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class="firstHeading mw-first-heading"><span class="mw-page-title-main">Maxime Bôcher</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://de.wikipedia.org/wiki/Maxime_B%C3%B4cher" title="Maxime Bôcher – German" lang="de" hreflang="de" data-title="Maxime Bôcher" 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/Maxime_B%C3%B4cher" title="Maxime Bôcher – Spanish" lang="es" hreflang="es" data-title="Maxime Bôcher" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Maxime_B%C3%B4cher" title="Maxime Bôcher – French" lang="fr" hreflang="fr" data-title="Maxime Bôcher" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Maxime_B%C3%B4cher" title="Maxime Bôcher – Indonesian" lang="id" hreflang="id" data-title="Maxime Bôcher" 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-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Maxime_B%C3%B4cher" title="Maxime Bôcher – Haitian Creole" lang="ht" hreflang="ht" data-title="Maxime Bôcher" 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-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D8%A7%D9%83%D8%B3%D9%8A%D9%85_%D8%A8%D9%88%D8%B4%D8%B1" title="ماكسيم بوشر – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ماكسيم بوشر" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Maxime_B%C3%B4cher" title="Maxime Bôcher – Polish" lang="pl" hreflang="pl" data-title="Maxime Bôcher" 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/Maxime_B%C3%B4cher" title="Maxime Bôcher – Portuguese" lang="pt" hreflang="pt" data-title="Maxime Bôcher" 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%91%D0%BE%D1%85%D0%B5%D1%80,_%D0%9C%D0%B0%D0%BA%D1%81%D0%B8%D0%BC" title="Бохер, Максим – Russian" lang="ru" hreflang="ru" data-title="Бохер, Максим" 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.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">Maxime Bôcher</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Maxime_B%C3%B4cher.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/f/f6/Maxime_B%C3%B4cher.jpg/220px-Maxime_B%C3%B4cher.jpg" decoding="async" width="220" height="297" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/f/f6/Maxime_B%C3%B4cher.jpg 1.5x" data-file-width="240" data-file-height="324" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1867-08-28</span>)</span>August 28, 1867<br /><div style="display:inline" class="birthplace"><a href="/wiki/Boston" title="Boston">Boston</a>, <a href="/wiki/Massachusetts" title="Massachusetts">Massachusetts</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">September 12, 1918<span style="display:none">(1918-09-12)</span> (aged 51)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Cambridge,_Massachusetts" title="Cambridge, Massachusetts">Cambridge, Massachusetts</a></div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><a href="/wiki/United_States" title="United States">American</a></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a><br /><a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Differential_equation" title="Differential equation">Differential equations</a>, <a href="/wiki/Series_(mathematics)" title="Series (mathematics)">series</a>, and <a href="/wiki/Algebra" title="Algebra">algebra</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/William_Charles_Brenke" title="William Charles Brenke">William Brenke</a><br /><a href="/wiki/David_Raymond_Curtiss" title="David Raymond Curtiss">David R. Curtiss</a><br /><a href="/wiki/Griffith_C._Evans" title="Griffith C. Evans">Griffith C. Evans</a><br /><a href="/wiki/Lester_R._Ford" title="Lester R. Ford">Lester R. Ford</a><br /><a href="/wiki/Walter_Burton_Ford" title="Walter Burton Ford">Walter B. Ford</a><br /><a href="/wiki/James_Waterman_Glover" title="James Waterman Glover">James W. Glover</a><br /><a href="/wiki/Charles_Napoleon_Moore" title="Charles Napoleon Moore">Charles N. Moore</a><br /><a href="/wiki/William_Henry_Roever" title="William Henry Roever">William H. Roever</a><br /><a href="/wiki/Joseph_Leonard_Walsh" class="mw-redirect" title="Joseph Leonard Walsh">Joseph L. Walsh</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Maxime Bôcher</b> (August 28, 1867 – September 12, 1918) was an American <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> who published about 100 papers on <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a>, <a href="/wiki/Series_(mathematics)" title="Series (mathematics)">series</a>, and <a href="/wiki/Algebra" title="Algebra">algebra</a>.<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> He also wrote elementary texts such as <i>Trigonometry</i> and <i>Analytic Geometry</i>.