they had never followed his advice before and then said: "That is why I can't even recommend Prof. J. Schur (now in Bonn) to you. He's too good for Zurich, and should be my successor in Berlin". <a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Hermann Weyl</a> got the job in Zurich. The efforts of Frobenius were finally successful in 1916, when Schur succeeded Johannes Knoblauch as adjunct professor. Frobenius died a year later, on 3 August 1917. Schur and Carathéodory were both named as the frontrunners for his successor. But they chose <a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Constantin Carathéodory</a> in the end. In 1919 Schur finally received a personal professorship, and in 1921 he took over the chair of the retired <a href="/wiki/Friedrich_Hermann_Schottky" class="mw-redirect" title="Friedrich Hermann Schottky">Friedrich Hermann Schottky</a>. In 1922, he was also added to the <a href="/wiki/Prussian_Academy_of_Sciences" title="Prussian Academy of Sciences">Prussian Academy of Sciences</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2018)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="During_the_time_of_Nazism">During the time of Nazism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=3" title="Edit section: During the time of Nazism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>After the takeover by the <a href="/wiki/Nazis" class="mw-redirect" title="Nazis">Nazis</a> and the elimination of the parliamentary opposition, the Law for the Restoration of the Professional Civil Service on 7 April 1933, prescribed the release of all distinguished public servants that held unpopular political opinions or who were "Jewish" in origin; a subsequent regulation<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> extended this to professors and therefore also to Schur. Schur was suspended and excluded from the university system. His colleague <a href="/wiki/Erhard_Schmidt" title="Erhard Schmidt">Erhard Schmidt</a> fought for his reinstatement, and since Schur had been a Prussian official before the <a href="/wiki/First_World_War" class="mw-redirect" title="First World War">First World War</a>,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> he was allowed to participate in certain special lectures on teaching in the winter semester of 1933/1934 again. Schur withdrew his application for leave from the Science Minister and passed up the offer of a visiting professorship at the <a href="/wiki/University_of_Wisconsin%E2%80%93Madison" title="University of Wisconsin–Madison">University of Wisconsin–Madison</a> for the academic year 1933–34.<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> One element that likely played a role in the rejection of the offer was that Schur no longer felt he could cope with the requirements that would have come with a new beginning in an English-speaking environment.<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> </p><p>Already in 1932, Schur's daughter Hilde had married the doctor Chaim Abelin in Bern.<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> As a result, Issai Schur visited his daughter in Bern several times. In Zurich he met often with <a href="/wiki/George_P%C3%B3lya" title="George Pólya">George Pólya</a>, with whom he was on friendly terms since before the First World War.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>On such a trip to Switzerland in the summer of 1935, a letter reached Schur from <a href="/wiki/Ludwig_Bieberbach" title="Ludwig Bieberbach">Ludwig Bieberbach</a> signed on behalf of the Rector's, stating that Schur should urgently seek him out in the University of Berlin.<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> They needed to discuss an important matter with him. It involved Schur's dismissal on 30 September 1935.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>Schur remained a member of the Prussian Academy of Sciences after his release as a professor, but a little later he lost this last remnant of his official position. Due to an intervention from Bieberbach in the spring of 1938 he was forced to explain his resignation from the commission of the Academy.<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> His membership in the Advisory Board of <a href="/wiki/Mathematische_Zeitschrift" title="Mathematische Zeitschrift">Mathematische Zeitschrift</a> was ended in early 1939.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Emigration">Emigration</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=4" title="Edit section: Emigration"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Schur_tomb.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Schur_tomb.jpg/250px-Schur_tomb.jpg" decoding="async" width="250" height="376" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/bb/Schur_tomb.jpg 1.5x" data-file-width="328" data-file-height="493" /></a><figcaption>Schur's grave at <a href="/wiki/Trumpeldor_Cemetery" title="Trumpeldor Cemetery">Trumpeldor Cemetery</a></figcaption></figure> <p>Schur found himself lonely after the flight of many of his students and the expulsion of renowned scientists from his previous place of work. Only Dr. Helmut Grunsky had been friendly to him, as Schur reported in the late thirties to his expatriate student Max Menachem Schiffer.