George David Birkhoff (March 21, 1884 – November 12, 1944) was an
American mathematician
This is a list of American mathematicians.
List
* James Waddell Alexander II (1888–1971)
* Stephanie B. Alexander, elected in 2014 as a fellow of the American Mathematical Society "for contributions to geometry, for high-quality exposition, an ...
best known for what is now called the
ergodic theorem
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
. Birkhoff was one of the most important leaders in American mathematics in his generation, and during his time he was considered by many to be the preeminent American mathematician.
The
George D. Birkhoff House, his residence in
Cambridge, Massachusetts
Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Boston metropolitan area, the cities population of the 2020 U.S. census was 118,403, making it the fourth most populous city in the state, behind Boston, ...
, has been designated a
National Historic Landmark
A National Historic Landmark (NHL) is a building, district, object, site, or structure that is officially recognized by the United States government for its outstanding historical significance. Only some 2,500 (~3%) of over 90,000 places listed ...
.
Personal life
He was born in
Overisel Township, Michigan
Overisel Township is a civil township of Allegan County in the U.S. state of Michigan. The population was 3,113 at the 2020 census.
Overisel was named after the Dutch province of Overijssel. Overisel is the birthplace of mathematician George Da ...
, the son of David Birkhoff and Jane Gertrude Droppers. The mathematician
Garrett Birkhoff
Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician. He is best known for his work in lattice theory.
The mathematician George Birkhoff (1884–1944) was his father.
Life
The son of the mathematician Geo ...
(1911–1996) was his son.
Career
Birkhoff obtained his A.B. and A.M. from
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
. He completed his
Ph.D.
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...
in 1907, on
differential equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
, at the
University of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...
. While
E. H. Moore
Eliakim Hastings Moore (; January 26, 1862 – December 30, 1932), usually cited as E. H. Moore or E. Hastings Moore, was an American mathematician.
Life
Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, di ...
was his supervisor, he was most influenced by the writings of
Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
. After teaching at the
University of Wisconsin–Madison
A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...
and
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
, he taught at Harvard from 1912 until his death.
Awards and honors
In 1923, he was awarded the inaugural
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 (contributed by members of that society). It is awarded every three years (formerly every five year ...
by the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
for his paper in 1917 containing, among other things, what is now called the
Birkhoff curve shortening process.
He was elected to the
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
, the
American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...
, the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
, the
Académie des Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...
in Paris, the
Pontifical Academy of Sciences
The Pontifical Academy of Sciences ( it, Pontificia accademia delle scienze, la, Pontificia Academia Scientiarum) is a Academy of sciences, scientific academy of the Vatican City, established in 1936 by Pope Pius XI. Its aim is to promote the ...
, and the London and Edinburgh Mathematical Societies.
The
George David Birkhoff Prize
The George David Birkhoff Prize in applied mathematics is awarded – jointly by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM) – in honour of George David Birkhoff (1884–1944). It is cur ...
in applied mathematics is awarded jointly by the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
and the
Society for Industrial and Applied Mathematics in his honor.
Service
*Vice-president of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
, 1919.
*President of the American Mathematical Society, 1925–1926.
*Editor of
Transactions of the American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...
, 1920–1924.
Work
In 1912, attempting to solve the
four color problem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sha ...
, Birkhoff introduced the
chromatic polynomial
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to s ...
. Even though this line of attack did not prove fruitful, the polynomial itself became an important object of study in
algebraic graph theory
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph th ...
.
In 1913, he proved Poincaré's "
Last Geometric Theorem," a special case of the
three-body problem
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's ...
, a result that made him world-famous. In 1927, he published his
Dynamical Systems'. He wrote on the foundations of relativity and quantum mechanics, publishing (with
R. E. Langer) the monograph ''Relativity and Modern Physics'' in 1923. In 1923, Birkhoff also proved that the
Schwarzschild geometry
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assump ...
is the unique spherically symmetric solution of the
Einstein field equations
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were published by Einstein in 1915 in the form ...
. A consequence is that
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
s are not merely a mathematical curiosity, but could result from any spherical star having sufficient mass.
Birkhoff's most durable result has been his 1931 discovery of what is now called the
ergodic theorem
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
. Combining insights from
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
on the
ergodic hypothesis with
measure theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simil ...
, this theorem solved, at least in principle, a fundamental problem of
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
. The ergodic theorem has also had repercussions for dynamics,
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
,
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
, and
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...
. He also worked on
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
, the
Riemann–Hilbert problem, and the
four colour problem. He proposed an axiomatization of
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small ...
different from Hilbert's (see
Birkhoff's axioms In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry in the plane, sometimes referred to as Birkhoff's axioms. These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protrac ...
); this work culminated in his text ''Basic Geometry'' (1941).
His 1933 ''
Aesthetic Measure'' proposed a
mathematical theory of aesthetics. While writing this book, he spent a year studying the art, music and poetry of various cultures around the world. His 1938 ''Electricity as a Fluid'' combined his ideas on philosophy and science. His 1943 theory of gravitation is also puzzling since Birkhoff knew (but didn't seem to mind) that his theory allows as sources only matter which is a
perfect fluid
In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure ''p''. Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in whi ...
in which the
speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...
must equal the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
.