<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> <a href="/wiki/B%C3%B4cher%27s_theorem" title="Bôcher's theorem">Bôcher's theorem</a>, <a href="#Bôcher's_equation">Bôcher's equation</a>, and the <a href="/wiki/B%C3%B4cher_Memorial_Prize" title="Bôcher Memorial Prize">Bôcher Memorial Prize</a> are named after him. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Life">Life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maxime_B%C3%B4cher&action=edit&section=1" title="Edit section: Life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bôcher was born in <a href="/wiki/Boston" title="Boston">Boston</a>, <a href="/wiki/Massachusetts" title="Massachusetts">Massachusetts</a>. His parents were Caroline Little and <a href="/w/index.php?title=Ferdinand_B%C3%B4cher&action=edit&redlink=1" class="new" title="Ferdinand Bôcher (page does not exist)">Ferdinand Bôcher</a>. Maxime's father was professor of modern languages at the <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a> when Maxime was born, and became Professor of <a href="/wiki/French_language" title="French language">French</a> at <a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a> in 1872. </p><p>Bôcher received an excellent education from his parents and from a number of public and private schools in Massachusetts. He graduated from the <a href="/wiki/Cambridge_Rindge_and_Latin_School" title="Cambridge Rindge and Latin School">Cambridge Latin School</a> in 1883. He received his first degree from Harvard in 1888. At Harvard, he studied a wide range of topics, including <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, <a href="/wiki/Latin" title="Latin">Latin</a>, <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, philosophy, zoology, <a href="/wiki/Geography" title="Geography">geography</a>, <a href="/wiki/Geology" title="Geology">geology</a>, meteorology, Roman art, and <a href="/wiki/Music" title="Music">music</a>. </p><p>Bôcher was awarded many prestigious prizes, which allowed him to travel to Europe to do research. The <a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a> was then the leading mathematics university, and he attended there lectures by <a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a>, <a href="/wiki/Arthur_Moritz_Schoenflies" title="Arthur Moritz Schoenflies">Arthur Moritz Schoenflies</a>, <a href="/wiki/Hermann_Schwarz" title="Hermann Schwarz">Hermann Schwarz</a>, <a href="/wiki/Issai_Schur" title="Issai Schur">Issai Schur</a> and <a href="/wiki/Woldemar_Voigt" title="Woldemar Voigt">Woldemar Voigt</a>. He was awarded a doctorate in 1891 for his dissertation <i>Über die Reihenentwicklungen der Potentialtheorie</i> (<a href="/wiki/German_language" title="German language">German</a> for "On the Development of the Potential Function into Series"); he was encouraged to study this topic by Klein. He received a Göttingen university prize for this work. </p><p>Bocher was elected to the <a href="/wiki/American_Academy_of_Arts_and_Sciences" title="American Academy of Arts and Sciences">American Academy of Arts and Sciences</a> in 1899,<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> the United States <a href="/wiki/National_Academy_of_Sciences" title="National Academy of Sciences">National Academy of Sciences</a> in 1909,<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> and the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a> in 1916.<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> </p><p>In Göttingen he met Marie Niemann, and they were married in July 1891. They had three children, Helen, Esther, and Frederick. He returned with his wife to Harvard where he was appointed as an instructor. In 1894 he was promoted to assistant professor, due to his impressive record. He became a full professor of mathematics in 1904. He was president of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a> from 1908 to 1910.<sup id="cite_ref-amer_6-0" class="reference"><a href="#cite_note-amer-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Although he was only 46 years old, there were already signs that his weak health was failing. He died at his <a href="/wiki/Cambridge,_Massachusetts" title="Cambridge, Massachusetts">Cambridge</a> home after suffering a prolonged illness. </p> <div class="mw-heading mw-heading2"><h2 id="Bôcher's_theorem"><span id="B.C3.B4cher.27s_theorem"></span>Bôcher's theorem</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maxime_B%C3%B4cher&action=edit&section=2" title="Edit section: Bôcher's theorem"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/B%C3%B4cher%27s_theorem" title="Bôcher's theorem">Bôcher's theorem</a> states that the finite <a href="/wiki/Zero_of_a_function" title="Zero of a function">zeros</a> of the <a