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> The Gestapo was everywhere. Since Schur had announced to his wife his intentions to commit suicide in case of a summons to the Gestapo,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> in the summer of 1938 his wife took his letters, and with them a summons from the Gestapo, sent Issai Schur to a relaxing stay in a home outside of Berlin and went with medical certificate allowing her to meet the Gestapo in place of her husband. There they flatly asked why they were still staying in Germany. But there were economic obstacles to the planned emigration: emigrating Germans had a pre-departure <a href="/wiki/Reich_Flight_Tax" title="Reich Flight Tax">Reich Flight Tax</a> to pay, which was a quarter of their assets. Now Schur's wife had inherited a mortgage on a house in Lithuania, which because of the Lithuanian foreign exchange determination could not be repaid. On the other hand, Schur was forbidden to default or leave the mortgage to the German Reich. Thus the Schurs lacked cash and cash equivalents. Finally, the missing sum of money was somehow supplied, and to this day it does not seem to be clear who were the donors. </p><p>Schur was able to leave Germany in early 1939.<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> His health, however, was already severely compromised. He traveled in the company of a nurse to his daughter in Bern, where his wife also followed a few days later. There they remained for several weeks and then emigrated to Palestine. Two years later, on his 66th birthday, on 10 January 1941, he died in Tel Aviv of a <a href="/wiki/Heart_attack" class="mw-redirect" title="Heart attack">heart attack</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Work">Work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=5" title="Edit section: Work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Schur continued the work of his teacher Frobenius with many important works for <a href="/wiki/Group_theory" title="Group theory">group theory</a> and <a href="/wiki/Representation_theory" title="Representation theory">representation theory</a>. In addition, he published important results and elegant proofs of known results in almost all branches of classical algebra and number theory. His collected works<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> are proof of this. There, his work on the theory of integral equations and infinite series can be found. </p> <div class="mw-heading mw-heading3"><h3 id="Linear_groups">Linear groups</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=6" title="Edit section: Linear groups"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In his doctoral thesis <i>Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen</i> Issai Schur determined the polynomial representations of the general linear group <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 GL(n,\mathbb {C} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GL(n,\mathbb {C} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33d1e9acb19bdad5440b69b1dc1d2dc31dc6e45c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.326ex; height:2.843ex;" alt="{\displaystyle GL(n,\mathbb {C} )}"></span> on the field <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} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {C} }"></span> of <a href="/wiki/Complex_number" title="Complex number">complex numbers</a>. The results and methods of this work are still relevant today.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> In his book, <a href="/wiki/Sandy_Green_(mathematician)" title="Sandy Green (mathematician)">J.A. Green</a> determined the polynomial representations 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 GL(n,\mathbb {K} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">K</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GL(n,\mathbb {K} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/472bffb7f50b95ff3b979c6fa2253a3a5790489a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.456ex; height:2.843ex;" alt="{\displaystyle GL(n,\mathbb {K} )}"></span> over infinite fields <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 {K} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">K</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {K} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1848c435e64864e9ad4efa7e46bd6bc900c35c99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \mathbb {K} }"></span> with arbitrary characteristic.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> It is mainly based on Schur's dissertation. Green writes, "This remarkable work (of Schur) contained many very original ideas, developed with superb algebraic skill. Schur showed that these (polynomial) representations are completely reducible, that each irreducible one is "homogeneous" of some degree <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\geq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>≥</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\geq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa96c19954fcda2695f988938ccf091d2bc2bbae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.31ex; height:2.343ex;" alt="{\displaystyle r\geq 0}"></span>, and that the equivalence types of irreducible polynomial representations 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 GL_{n}(\mathbb {C} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GL_{n}(\mathbb {C} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2af4bb1bcc02ba0284f08ccd4d34276366728834" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.115ex; height:2.843ex;" alt="{\displaystyle GL_{n}(\mathbb {C} )}"></span>, of fixed homogeneous degree <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>, are in one-one correspondence with the partitions <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 \lambda =(\lambda _{1},\ldots ,\lambda _{n})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda =(\lambda _{1},\ldots ,\lambda _{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c462fb6c1ed05828cb6b40fe79c179ec175ccd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.424ex; height:2.843ex;" alt="{\displaystyle \lambda =(\lambda _{1},\ldots ,\lambda _{n})}"></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 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> into not more than <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> parts. Moreover Schur showed that the character of an irreducible representation of type <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 \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> is given by a certain symmetric function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\underline {S}}_{\lambda }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <munder> <mi>S</mi> <mo>_</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>λ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\underline {S}}_{\lambda }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98a7e132f438cbb863f9de4bf6d7e5d2207fe91d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.666ex; margin-left: -0.048ex; margin-bottom: -0.672ex; width:2.739ex; height:3.176ex;" alt="{\displaystyle {\underline {S}}_{\lambda }}"></span> 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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> variables (since described as a "Schur function")." According to Green, the methods of Schur's dissertation today are important for the theory of algebraic groups.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p><p>In 1927 Schur, in his work <i>On the rational representations of the general linear group</i>, gave new proofs for the main results of his dissertation. If <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 V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> is the natural <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>-dimensional <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} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {C} }"></span> vector space on which <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 GL(n,\mathbb {C} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GL(n,\mathbb {C} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33d1e9acb19bdad5440b69b1dc1d2dc31dc6e45c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.326ex; height:2.843ex;" alt="{\displaystyle GL(n,\mathbb {C} )}"></span> operates, and if <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> is a natural number, then the <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>-fold tensor product <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 V^{\otimes r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊗</mo> <mi>r</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V^{\otimes r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fed0fd9279e024f84a3fb090c9f9139177a1ecf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.169ex; height:2.509ex;" alt="{\displaystyle V^{\otimes r}}"></span> over <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} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {C} }"></span> is a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle GL(n,\mathbb {C} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GL(n,\mathbb {C} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33d1e9acb19bdad5440b69b1dc1d2dc31dc6e45c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.326ex; height:2.843ex;" alt="{\displaystyle GL(n,\mathbb {C} )}"></span>-module, on which the symmetric group <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 S_{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/584f349f7b6bf04464096bd439ab9f95695bae59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.399ex; height:2.509ex;" alt="{\displaystyle S_{r}}"></span> of degree <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> also operates by permutation of the tensor factors of each generator <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 v_{1}\otimes \ldots \otimes v_{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⊗</mo> <mo>…</mo> <mo>⊗</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{1}\otimes \ldots \otimes v_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36f0c902be42ecc63b6faba0644173a53ef632b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.687ex; height:2.343ex;" alt="{\displaystyle v_{1}\otimes \ldots \otimes v_{r}}"></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 V^{\otimes r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊗</mo> <mi>r</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V^{\otimes r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fed0fd9279e024f84a3fb090c9f9139177a1ecf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.169ex; height:2.509ex;" alt="{\displaystyle V^{\otimes r}}"></span>. By exploiting these <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 S_{r}-GL(n,\mathbb {C} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>−</mo> <mi>G</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{r}-GL(n,\mathbb {C} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3dc3921083badd83f71fcdfaf48e9b26aade25c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.565ex; height:2.843ex;" alt="{\displaystyle S_{r}-GL(n,\mathbb {C} )}"></span>-bimodule actions on <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 V^{\otimes r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⊗</mo> <mi>r</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V^{\otimes r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fed0fd9279e024f84a3fb090c9f9139177a1ecf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.169ex; height:2.509ex;" alt="{\displaystyle V^{\otimes r}}"></span>, Schur manages to find elegant proofs of his sentences. This work of Schur was once very well known.