Maxime Bôcher
Born	(1867-08-28)August 28, 1867 Boston,Massachusetts, U.S.
Died	September 12, 1918(1918-09-12) (aged 51) Cambridge, Massachusetts, U.S.
Alma mater	Harvard University University of Göttingen
Known for	Differential equations,series, andalgebra
Scientific career
Fields	Mathematics
Institutions	Harvard University
Doctoral advisor	Felix Klein
Doctoral students	William Brenke David R. Curtiss Griffith C. Evans Lester R. Ford Walter B. Ford James W. Glover Charles N. Moore William H. Roever Joseph L. Walsh

Maxime Bôcher (August 28, 1867 – September 12, 1918) was an Americanmathematician who published about 100 papers ondifferential equations,series, andalgebra.^[1] He also wrote elementary texts such asTrigonometry andAnalytic Geometry.^[2]Bôcher's theorem,Bôcher's equation, and theBôcher Memorial Prize are named after him.

Bôcher was born inBoston,Massachusetts. His parents were Caroline Little andFerdinand Bôcher. Maxime's father was professor of modern languages at theMassachusetts Institute of Technology when Maxime was born, and became Professor ofFrench atHarvard University in 1872.

Bôcher received an excellent education from his parents and from a number of public and private schools in Massachusetts. He graduated from theCambridge Latin School in 1883. He received his first degree from Harvard in 1888. At Harvard, he studied a wide range of topics, includingmathematics,Latin,chemistry, philosophy, zoology,geography,geology, meteorology, Roman art, andmusic.

Bôcher was awarded many prestigious prizes, which allowed him to travel to Europe to do research. TheUniversity of Göttingen was then the leading mathematics university, and he attended there lectures byFelix Klein,Arthur Moritz Schoenflies,Hermann Schwarz,Issai Schur andWoldemar Voigt. He was awarded a doctorate in 1891 for his dissertationÜber die Reihenentwicklungen der Potentialtheorie (German 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.

Bocher was elected to theAmerican Academy of Arts and Sciences in 1899,^[3] the United StatesNational Academy of Sciences in 1909,^[4] and theAmerican Philosophical Society in 1916.^[5]

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 theAmerican Mathematical Society from 1908 to 1910.^[6]

Although he was only 46 years old, there were already signs that his weak health was failing. He died at hisCambridge home after suffering a prolonged illness.

Bôcher's theorem states that the finitezeros of thederivative${\displaystyle r^{\prime }(z)}$ of a non-constantrational function${\displaystyle r(z)}$ that are not multiple zeros of${\displaystyle r(z)}$ are the positions of equilibrium in the field of force due to particles of positive mass at the zeros of${\displaystyle r(z)}$ and particles ofnegative mass at thepoles of${\displaystyle r(z)}$, with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.

Bôcher's equation is a second-orderordinary differential equation of the form:

${\displaystyle y^{″}+\frac{1}{2}\left[\frac{m_1}{x-a_1}+\cdots +\frac{m_{n-1}}{x-a_{n-1}}\right]y^{\prime }+\frac{1}{4}\left[\frac{A_0+A_{1}x+\cdots +A_{\ell }{x}^{\ell }}{(x-a_1{)}_1^m(x-a_2{)}_2^m\cdots (x-a_{n-1}{)}_{n-1}^m}\right]y=0.}$

TheBôcher Memorial Prize is awarded by the American Mathematical Society every five years for notable research inanalysis that has appeared in a recognized North American journal.

Winners have includedJames W. Alexander II (1928),Eric Temple Bell (1924),George D. Birkhoff (1923),Paul J. Cohen (1964),Solomon Lefschetz (1924),Marston Morse andNorbert Wiener (1933), andJohn von Neumann (1938).

• 1894:Ueber die Reihenentwicklungen der Potentialtheorie viaInternet Archive
• 1900: "Randwertaufgaben bei Gewöhnlich Differentialgleichung",Encyclopädie der mathematischen Wissenschaften Band 2–1–1.
• 1907: (with E.P.R.DuVal)Introduction to Higher Algebra viaHathiTrust
• 1909:Introduction to the study of Integral Equations via Internet Archive
• 1917:Leçons sur les méthodes de Sturm dans la théorie des équations différentielles linéaires et leurs développements modernes via Internet Archive.

Bôcher was one of the editors of theAnnals of Mathematics and of theTransactions of the American Mathematical Society.^[6]

• O'Connor, John J.;Robertson, Edmund F.,"Maxime Bôcher",MacTutor History of Mathematics Archive,University of St Andrews
• Maxime Bocher biographical memoirs of the national academy of sciences.
• Maxime Bôcher at theMathematics Genealogy Project
• National Academy of Sciences Biographical Memoir

• 19th-century American mathematicians
• 20th-century American mathematicians
• American mathematical analysts
• Harvard University Department of Mathematics faculty
• Harvard University alumni
• University of Göttingen alumni
• 1867 births
• 1918 deaths
• Presidents of the American Mathematical Society
• Cambridge Rindge and Latin School alumni
• Mathematicians from Boston
• Members of the United States National Academy of Sciences
• Members of the American Philosophical Society

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