href="/wiki/Derivative" title="Derivative">derivative</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 r'(z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>r</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r'(z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47e9a249fcdba62b148a20c8b01e80a70253da43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.631ex; height:3.009ex;" alt="{\displaystyle r'(z)}"></span> of a non-<a href="/wiki/Constant_function" title="Constant function">constant</a> <a href="/wiki/Rational_function" title="Rational function">rational function</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 r(z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r(z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2fb3c54b8d10544b170baeae4ab46bad371a1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.946ex; height:2.843ex;" alt="{\displaystyle r(z)}"></span> that are not multiple zeros 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(z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r(z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2fb3c54b8d10544b170baeae4ab46bad371a1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.946ex; height:2.843ex;" alt="{\displaystyle r(z)}"></span> are the positions of equilibrium in the field of force due to particles of positive mass at the zeros 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(z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r(z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2fb3c54b8d10544b170baeae4ab46bad371a1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.946ex; height:2.843ex;" alt="{\displaystyle r(z)}"></span> and particles of <a href="/wiki/Negative_mass" title="Negative mass">negative mass</a> at the <a href="/wiki/Zeros_and_poles" title="Zeros and poles">poles</a> 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(z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r(z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2fb3c54b8d10544b170baeae4ab46bad371a1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.946ex; height:2.843ex;" alt="{\displaystyle r(z)}"></span>, with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance. </p> <div class="mw-heading mw-heading2"><h2 id="Bôcher's_equation"><span id="B.C3.B4cher.27s_equation"></span>Bôcher's equation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maxime_B%C3%B4cher&action=edit&section=3" title="Edit section: Bôcher's equation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bôcher's equation is a second-order <a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">ordinary differential equation</a> of the form: </p> <dl><dd><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 y''+{\frac {1}{2}}\left[{\frac {m_{1}}{x-a_{1}}}+\cdots +{\frac {m_{n-1}}{x-a_{n-1}}}\right]y'+{\frac {1}{4}}\left[{\frac {A_{0}+A_{1}x+\cdots +A_{\ell }x^{\ell }}{(x-a_{1})_{1}^{m}(x-a_{2})_{2}^{m}\cdots (x-a_{n-1})_{n-1}^{m}}}\right]y=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>y</mi> <mo>″</mo> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mi>x</mi> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mrow> <mi>x</mi> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ℓ</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ℓ</mi> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msubsup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msubsup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msubsup> <mo>⋯</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msubsup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> <mi>y</mi> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y''+{\frac {1}{2}}\left[{\frac {m_{1}}{x-a_{1}}}+\cdots +{\frac {m_{n-1}}{x-a_{n-1}}}\right]y'+{\frac {1}{4}}\left[{\frac {A_{0}+A_{1}x+\cdots +A_{\ell }x^{\ell }}{(x-a_{1})_{1}^{m}(x-a_{2})_{2}^{m}\cdots (x-a_{n-1})_{n-1}^{m}}}\right]y=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d324b409c4ce5af56a87bff869cd1932fae32f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:89.905ex; height:7.509ex;" alt="{\displaystyle y''+{\frac {1}{2}}\left[{\frac {m_{1}}{x-a_{1}}}+\cdots +{\frac {m_{n-1}}{x-a_{n-1}}}\right]y'+{\frac {1}{4}}\left[{\frac {A_{0}+A_{1}x+\cdots +A_{\ell }x^{\ell }}{(x-a_{1})_{1}^{m}(x-a_{2})_{2}^{m}\cdots (x-a_{n-1})_{n-1}^{m}}}\right]y=0.