Influence on hiring practices
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
and
Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher i ...
, among others, accused
Birkhoff of advocating
anti-Semitic
Antisemitism (also spelled anti-semitism or anti-Semitism) is hostility to, prejudice towards, or discrimination against Jews. A person who holds such positions is called an antisemite. Antisemitism is considered to be a form of racism.
Antis ...
hiring practices. During the 1930s, when many Jewish mathematicians fled Europe and tried to obtain jobs in the USA, Birkhoff is alleged to have influenced the hiring process at American institutions to exclude Jews. Birkhoff's anti-Semitic views and remarks are well-documented, but
Saunders Mac Lane
Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.
Early life and education
Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville ...
has argued that Birkhoff's efforts were motivated less by animus towards Jews than by a desire to find jobs for home-grown American mathematicians.
However, Birkhoff took a particular liking to certain Jewish mathematicians, including
Stanislaw Ulam
Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapon ...
.
Gian-Carlo Rota
Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, pro ...
writes: "Like other persons rumored to be anti-Semitic, he would occasionally feel the urge to shower his protective instincts on some good-looking young Jew. Ulam's sparkling manners were diametrically opposite to Birkhoff's hard-working, aggressive, touchy personality. Birkhoff tried to keep Ulam at Harvard, but his colleagues balked at the idea."
[''From cardinals to chaos: reflections on the life and legacy of Stanislaw Ulam'', Necia Grant Cooper, Roger Eckhardt, Nancy Shera, CUP Archive, 1989, Chapter: ''The Lost Cafe'' by Gian-Carlo Rota, page 26]
Selected publications
*
*
*
*Birkhoff, George David and Ralph Beatley. 1959. ''Basic Geometry,'' 3rd ed. Chelsea Publishing Co.
eprint: American Mathematical Society, 2000.
See also
*
Birkhoff factorization In mathematics, Birkhoff factorization or Birkhoff decomposition, introduced by , is the factorization of an invertible matrix ''M'' with coefficients that are Laurent polynomials in ''z'' into a product ''M'' = ''M''+''M''0''M''−, w ...
*
Birkhoff–Grothendieck theorem
In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over \mathbb^1 is a direct sum of holomorphic line bundles. The theorem was ...
*
Birkhoff's theorem
*
Birkhoff's axioms In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry in the plane, sometimes referred to as Birkhoff's axioms. These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protrac ...
*
Birkhoff interpolation
In mathematics, Birkhoff interpolation is an extension of polynomial interpolation. It refers to the problem of finding a polynomial ''p'' of degree ''d'' such that certain derivatives have specified values at specified points:
: p^(x_i) = y_i \qq ...
*
Birkhoff–Kellogg invariant-direction theorem
*
Poincaré–Birkhoff theorem
In symplectic topology and dynamical systems, Poincaré–Birkhoff theorem (also known as Poincaré–Birkhoff fixed point theorem and Poincaré's last geometric theorem) states that every area-preserving, orientation-preserving homeomorphism of a ...
*
Equidistribution theorem
In mathematics, the equidistribution theorem is the statement that the sequence
:''a'', 2''a'', 3''a'', ... mod 1
is uniformly distributed on the circle \mathbb/\mathbb, when ''a'' is an irrational number. It is a special case of the ergodic ...
*
Chromatic polynomial
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to s ...
*
Recurrent point In mathematics, a recurrent point for a function ''f'' is a point that is in its own limit set by ''f''. Any neighborhood containing the recurrent point will also contain (a countable number of) iterates of it as well.
Definition
Let X be a Haus ...
*
Topological dynamics In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.
Scope
The central object of study in topol ...
Notes
References
*Aubin, David, 2005, "Dynamical systems" in
Grattan-Guinness, I., ed., ''Landmark Writings in Western Mathematics''. Elsevier: 871–81.
*
*
Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Fey ...
, 19nn. ''Black Holes and Time Warps''. W. W. Norton. .
*
*
Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher i ...
, 1956. ''I am a Mathematician''. MIT Press. Especially pp. 27–28.
*George D. Birkhoff, Proc Natl Acad Sci U S A. 1943 August; 29(8): 231–239, "Matter, Electricity and Gravitation in Flat Space-Time".
Further reading
*
External links
*
*
*
Birkhoff's biography− from
National Academies Press
The US National Academies Press (NAP) was created to publish the reports issued by the National Academies of Sciences, Engineering, and Medicine, the National Academy of Engineering, the National Academy of Medicine, and the National Research C ...
, by
Oswald Veblen
Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...
.
National Academy of Sciences Biographical Memoir
{{DEFAULTSORT:Birkhoff, George David
1884 births
1944 deaths
20th-century American mathematicians
Harvard University alumni
University of Chicago alumni
University of Wisconsin–Madison faculty
Princeton University faculty
Harvard University faculty
Topologists
American relativity theorists
Presidents of the American Mathematical Society
Members of the United States National Academy of Sciences
Members of the Pontifical Academy of Sciences
Mathematicians from Michigan
Fellows of the Royal Society of Edinburgh
Members of the Göttingen Academy of Sciences and Humanities