Maxime Bôcher
Encyclopedia
Maxime Bôcher was an American
mathematician
who published about 100 papers on differential equation
s, series
, and algebra
. He also wrote elementary texts such as Trigonometry
and Analytic Geometry
. Bôcher's theorem
, Bôcher's equation, and the Bôcher Memorial Prize
are named after him.
when Maxime was born, and became Professor of French at Harvard in 1872.
Bôcher received an excellent education from his parents and from a number of public and private schools in Massachusetts. He graduated from the 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
.
Bôcher was awarded many prestigious prizes, which allowed him to travel to Europe to research. Göttingen was then the leading mathematics university there, and he attended lectures by Klein
, Schönflies, Schwarz
, Schur
and 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.
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.
Although he was only 46 years old, there were already signs that his weak health was failing. He died at his Cambridge
home after suffering a prolonged illness.
states that the finite zeros of the derivative
of a nonconstant rational function 
that are not multiple zeros of 
are the positions of equilibrium in the field of force due to particles of positive mass at the zeros of 
and particles of negative mass at the poles of 
, with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.
is awarded by the American Mathematical Society every five years for notable research in analysis that has appeared in a recognized North American journal.
Winners have included James W. Alexander (1928), Eric Temple Bell
(1924), George D. Birkhoff (1923), Paul J. Cohen
(1964), Solomon Lefschetz
(1924), Marston Morse
and Norbert Wiener
(1933), and John von Neumann
(1938).
, of the Transactions of the American Mathematical Society
, and collaborator on the Encyclopädie der mathematischen Wissenschaften. His final book was Leçons sur les méthodes de Sturm dans la théorie des équations différentielles linéaires et leurs développements modernes (circa 1917).
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who published about 100 papers on differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s, series
Series (mathematics)
A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....
, and algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
. He also wrote elementary texts such as Trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
and Analytic Geometry
Analytic geometry
Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties...
. Bôcher's theorem
Bôcher's theorem
In mathematics, Bôcher's theorem can refer to one of two theorems proved by the American mathematician Maxime Bôcher.-Bôcher's theorem in complex analysis:...
, Bôcher's equation, and the Bôcher Memorial Prize
Bôcher Memorial Prize
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 . It is awarded every five years for a notable research memoir in analysis that has appeared during the past six years in a recognized North American...
are named after him.
Life
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 TechnologyMassachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
when Maxime was born, and became Professor of French at Harvard in 1872.
Bôcher received an excellent education from his parents and from a number of public and private schools in Massachusetts. He graduated from the Cambridge Latin School
Cambridge Rindge and Latin School
The Cambridge Rindge and Latin School is a public high school in Cambridge, Massachusetts, United States.The school, serving grades 9 through 12, is a part of the Cambridge Public Schools....
in 1883. He received his first degree from Harvard in 1888. At Harvard, he studied a wide range of topics, including mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
, chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, philosophy, zoology, geography
Geography
Geography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...
, geology
Geology
Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...
, meteorology, Roman art, and music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
.
Bôcher was awarded many prestigious prizes, which allowed him to travel to Europe to research. Göttingen was then the leading mathematics university there, and he attended lectures by Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
, Schönflies, Schwarz
Hermann Schwarz
Karl Hermann Amandus Schwarz was a German mathematician, known for his work in complex analysis. He was born in Hermsdorf, Silesia and died in Berlin...
, Schur
Issai Schur
Issai Schur was a mathematician who worked in Germany for most of his life. He studied at Berlin...
and Voigt
Woldemar Voigt
Woldemar Voigt was a German physicist, who taught at the Georg August University of Göttingen. Voigt eventually went on to head the Mathematical Physics Department at Göttingen and was succeeded in 1914 by Peter Debye, who took charge of the theoretical department of the Physical Institute...
. 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.
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
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
from 1908 to 1910.
Although he was only 46 years old, there were already signs that his weak health was failing. He died at his Cambridge
Cambridge, Massachusetts
Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent...
home after suffering a prolonged illness.
Bôcher's theorem
Bôcher's theoremBôcher's theorem
In mathematics, Bôcher's theorem can refer to one of two theorems proved by the American mathematician Maxime Bôcher.-Bôcher's theorem in complex analysis:...
states that the finite zeros of the derivative
of a nonconstant rational function that are not multiple zeros of are the positions of equilibrium in the field of force due to particles of positive mass at the zeros of and particles of negative mass at the poles of , 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
Bôcher's equation is a second-order ordinary differential equation of the form:The Bôcher Memorial Prize
The Bôcher Memorial PrizeBôcher Memorial Prize
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 . It is awarded every five years for a notable research memoir in analysis that has appeared during the past six years in a recognized North American...
is awarded by the American Mathematical Society every five years for notable research in analysis that has appeared in a recognized North American journal.
Winners have included James W. Alexander (1928), Eric Temple Bell
Eric Temple Bell
Eric Temple Bell , was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life...
(1924), George D. Birkhoff (1923), Paul J. Cohen
Paul Cohen (mathematician)
Paul Joseph Cohen was an American mathematician best known for his proof of the independence of the continuum hypothesis and the axiom of choice from Zermelo–Fraenkel set theory, the most widely accepted axiomatization of set theory.-Early years:Cohen was born in Long Branch, New Jersey, into a...
(1964), Solomon Lefschetz
Solomon Lefschetz
Solomon Lefschetz was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.-Life:...
(1924), Marston Morse
Marston Morse
Harold Calvin Marston Morse was an American mathematician best known for his work on the calculus of variations in the large, a subject where he introduced the technique of differential topology now known as Morse theory...
and Norbert Wiener
Norbert Wiener
Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...
(1933), and John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
(1938).
Works
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 MathematicsAnnals of Mathematics
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
, of the Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society is a monthly mathematics journal published by the American Mathematical Society. It started in 1900...
, and collaborator on the Encyclopädie der mathematischen Wissenschaften. His final book was Leçons sur les méthodes de Sturm dans la théorie des équations différentielles linéaires et leurs développements modernes (circa 1917).
External links
- Maxime Bocher biographical memoirs of the national academy of sciences.