}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="The_Bôcher_Memorial_Prize"><span id="The_B.C3.B4cher_Memorial_Prize"></span>The Bôcher Memorial Prize</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maxime_B%C3%B4cher&action=edit&section=4" title="Edit section: The Bôcher Memorial Prize"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/B%C3%B4cher_Memorial_Prize" title="Bôcher Memorial Prize">Bôcher Memorial Prize</a> is awarded by the American Mathematical Society every five years for notable research in <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">analysis</a> that has appeared in a recognized North American journal. </p><p>Winners have included <a href="/wiki/James_Waddell_Alexander_II" title="James Waddell Alexander II">James W. Alexander II</a> (1928), <a href="/wiki/Eric_Temple_Bell" title="Eric Temple Bell">Eric Temple Bell</a> (1924), <a href="/wiki/George_D._Birkhoff" class="mw-redirect" title="George D. Birkhoff">George D. Birkhoff</a> (1923), <a href="/wiki/Paul_Cohen_(mathematician)" class="mw-redirect" title="Paul Cohen (mathematician)">Paul J. Cohen</a> (1964), <a href="/wiki/Solomon_Lefschetz" title="Solomon Lefschetz">Solomon Lefschetz</a> (1924), <a href="/wiki/Marston_Morse" title="Marston Morse">Marston Morse</a> and <a href="/wiki/Norbert_Wiener" title="Norbert Wiener">Norbert Wiener</a> (1933), and <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> (1938). </p> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Maxime_B%C3%B4cher&action=edit&section=5" title="Edit section: Works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>1894: <a rel="nofollow" class="external text" href="https://archive.org/details/acv1533.0001.001.umich.edu">Ueber die Reihenentwicklungen der Potentialtheorie</a> via <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a></li> <li>1900: "Randwertaufgaben bei Gewöhnlich Differentialgleichung", <a href="/wiki/Klein%27s_encyclopedia" class="mw-redirect" title="Klein's encyclopedia"><i>Encyclopädie der mathematischen Wissenschaften</i></a> Band 2–1–1.</li> <li>1907: (with E.P.R.DuVal) <a rel="nofollow" class="external text" href="https://babel.hathitrust.org/cgi/pt?id=uc1.b4248862;view=1up;seq=7">Introduction to Higher Algebra</a> via <a href="/wiki/HathiTrust" title="HathiTrust">HathiTrust</a></li> <li>1909: <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontost00bcuoft">Introduction to the study of Integral Equations</a> via Internet Archive</li> <li>1917: <a rel="nofollow" class="external text" href="https://archive.org/details/leonssurlesm00bcuoft">Leçons sur les méthodes de Sturm dans la théorie des équations différentielles linéaires et leurs développements modernes</a> via Internet Archive.</li></ul> <p>Bôcher was one of the editors of the <i><a href="/wiki/Annals_of_Mathematics" title="Annals of Mathematics">Annals of Mathematics</a></i>, of the <a href="/wiki/Transactions_of_the_American_Mathematical_Society" title="Transactions of the American Mathematical Society"><i>Transactions</i> of the American Mathematical Society</a>.<sup id="cite_ref-amer_6-1" class="reference"><a href="#cite_note-amer-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <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=Maxime_B%C3%B4cher&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output 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.cs1-maint{color:#18911f}}</style><cite id="CITEREFBirkhoff,_George_D.1919" class="citation journal cs1"><a href="/wiki/George_David_Birkhoff" title="George David Birkhoff">Birkhoff, George D.</a> (1919). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1431557">"The scientific work of Maxime Bôcher"</a>. <i><a href="/wiki/Bulletin_of_the_American_Mathematical_Society" title="Bulletin of the American Mathematical Society">Bulletin of the American Mathematical Society</a></i>. <b>25</b> (5): 197–215. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1919-03172-3">10.1090/s0002-9904-1919-03172-3</a></span>. <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=1560177">1560177</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+American+Mathematical+Society&rft.atitle=The+scientific+work+of+Maxime+B%C3%B4cher&rft.volume=25&rft.issue=5&rft.pages=197-215&rft.date=1919&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1919-03172-3&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1560177%23id-name%3DMR&rft.au=Birkhoff%2C+George+D.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1431557&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMaxime+B%C3%B4cher" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOsgood,_William_F.1919" class="citation journal cs1"><a href="/wiki/William_Fogg_Osgood" title="William Fogg Osgood">Osgood, William F.</a> (1919). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1919-03198-x">"The life and services of Maxime Bôcher"</a>. <i><a href="/wiki/Bulletin_of_the_American_Mathematical_Society" title="Bulletin of the American Mathematical Society">Bulletin of the American Mathematical Society</a></i>. <b>25</b> (8): 337–350. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1919-03198-x">10.1090/s0002-9904-1919-03198-x</a></span>. <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=1560199">1560199</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+American+Mathematical+Society&rft.atitle=The+life+and+services+of+Maxime+B%C3%B4cher&rft.volume=25&rft.issue=8&rft.pages=337-350&rft.date=1919&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1919-03198-x&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1560199%23id-name%3DMR&rft.au=Osgood%2C+William+F.&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9904-1919-03198-x&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMaxime+B%C3%B4cher" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.amacad.org/person/maxime-bocher">"Maxime Bocher"</a>. <i>American Academy of Arts & Sciences</i>. 2023-02-09<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-10-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=American+Academy+of+Arts+%26+Sciences&rft.atitle=Maxime+Bocher&rft.date=2023-02-09&rft_id=https%3A%2F%2Fwww.amacad.org%2Fperson%2Fmaxime-bocher&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMaxime+B%C3%B4cher" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nasonline.org/member-directory/deceased-members/20001748.html">"Maxime Bocher"</a>. <i>www.nasonline.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-10-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.nasonline.org&rft.atitle=Maxime+Bocher&rft_id=https%3A%2F%2Fwww.nasonline.org%2Fmember-directory%2Fdeceased-members%2F20001748.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMaxime+B%C3%B4cher" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://search.amphilsoc.org/memhist/search?creator=Maxime+Bocher&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced">"APS Member History"</a>. <i>search.amphilsoc.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-10-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=search.amphilsoc.org&rft.atitle=APS+Member+History&rft_id=https%3A%2F%2Fsearch.amphilsoc.org%2Fmemhist%2Fsearch%3Fcreator%3DMaxime%2BBocher%26title%3D%26subject%3D%26subdiv%3D%26mem%3D%26year%3D%26year-max%3D%26dead%3D%26keyword%3D%26smode%3Dadvanced&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMaxime+B%C3%B4cher" class="Z3988"></span></span> </li> <li id="cite_note-amer-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-amer_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-amer_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">This article incorporates text from a publication now in the <a href="/wiki/Public_domain" title="Public domain">public domain</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRines1920" class="citation encyclopaedia cs1">Rines, George Edwin, ed. (1920). <span class="cs1-ws-icon" title="s:The Encyclopedia Americana (1920)/Bocher, Maxime"><a class="external text" href="https://en.wikisource.org/wiki/The_Encyclopedia_Americana_(1920)/Bocher,_Maxime">"Bocher, Maxime" </a></span>. <i><a href="/wiki/Encyclopedia_Americana" title="Encyclopedia Americana">Encyclopedia Americana</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Bocher%2C+Maxime&rft.btitle=Encyclopedia+Americana&rft.date=1920&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMaxime+B%C3%B4cher" class="Z3988"></span></span> </li> </ol></div></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=Maxime_B%C3%B4cher&action=edit&section=7" 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/Bocher.html">"Maxime Bôcher"</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=Maxime+B%C3%B4cher&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%2FBocher.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMaxime+B%C3%B4cher" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://books.nap.edu/html/biomems/mbocher.html">Maxime Bocher</a> biographical memoirs of the national academy of sciences.</li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=7431">Maxime Bôcher</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/bcher-maxime.pdf">National Academy of Sciences Biographical Memoir</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 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McClintock">Emory McClintock</a> (1891–1894)</span></li> <li><span class="nowrap"><a href="/wiki/George_William_Hill" title="George William Hill">George William Hill</a> (1895–1896)</span></li> <li><span class="nowrap"><a href="/wiki/Simon_Newcomb" title="Simon Newcomb">Simon Newcomb</a> (1897–1898)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Simpson_Woodward" title="Robert Simpson Woodward">Robert Simpson Woodward</a> (1899–1900)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1901–1924</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/E._H._Moore" title="E. H. Moore">E. H. Moore</a> (1901–1902)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_Fiske" title="Thomas