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Professorship_in_Berlin">Professorship in Berlin</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=7" title="Edit section: Professorship in Berlin"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Schur lived in Berlin as a highly respected member of the academic world, an apolitical scholar. A leading mathematician and outstanding and very successful teacher, he held a prestigious chair at the University of Berlin for 16 years.<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> Until 1933, his research group had an excellent reputation at the University of Berlin in Germany and beyond. With Schur in the center, his faculty worked with representation theory, which was extended by his students in different directions (including solvable groups, combinatorics, matrix theory).<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> Schur made fundamental contributions to algebra and group theory which, according to <a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Hermann Weyl</a>, were comparable in scope and depth to those of <a href="/wiki/Emmy_Noether" title="Emmy Noether">Emmy Noether</a> (1882–1935).<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> </p><p>When Schur's lectures were canceled in 1933, there was an outcry among the students and professors who appreciated him and liked him.<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> By the efforts of his colleague <a href="/wiki/Erhard_Schmidt" title="Erhard Schmidt">Erhard Schmidt</a> Schur was allowed to continue lecturing until the end of September 1935 for the time being.<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> Schur was the last Jewish professor who lost his job at this time.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Zurich_lecture">Zurich lecture</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=8" title="Edit section: Zurich lecture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In Switzerland, Schur's colleagues Heinz Hopf and George Pólya were informed of the dismissal of Schur in 1935. They tried to help as best they could.<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> On behalf of the Mathematical Seminars chief <a href="/wiki/Michel_Plancherel" title="Michel Plancherel">Michel Plancherel</a>, on 12 December 1935<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> the school board president Arthur Rohn invited Schur to <i>une série de conférences sur la théorie de la représentation des groupes finis</i>. At the same time he asked that the formal invitation should come from President Rohn, <i>comme le prof. Schur doit obtenir l'autorisation du ministère compétent de donner ces conférences</i>. George Pólya arranged from this invitation of the Mathematical Seminars the Conference of the Department of Mathematics and Physics on 16 December.<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> Meanwhile, on 14 December the official invitation letter from President Rohn had already been dispatched to Schur.<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> Schur was promised for his guest lecture a fee of CHF 500. </p><p>Schur did not reply until 28 January 1936, on which day he was first in the possession of the required approval of the local authority.<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> He declared himself willing to accept the invitation. He envisaged beginning the lecture on 4 February.<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> Schur spent most of the month of February in Switzerland. Before his return to Germany he visited his daughter in Bern for a few days, and on 27 February he returned via Karlsruhe, where his sister lived, to Berlin. In a letter to Pólya from Berne, he concludes with the words: <i>From Switzerland I take farewell with a heavy heart</i>.<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> </p><p>In Berlin, meanwhile, mathematician and Nazi Ludwig Bieberbach, in a letter dated 20 February 1936, informed the Reich Minister for Science, Art, and Education on the journey of Schur, and announced that he wanted to find out what was the content of the lecture in Zurich.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Significant_students">Significant students</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=9" title="Edit section: Significant students"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Schur had a total of 26<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> graduate students, some of whom acquired a mathematical reputation. Among them are </p> <ul><li><a href="/wiki/Alfred_Brauer" title="Alfred Brauer">Alfred Brauer</a>, University of Berlin (1928)</li> <li><a href="/wiki/Richard_Brauer" title="Richard Brauer">Richard Brauer</a>, University of Berlin (1925)</li> <li><a href="/w/index.php?title=Karl_D%C3%B6rge&action=edit&redlink=1" class="new" title="Karl Dörge (page does not exist)">Karl Dörge</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Karl_D%C3%B6rge" class="extiw" title="de:Karl Dörge">de</a>]</span>, University of Berlin (1925)</li> <li><a href="/wiki/Bernhard_Neumann" title="Bernhard Neumann">Bernhard Neumann</a>, University of Berlin, Cambridge University (1932, 1935)</li> <li><a href="/wiki/F%C3%A9lix_Pollaczek" title="Félix Pollaczek">Félix Pollaczek</a>, University of Berlin (1922)</li> <li><a href="/wiki/Heinz_Pruefer" class="mw-redirect" title="Heinz Pruefer">Heinz Pruefer</a>, University of