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| {{Infobox scientist
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| |name = Maxime Bôcher
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| |image = Maxime Bôcher.jpg
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| |image_size =
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| |caption =
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| |birth_date = {{Birth date|1867|08|28|mf=y}}
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| |birth_place = [[Boston, Massachusetts]]
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| |death_date = {{death date and age|1918|09|12|1867|08|28|mf=y}}
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| |death_place = [[Cambridge, Massachusetts]]
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| |nationality = [[United States|American]]
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| |field = [[Mathematics]]
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| |work_institutions = [[Harvard University]]
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| |alma_mater = [[Harvard University]]<br>[[University of Göttingen]]
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| |doctoral_advisor = [[Felix Klein]]
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| |doctoral_students = [[William Charles Brenke|William Brenke]]<br>[[David Raymond Curtiss|David R. Curtiss]]<br>[[Griffith C. Evans]]<br>[[Lester R. Ford]]<br>[[Walter Burton Ford|Walter B. Ford]]<br>[[Charles Napoleon Moore|Charles N. Moore]]<br>[[Joseph Leonard Walsh|Joseph L. Walsh]]
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| |known_for = [[Differential equation]]s, [[series (mathematics)|series]], and [[algebra]]
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| |prizes =
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| }}
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| '''Maxime Bôcher''' (August 28, 1867 – September 12, 1918) was an [[United States|American]] [[mathematician]] who published about 100 papers on [[differential equation]]s, [[series (mathematics)|series]], and [[algebra]].<ref>{{cite journal|author=Birkhoff, George D.|authorlink=George David Birkhoff|title=The scientific work of Maxime Bôcher|journal=Bull. Amer. Math. Soc.|year=1919|volume=25|issue=5|pages=197–215|mr=1560177}}</ref> He also wrote elementary texts such as ''[[Trigonometry]]'' and ''[[Analytic Geometry]]''.<ref>{{cite journal|author=Osgood, William F.|authorlink=William Fogg Osgood|title=The life and services of Maxime Bôcher|journal=Bull. Amer. Math. Soc.|year=1919|volume=25|issue=8|pages=337–350|mr=1560199}}</ref> [[Bôcher's theorem]], [[Bôcher's equation]], and the [[Bôcher Memorial Prize]] are named after him.
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| == Life ==
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| Bôcher was born in [[Boston, Massachusetts]]. His parents were Caroline Little and [[Ferdinand Bôcher]]. Maxime's father was professor of modern languages at the [[Massachusetts Institute of Technology]] when Maxime was born, and became Professor of French at [[Harvard]] in 1872.
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| Bôcher received an excellent education from his parents and from a number of public and private schools in Massachusetts. He graduated from the [[Cambridge Rindge and Latin School|Cambridge Latin School]] in 1883. He received his first degree from Harvard in 1888. At Harvard, he studied a wide range of topics, including [[mathematics]], [[Latin]], [[chemistry]], philosophy, zoology, [[geography]], [[geology]], meteorology, Roman art, and [[music]].
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| Bôcher was awarded many prestigious prizes, which allowed him to travel to Europe to research. [[University of Göttingen|Göttingen]] was then the leading mathematics university there, and he attended lectures by [[Felix Klein|Klein]], [[Schönflies]], [[Hermann Schwarz|Schwarz]], [[Issai Schur|Schur]] and [[Woldemar Voigt|Voigt]]. He was awarded a doctorate in 1891 for his dissertation ''Über die Reihenentwicklungen der Potentialtheorie'' (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.
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| 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 [[American Mathematical Society]] from 1908 to 1910.<ref name=amer>{{Americana|wstitle=Bocher, Maxime|year=1920|inline=1}}</ref>
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| Although he was only 46 years old, there were already signs that his weak health was failing. He died at his [[Cambridge, Massachusetts|Cambridge]] home after suffering a prolonged illness.
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| == Bôcher's theorem ==
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| [[Bôcher's theorem]] states that the finite zeros of the derivative <math> r'(z) </math> of a nonconstant rational function <math> r(z) </math> that are not multiple zeros of <math> r(z) </math> are the positions of equilibrium in the field of force due to particles of positive mass at the zeros of <math> r(z) </math> and particles of negative mass at the poles of <math> r(z) </math>, with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.
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| == Bôcher's equation ==
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| Bôcher's equation is a second-order ordinary differential equation of the form:
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| :<math> 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_1x+ \cdots +A_\ell x^\ell}{(x-a_1)^m_1 (x-a_2)^m_2 \cdots (x-a_{n-1})^m_{n-1}} \right]y=0. </math>
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| == The Bôcher Memorial Prize ==
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| The [[Bôcher Memorial Prize]] is awarded by the American Mathematical Society every five years for notable research in analysis that has appeared in a recognized North American journal.
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| Winners have included [[James W. Alexander II]] (1928), [[Eric Temple Bell]] (1924), [[George D. Birkhoff]] (1923), [[Paul Cohen (mathematician)|Paul J. Cohen]] (1964), [[Solomon Lefschetz]] (1924), [[Marston Morse]] and [[Norbert Wiener]] (1933), and [[John von Neumann]] (1938).
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| == Works ==
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| He wrote ''Introduction to Higher Algebra'' (1907) and ''Introduction to the Study of Integral Equations'' (1909). He was one of the editors of the ''[[Annals of Mathematics]]'', of the [[Transactions of the American Mathematical Society|''Transactions'' of the American Mathematical Society]], and collaborator on the ''Encyclopädie der mathematischen Wissenschaften''.<ref name="amer" /> His final book was ''Leçons sur les méthodes de Sturm dans la théorie des équations différentielles linéaires et leurs développements modernes'' (circa 1917).
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| == References ==
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| {{reflist}}
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| == External links ==
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| *{{MacTutor Biography|id=Bocher}}
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| * [http://books.nap.edu/html/biomems/mbocher.html Maxime Bocher] biographical memoirs of the national academy of sciences.
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| *{{MathGenealogy|id=7431}}
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| *[http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/bcher-maxime.pdf National Academy of Sciences Biographical Memoir]
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| {{Authority control|VIAF=76400075|LCCN=n/84/803771|GND=116212039}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME =Bocher, Maxime
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION =United States mathematician
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| | DATE OF BIRTH =August 28, 1867
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| | PLACE OF BIRTH =[[Boston, Massachusetts]]
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| | DATE OF DEATH =September 12, 1918
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| | PLACE OF DEATH =[[Cambridge, Massachusetts]]
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| }}
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| {{DEFAULTSORT:Bocher, Maxime}}
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| [[Category:19th-century American mathematicians]]
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| [[Category:20th-century American mathematicians]]
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| [[Category:American mathematicians]]
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| [[Category:Mathematical analysts]]
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| [[Category:Harvard University faculty]]
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| [[Category:Harvard University alumni]]
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| [[Category:University of Göttingen alumni]]
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| [[Category:1867 births]]
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| [[Category:1918 deaths]]
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| [[Category:Presidents of the American Mathematical Society]]
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