Fiske">Thomas Fiske</a> (1903–1904)</span></li> <li><span class="nowrap"><a href="/wiki/William_Fogg_Osgood" title="William Fogg Osgood">William Fogg Osgood</a> (1905–1906)</span></li> <li><span class="nowrap"><a href="/wiki/Henry_Seely_White" title="Henry Seely White">Henry Seely White</a> (1907–1908)</span></li> <li><span class="nowrap"><a class="mw-selflink selflink">Maxime Bôcher</a> (1909–1910)</span></li> <li><span class="nowrap"><a href="/wiki/Henry_Burchard_Fine" title="Henry Burchard Fine">Henry Burchard Fine</a> (1911–1912)</span></li> <li><span class="nowrap"><a href="/wiki/Edward_Burr_Van_Vleck" title="Edward Burr Van Vleck">Edward Burr Van Vleck</a> (1913–1914)</span></li> <li><span class="nowrap"><a href="/wiki/Ernest_William_Brown" title="Ernest William Brown">Ernest William Brown</a> (1915–1916)</span></li> <li><span class="nowrap"><a href="/wiki/Leonard_Eugene_Dickson" title="Leonard Eugene Dickson">Leonard Eugene Dickson</a> (1917–1918)</span></li> <li><span class="nowrap"><a href="/wiki/Frank_Morley" title="Frank Morley">Frank Morley</a> (1919–1920)</span></li> <li><span class="nowrap"><a href="/wiki/Gilbert_Ames_Bliss" title="Gilbert Ames Bliss">Gilbert Ames Bliss</a> (1921–1922)</span></li> <li><span class="nowrap"><a href="/wiki/Oswald_Veblen" title="Oswald Veblen">Oswald Veblen</a> (1923–1924)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1925–1950</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/George_David_Birkhoff" title="George David Birkhoff">George David Birkhoff</a> (1925–1926)</span></li> <li><span class="nowrap"><a href="/wiki/Virgil_Snyder" title="Virgil Snyder">Virgil Snyder</a> (1927–1928)</span></li> <li><span class="nowrap"><a href="/wiki/Earle_Raymond_Hedrick" title="Earle Raymond Hedrick">Earle Raymond Hedrick</a> (1929–1930)</span></li> <li><span class="nowrap"><a href="/wiki/Luther_P._Eisenhart" title="Luther P. Eisenhart">Luther P. Eisenhart</a> (1931–1932)</span></li> <li><span class="nowrap"><a href="/wiki/Arthur_Byron_Coble" title="Arthur Byron Coble">Arthur Byron Coble</a> (1933–1934)</span></li> <li><span class="nowrap"><a href="/wiki/Solomon_Lefschetz" title="Solomon Lefschetz">Solomon Lefschetz</a> (1935–1936)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Lee_Moore" title="Robert Lee Moore">Robert Lee Moore</a> (1937–1938)</span></li> <li><span class="nowrap"><a href="/wiki/Griffith_C._Evans" title="Griffith C. Evans">Griffith C. Evans</a> (1939–1940)</span></li> <li><span class="nowrap"><a href="/wiki/Marston_Morse" title="Marston Morse">Marston Morse</a> (1941–1942)</span></li> <li><span class="nowrap"><a href="/wiki/Marshall_H._Stone" title="Marshall H. Stone">Marshall H. Stone</a> (1943–1944)</span></li> <li><span class="nowrap"><a href="/wiki/Theophil_Henry_Hildebrandt" title="Theophil Henry Hildebrandt">Theophil Henry Hildebrandt</a> (1945–1946)</span></li> <li><span class="nowrap"><a href="/wiki/Einar_Hille" title="Einar Hille">Einar Hille</a> (1947–1948)</span></li> <li><span class="nowrap"><a href="/wiki/Joseph_L._Walsh" title="Joseph L. Walsh">Joseph L. Walsh</a> (1949–1950)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1951–1974</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> (1951–1952)</span></li> <li><span class="nowrap"><a href="/wiki/Gordon_Thomas_Whyburn" class="mw-redirect" title="Gordon Thomas Whyburn">Gordon Thomas Whyburn</a> (1953–1954)</span></li> <li><span class="nowrap"><a href="/wiki/Raymond_Louis_Wilder" title="Raymond Louis Wilder">Raymond Louis Wilder</a> (1955–1956)</span></li> <li><span class="nowrap"><a href="/wiki/Richard_Brauer" title="Richard Brauer">Richard Brauer</a> (1957–1958)</span></li> <li><span class="nowrap"><a href="/wiki/Edward_J._McShane" title="Edward J. McShane">Edward J. McShane</a> (1959–1960)</span></li> <li><span class="nowrap"><a href="/wiki/Deane_Montgomery" title="Deane Montgomery">Deane Montgomery</a> (1961–1962)</span></li> <li><span class="nowrap"><a href="/wiki/Joseph_L._Doob" title="Joseph L. Doob">Joseph L. Doob</a> (1963–1964)</span></li> <li><span class="nowrap"><a href="/wiki/Abraham_Adrian_Albert" class="mw-redirect" title="Abraham Adrian Albert">Abraham Adrian Albert</a> (1965–1966)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_B._Morrey_Jr." title="Charles B. Morrey Jr.">Charles B. Morrey Jr.