Berlin, (1921)</li> <li><a href="/wiki/Richard_Rado" title="Richard Rado">Richard Rado</a>, University of Berlin, Cambridge University (1933, 1935)</li> <li><a href="/wiki/Isaac_Jacob_Schoenberg" title="Isaac Jacob Schoenberg">Isaac Jacob Schoenberg</a>, Alexandru Ioan Cuza University of Iaşi (1926)</li> <li><a href="/wiki/Wilhelm_Specht" title="Wilhelm Specht">Wilhelm Specht</a>, University of Berlin (1932)</li> <li><a href="/wiki/Helmut_Wielandt" title="Helmut Wielandt">Helmut Wielandt</a>, University of Berlin (1935)</li></ul> <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=Issai_Schur&action=edit&section=10" title="Edit section: Legacy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Concepts_named_after_Schur">Concepts named after Schur</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=11" title="Edit section: Concepts named after Schur"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Among others, the following concepts are named after Issai Schur: </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/List_of_things_named_after_Issai_Schur" title="List of things named after Issai Schur">List of things named after Issai Schur</a></li> <li><a href="/wiki/Schur_algebra" title="Schur algebra">Schur algebra</a></li> <li><a href="/wiki/Schur_complement" title="Schur complement">Schur complement</a></li> <li><a href="/wiki/Schur_index" class="mw-redirect" title="Schur index">Schur index</a></li> <li><a href="/wiki/Schur_indicator" class="mw-redirect" title="Schur indicator">Schur indicator</a></li> <li><a href="/wiki/Schur_multiplier" title="Schur multiplier">Schur multiplier</a></li> <li><a href="/wiki/Schur_orthogonality_relations" title="Schur orthogonality relations">Schur orthogonality relations</a></li> <li><a href="/wiki/Schur_polynomial" title="Schur polynomial">Schur polynomial</a></li> <li><a href="/wiki/Hadamard_product_(matrices)" title="Hadamard product (matrices)">Schur product</a></li> <li><a href="/wiki/Schur_test" title="Schur test">Schur test</a></li> <li><a href="/wiki/Schur%27s_inequality" title="Schur's inequality">Schur's inequality</a></li> <li><a href="/wiki/Schur%27s_theorem" title="Schur's theorem">Schur's theorem</a></li> <li><a href="/wiki/Schur-convex_function" title="Schur-convex function">Schur-convex function</a></li> <li><a href="/wiki/Schur%E2%80%93Weyl_duality" title="Schur–Weyl duality">Schur–Weyl duality</a></li> <li><a href="/wiki/Lehmer%E2%80%93Schur_algorithm" title="Lehmer–Schur algorithm">Lehmer–Schur algorithm</a></li> <li><a href="/wiki/Schur%27s_property" title="Schur's property">Schur's property</a> for normed spaces.</li> <li><a href="/wiki/Jordan%E2%80%93Schur_theorem" title="Jordan–Schur theorem">Jordan–Schur theorem</a></li> <li><a href="/wiki/Schur%E2%80%93Zassenhaus_theorem" title="Schur–Zassenhaus theorem">Schur–Zassenhaus theorem</a></li> <li><a href="/w/index.php?title=Schur_triple&action=edit&redlink=1" class="new" title="Schur triple (page does not exist)">Schur triple</a></li> <li><a href="/wiki/Schur_decomposition" title="Schur decomposition">Schur decomposition</a></li> <li><a href="/wiki/Quadratic_residue#The_P.C3.B3lya.E2.80.93Vinogradov_inequality" title="Quadratic residue">Schur's lower bound</a></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Quotes">Quotes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=12" title="Edit section: Quotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In his commemorative speech, Alfred Brauer (PhD candidate of Schur) spoke about Issai Schur as follows:<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> <i>As a teacher, Schur was excellent. His lectures were very clear, but not always easy and required cooperation – During the winter semester of 1930, the number of students who wanted to attend Schur's theory of numbers lecture, was such that the second largest university lecture hall with about 500 seats was too small. His most human characteristics were probably his great modesty, his helpfulness and his human interest in his students.</i> </p><p>Heinz Hopf, who had been in Berlin before his appointment to Zurich at the ETH Privatdozent, held – as is clear from oral statements and also from letters – Issai Schur as a mathematician and greatly appreciated man. Here, this appreciation was based entirely on reciprocity: in a letter of 1930 to George Pólya on the occasion of the re-appointment of Hermann Weyl, Schur says of Hopf: <i>Hopf is a very excellent teacher, a mathematician of strong temperament and strong effect, a master's discipline, trained excellent in other areas. – If I have to characterize him as a man, it may suffice if I say that I sincerely look forward to each time I meet with him</i>. </p><p>Schur was, however, known for putting a correct distance in personal affairs. The testimony of Hopf is in accordance with statements of Schur's former students in Berlin, by Walter Ledermann and Bernhard Neumann.