</a> (1967–1968)</span></li> <li><span class="nowrap"><a href="/wiki/Oscar_Zariski" title="Oscar Zariski">Oscar Zariski</a> (1969–1970)</span></li> <li><span class="nowrap"><a href="/wiki/Nathan_Jacobson" title="Nathan Jacobson">Nathan Jacobson</a> (1971–1972)</span></li> <li><span class="nowrap"><a href="/wiki/Saunders_Mac_Lane" title="Saunders Mac Lane">Saunders Mac Lane</a> (1973–1974)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1975–2000</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Lipman_Bers" title="Lipman Bers">Lipman Bers</a> (1975–1976)</span></li> <li><span class="nowrap"><a href="/wiki/R._H._Bing" title="R. H. Bing">R. H. Bing</a> (1977–1978)</span></li> <li><span class="nowrap"><a href="/wiki/Peter_Lax" title="Peter Lax">Peter Lax</a> (1979–1980)</span></li> <li><span class="nowrap"><a href="/wiki/Andrew_M._Gleason" title="Andrew M. Gleason">Andrew M. Gleason</a> (1981–1982)</span></li> <li><span class="nowrap"><a href="/wiki/Julia_Robinson" title="Julia Robinson">Julia Robinson</a> (1983–1984)</span></li> <li><span class="nowrap"><a href="/wiki/Irving_Kaplansky" title="Irving Kaplansky">Irving Kaplansky</a> (1985–1986)</span></li> <li><span class="nowrap"><a href="/wiki/George_Mostow" title="George Mostow">George Mostow</a> (1987–1988)</span></li> <li><span class="nowrap"><a href="/wiki/William_Browder_(mathematician)" title="William Browder (mathematician)">William Browder</a> (1989–1990)</span></li> <li><span class="nowrap"><a href="/wiki/Michael_Artin" title="Michael Artin">Michael Artin</a> (1991–1992)</span></li> <li><span class="nowrap"><a href="/wiki/Ronald_Graham" title="Ronald Graham">Ronald Graham</a> (1993–1994)</span></li> <li><span class="nowrap"><a href="/wiki/Cathleen_Synge_Morawetz" title="Cathleen Synge Morawetz">Cathleen Synge Morawetz</a> (1995–1996)</span></li> <li><span class="nowrap"><a href="/wiki/Arthur_Jaffe" title="Arthur Jaffe">Arthur Jaffe</a> (1997–1998)</span></li> <li><span class="nowrap"><a href="/wiki/Felix_Browder" title="Felix Browder">Felix Browder</a> (1999–2000)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">2001–2024</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Hyman_Bass" title="Hyman Bass">Hyman Bass</a> (2001–2002)</span></li> <li><span class="nowrap"><a href="/wiki/David_Eisenbud" title="David Eisenbud">David Eisenbud</a> (2003–2004)</span></li> <li><span class="nowrap"><a href="/wiki/James_Arthur_(mathematician)" title="James Arthur (mathematician)">James Arthur</a> (2005–2006)</span></li> <li><span class="nowrap"><a href="/wiki/James_Glimm" title="James Glimm">James Glimm</a> (2007–2008)</span></li> <li><span class="nowrap"><a href="/wiki/George_Andrews_(mathematician)" title="George Andrews (mathematician)">George Andrews</a> (2009–2010)</span></li> <li><span class="nowrap"><a href="/wiki/Eric_Friedlander" title="Eric Friedlander">Eric Friedlander</a> (2011–2012)</span></li> <li><span class="nowrap"><a href="/wiki/David_Vogan" title="David Vogan">David Vogan</a> (2013–2014)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Bryant_(mathematician)" title="Robert Bryant (mathematician)">Robert Bryant</a> (2015–2016)</span></li> <li><span class="nowrap"><a href="/wiki/Ken_Ribet" title="Ken Ribet">Ken Ribet</a> (2017–2018)</span></li> <li><span class="nowrap"><a href="/wiki/Jill_Pipher" title="Jill Pipher">Jill Pipher</a> (2019–2020)</span></li> <li><span class="nowrap"><a href="/wiki/Ruth_Charney" title="Ruth Charney">Ruth Charney</a> (2021–2022)</span></li> <li><span class="nowrap"><a href="/wiki/Bryna_Kra" title="Bryna Kra">Bryna Kra</a> (2023–2024)</span></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q339406#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q339406#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control 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class="external text" href="https://isni.org/isni/0000000110715841">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/76400075">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/132802/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJht4GJ9M6QqQhchR3FkDq">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/116212039">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n84803771">United States</a></span></li><li><span class="uid"><a 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href="https://www.scopus.com/authid/detail.uri?authorId=17333698900">Scopus</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:bocher.maxime">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/259604">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/984180">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd116212039.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/116212039">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/068529880">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w67h367x">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" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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