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Publications">Publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=13" title="Edit section: Publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFSchur1968" class="citation cs2">Schur, Issai (1968), Grunsky, Helmut (ed.), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=mv7uAAAAMAAJ"><i>Vorlesungen über Invariantentheorie</i></a>, Die Grundlehren der mathematischen Wissenschaften, vol. 143, Berlin, New York: <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780387041391" title="Special:BookSources/9780387041391"><bdi>9780387041391</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=0229674">0229674</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+Invariantentheorie&rft.place=Berlin%2C+New+York&rft.series=Die+Grundlehren+der+mathematischen+Wissenschaften&rft.pub=Springer-Verlag&rft.date=1968&rft.isbn=9780387041391&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0229674%23id-name%3DMR&rft.aulast=Schur&rft.aufirst=Issai&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dmv7uAAAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIssai+Schur" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchur1973" class="citation cs2">Schur, Issai (1973), Brauer, Alfred; Rohrbach, Hans (eds.), <i>Gesammelte Abhandlungen</i>, Berlin, New York: <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-05630-0" title="Special:BookSources/978-3-540-05630-0"><bdi>978-3-540-05630-0</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0462891">0462891</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gesammelte+Abhandlungen&rft.place=Berlin%2C+New+York&rft.pub=Springer-Verlag&rft.date=1973&rft.isbn=978-3-540-05630-0&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0462891%23id-name%3DMR&rft.aulast=Schur&rft.aufirst=Issai&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIssai+Schur" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Issai_Schur&action=edit&section=14" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Ledermann, Walter, and Neumann, Peter M.; "The Life of Issai Schur through Letters and Other Documents", in Joseph, Melnikov, Rentschler (2003), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KvLxBwAAQBAJ&pg=PR45">p. 45.</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLedermann1983" class="citation journal cs1">Ledermann, W. (1983). "Issai Schur and his school in Berlin". <i>Bull. London Math. Soc</i>. <b>15</b> (2): 97–106. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1112%2Fblms%2F15.2.97">10.1112/blms/15.2.97</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+London+Math.+Soc.&rft.atitle=Issai+Schur+and+his+school+in+Berlin&rft.volume=15&rft.issue=2&rft.pages=97-106&rft.date=1983&rft_id=info%3Adoi%2F10.1112%2Fblms%2F15.2.97&rft.aulast=Ledermann&rft.aufirst=W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIssai+Schur" 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">Vogt, Annette. Issai Schur: als Wissenschaftler vertrieben. In Schoeps, Grozinger & Mattenklott [401, S. 217–235 (1999)]</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">The Kopelman Foundation. Mogiljow. JewishGen Belarus SIG, on <i>The Jewish Encyclopedia Web site</i> www.jewishgen.org/belarus/je_mogilev.htm conceived, created, and funded by The Kopelman Foundation, accessed 28 December 2003.</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">Blaushild, Immanuel. Libau. In Snyder [423, §1 (c. 1995)]</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">Snyder, Stephen, project coordinator. <i>A Town Named Libau (Liepaja, Latvia)</i>. JewishGen Web site www.Jewlshgen.org/ylzkor/libau/libau.html accessed 27 December 2003. (Translation of the 36-page booklet: <i>A Town Named Libau in English, German and Hebrew and additional material about Libau</i>, Editor and Publisher of booklet unknown, believed to have been published in Israel, 1985.)</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">Beare, Arlene, ed. <i>History of Latvia and Courland</i> Web site accessed 1 March 2004: www.jewishgen.org/Latvia/SIG_History_of_Latvia_and_Courland.html (This history is derived from a few sources including [38] but mainly edited from the presentation made by Ruvin Ferber at the 21st International Conference of Jewish Genealogy held in London in July 2001.)</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">vgl. Vogt, Anne</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">Schur, Issai. <a rel="nofollow" class="external text" href="https://gdz.sub.uni-goettingen.de/id/PPN271034092">Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen</a>. Doctoral dissertation, Universität Berlin, 1901; reprinted in Brauer k Rohrbach [71, Band I, pp. 1–72 (1973)]</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">vgl. Vogt, Anne</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">Chandler, Bruce; Magnus, Wilhelm. The History of Combinatorial Group Theory: A Case Study in the History of Ideas. Studies in the History of Mathematics and Physical Sciences 9. Springer-Verlag, New York, 1982.</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">vgl. Biographie der Leopoldino Carolina</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">Hermann Weyl: Nachlaß. Handschriften und Nachlässe, ETH Bibliothek, 1006:1.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Carl Friedrich Geiser (1843–1934), der bei Ludwig Schläfli in Bern promoviert hatte, war von 1873 bis 1913 ordentlicher Professor am Eidgenössischen Polytechnikum in Zürich.</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">3. Verordnung zur Durchführung des Berufsbeamtengesetzes. Vom 6. Mai 1933, <a href="/wiki/RGBl." class="mw-redirect" title="RGBl.">RGBl.</a> I S.245f.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Diese sogenannten "Altbeamten" waren von der Entlassung wegen jüdischer Abstammung vorerst ausgenommen, 1. Verordnung zur Durchführung des Berufsbeamtengesetzes. Vom 11. April 1933, <a href="/wiki/RGBl." class="mw-redirect" title="RGBl.">RGBl.</a> I S.195.</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">Walter Ledermann, <a href="/wiki/Peter_M._Neumann" title="Peter M. Neumann">Peter M. Neumann</a>: The Life of Issai Schur through Letters and other Documents. In Anthony Joseph et al. <i>Studies in Memory of Issai Schur</i>, Birkhäuser 2003. Brief des Ministeriums vom 11. September 1933, Brief von Schur vom 15. September 1933</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">Diese Ansicht vertritt Alfred Brauer in seiner Gedenkrede</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">Schur war sein 1906 mit der Ärztin Regina Frumkin verheiratet. Der Ehe entsprossen zwei Kinder Georg und Hilde. Georg, der etwas älter als Hilde war, studierte Physik und war später als Versicherungsmathematiker in Israel tätig.</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">George Pólya (1887–1985) hatte sich nach seinem Studium in Budapest 1914 und nach Aufenthalten in Göttingen und Paris an der ETH habilitiert. 1928 wurde er zum ordentlichen Professor ernannt. Ab 1940 war er dann in den USA tätig, zuletzt an der Stanford University. – Seine Bekanntschaften mit Schur geht auf die Zeit vor dem Ersten Weltkrieg zurück: Es existieren zahlreiche Briefe von Schur an Pólya aus den Jahren 1913/14, die in den Stanford University Libraries aufbewahrt werden</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">Mitteilung von Frau Susanne Abelin der Enkelin von Issai Schur, Sommer 2001. Der Brief vom 20. August 1935 ist in Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and other Documents. In Anthony Joseph et al. <i>Studies in Memory of Issai Schur</i>, Birkhäuser 2003. Seite lxxii</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">Die von Hitler und Göring unterschriebene <i>Entpflichtungsurkunde</i> datiert vom 28. September 1935. Siehe Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and other Documents. In Anthony Joseph et al. <i>Studies in Memory of Issai Schur</i>, Birkhäuser 2003. Seite lxxiv. Die Entlassung wäre anhand des <a href="/w/index.php?title=Reichsb%C3%BCrgergesetz&action=edit&redlink=1" class="new" title="Reichsbürgergesetz (page does not exist)">Reichsbürgergesetzes</a> ohnehin spätestens zum 31. Dezember 1935 verfügt worden</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">Der Vorgang ist beschrieben im Buch von Reinhard Siegmund-Schultze: <i>Mathematiker auf der Flucht vor Hitler.</i> Dokumente zur Geschichte der Mathematik, Band 10. Deutsche Mathematiker Vereinigung, Vieweg, 1998. Seite 69/70; die Austrittserklärung datiert vom 6. April 1938. Das Buch enthält darüber hinaus weitere interessante Angaben über die Situation von Schur in den dreißiger Jahren</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">Siehe Volker R. Remmert: <i>Mathematical Publishing in the Third Reich.</i> Math. Intelligencer 22 (3) 2000, Seite 22–30</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">"Long after the war, I talked to Grunsky about that remark and he literally started to cry: You know what I did? I sent him a postcard to contratulate him on his sixtieth birthday. I admired him so much and was very respectful in that card. How lonely he must have been to remember such a small thing", Schiffer, Menachem Max; Issai Schur. Some Personal Reminiscences (1986); 1998 in: Begehr, H. (Hrsg.), Mathematik in Berlin. Geschichte und Dokumentation, 1998 Aachen.</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">Siehe dazu und für das Folgende: Alfred Brauers Gedenkrede</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">Vergleiche den Brief des Reichsministers für Wissenschaft, Erziehung und Volksbildung an Issai Schur vom 24. Februar 1939. Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and other Documents. In Anthony Joseph et al. <i>Studies in Memory of Issai Schur</i>, Birkhäuser 2003. Seite lxxxi</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text">veröffentlicht von Alfred Brauer und Hans Rohrbach</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">See Festschrift der DMV Seite 549</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><i>Polynomial representations 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 GL(n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GL(n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf75d8678117da45a23cec0b548ac41a9598ba5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.614ex; height:2.843ex;" alt="{\displaystyle GL(n)}"></span></i> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-10258-0" title="Special:BookSources/978-0-387-10258-0">978-0-387-10258-0</a></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text">vgö. Chandler, Bruce; Magnus, Wilhelm.</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">Briining, Jochen; Ferus, Dirk; Siegmund-Schultze; Reinhard. Terror and Exile: Persecution and Expulsion of Mathematicians from Berlin between 1933 and 1945. An Exhibition on the Occasion of the International Congress of Mathematicians, Technische Universitat Berlin, 19 to 27 August 1998, Deutsche Mathematiker-Vereinigung, Berlin, 1998.</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">Pinl, Max; Furtmiiller, Lux. Mathematicians under Hitler. Seite 178</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">vgl. Briining, Jochen Seite 27</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">Pinl, Max; Furtmiiller, Lux. Mathematicians under Hitler. Seite 178</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">Soifer, Alexander. Issai Schur: Ramsey theory before Ramsey. Geombinatorics, 5 (1995), 6–23</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">Urs Stammbach <i>Die Zürcher Vorlesung von Issai Schur über Darstellungstheorie</i> Seite xiii, ETH-Bibliothek 2004</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"><i>Schulratsarchiv der ETH-Zürich.</i> Akten 1935/36, ETH-Bibliothek.</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"><i>Protokoller der Abteilung IX, Mathematik und Physik.</i> Protokolle der Konferenzen der Abt. IX, Hs 1079:3, Handschriften und Nachlässe, ETH-Bibliothek Zürich</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"><i>Schulratsarchiv der ETH-Zürich.</i> Missiven 1935, 3119, ETH-Bibliothek</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"><i>Schulratsarchiv der ETH-Zürich.</i> Akten 1935/36, ETH-Bibliothek</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">Gemäß einem später geschriebenen Lebenslauf – siehe Walter Ledermann, Peter M. Neumann: The Life of Issai Schur through Letters and other Documents. In Anthony Joseph et al. <i>Studies in Memory of Issai Schur.</i> Seite lxxvii, Birkhäuser 2003. – fanden die Vorlesungen zwischen dem 4. und dem 18. Februar statt</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">Siehe Department of Special Collections and University Archives, Stanford University Libraries, 26. Februar 1936.</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">Der Vorgang wird beschrieben in Charles Curtis: <i>Pioneers of representation theory.</i> History of Mathematics vol. 15, Amer. Math. Soc./London Math. Soc. 1999, Seite 131</span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://genealogy.math.ndsu.nodak.edu/id.php?id=9179&fChrono=1">Siehe Mathematics Genealogy Project, North Dakota State University</a></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text">Gedenkrede vom 8. November 1960 anlässlich der Schur-Gedenkfeier im Rahmen der 150-Jahrfeier der Universität Berlin. Siehe Issai Schur: Gesammelte Abhandlungen, Seiten v–xiv. Alfred Brauer hat 1928 bei Schur promoviert.</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text">Siehe <i>Interview with Bernhard Neumann</i>, <a href="/wiki/Newsletter_of_the_European_Mathematical_Society" class="mw-redirect" title="Newsletter of the European Mathematical Society">Newsletter of the European Mathematical Society</a>, 39, March 2001, 9–11; Walter Ledermann: <i>Issai Schur and his school in Berlin</i>, Bull. London Math. Soc. 15 (1983), 97–106. Bernhard Neumann doktorierte 1932, Walter Ledermann bestand das Examen für Lehramtskandidaten im Jahre 1933</span> </li> </ol></div></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=Issai_Schur&action=edit&section=15" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCurtis2003" class="citation cs2"><a href="/wiki/Charles_W._Curtis" title="Charles W. Curtis">Curtis, Charles W.</a> (2003), <a rel="nofollow" class="external text" href="https://books.google.com/books?isbn=0821826778"><i>Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer</i></a>, History of Mathematics, Providence, R.I.: <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-2677-5" title="Special:BookSources/978-0-8218-2677-5"><bdi>978-0-8218-2677-5</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=1715145">1715145</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Pioneers+of+Representation+Theory%3A+Frobenius%2C+Burnside%2C+Schur%2C+and+Brauer&rft.place=Providence%2C+R.I.&rft.series=History+of+Mathematics&rft.pub=American+Mathematical+Society&rft.date=2003&rft.isbn=978-0-8218-2677-5&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1715145%23id-name%3DMR&rft.aulast=Curtis&rft.aufirst=Charles+W.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fisbn%3D0821826778&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIssai+Schur" class="Z3988"></span><a rel="nofollow" class="external text" href="https://www.ams.org/journals/bull/2000-37-03/S0273-0979-00-00867-3/">Review</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJosephMelnikovRentschler2003" class="citation cs2">Joseph, Anthony; Melnikov, Anna; Rentschler, Rudolf, eds. (2003), <a rel="nofollow" class="external text" href="https://books.google.com/books?isbn=0817642080"><i>Studies in memory of Issai Schur</i></a>, Progress in Mathematics, vol. 210, Boston, MA: Birkhäuser Boston, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4612-0045-1">10.1007/978-1-4612-0045-1</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8176-4208-2" title="Special:BookSources/978-0-8176-4208-2"><bdi>978-0-8176-4208-2</bdi></a>, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1985184">1985184</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Studies+in+memory+of+Issai+Schur&rft.place=Boston%2C+MA&rft.series=Progress+in+Mathematics&rft.pub=Birkh%C3%A4user+Boston&rft.date=2003&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1985184%23id-name%3DMR&rft_id=info%3Adoi%2F10.1007%2F978-1-4612-0045-1&rft.isbn=978-0-8176-4208-2&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fisbn%3D0817642080&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIssai+Schur" class="Z3988"></span></li></ul> </div> <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=Issai_Schur&action=edit&section=16" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="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/Schur.html">"Issai Schur"</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=Issai+Schur&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%2FSchur.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIssai+Schur" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=9179">Issai Schur</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 .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist 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href="https://www.deutsche-biographie.de/pnd118795627.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118795627">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/031921728">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w62k05xg">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" 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