George David Birkhoff
George David Birkhoff (March 21, 1884 – November 12, 1944) was one of the top American mathematicians of his generation. He made valuable contributions to the theory of differential equations, dynamical systems, the four-color problem, the three-body problem, and general relativity. Today, Birkhoff is best remembered for the ergodic theorem.[1] The George D. Birkhoff House, his residence in Cambridge, Massachusetts, has been designated a National Historic Landmark.
George David Birkhoff
March 21, 1884
November 12, 1944 (aged 60)
American
Bôcher Memorial Prize (1923)
Newcomb Cleveland Prize (1926)
Harvard University
Yale University
Princeton University
Radcliffe College
Early life[edit]
He was born in Overisel Township, Michigan,[2] the son of two Dutch immigrants, David Birkhoff, who arrived in the United States in 1870, and Jane Gertrude Droppers.[3][4] Birkhoff's father worked as a physician in Chicago while he was a child.[4] From 1896 to 1902, he would attend the Lewis Institute as a teenager.[4]
Work[edit]
In 1912, attempting to solve the four color problem, Birkhoff introduced the chromatic polynomial. Even though this line of attack did not prove fruitful, the polynomial itself became an important object of study in algebraic graph theory.
In 1913, he proved Poincaré's "Last Geometric Theorem,"[10] a special case of the three-body problem, a result that made him world-famous and improved the international recognition of American mathematics.[5]
Birkhoff was also a contributor to the development of general relativity. 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 is the unique spherically symmetric solution of the Einstein field equations. A consequence is that black holes are not merely a mathematical curiosity, but could result from any spherical star having sufficient mass. His theorem was later used to develop the Oppenheimer–Snyder model. In 1927, he published his Dynamical Systems.
Birkhoff's most durable result has been his 1931 discovery of what is now called the ergodic theorem. Combining insights from physics on the ergodic hypothesis with measure theory, this theorem solved, at least in principle, a fundamental problem of statistical mechanics. The ergodic theorem has also had repercussions for dynamics, probability theory, group theory, and functional analysis. He also worked on number theory, the Riemann–Hilbert problem, and the four colour problem. He proposed an axiomatization of Euclidean geometry different from Hilbert's (see Birkhoff's axioms); this work culminated in his text Basic Geometry (1941).
His 1933 Aesthetic Measure proposed a mathematical theory of aesthetics.[11] 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 which the speed of sound must equal the speed of light.
Recognition[edit]
In 1923, he was awarded the inaugural Bôcher Memorial Prize by the American Mathematical Society for his paper in 1917 containing, among other things, what is now called the Birkhoff curve shortening process.[21]
He was elected to the National Academy of Sciences, the American Philosophical Society, the American Academy of Arts and Sciences, the Académie des Sciences in Paris, the Pontifical Academy of Sciences,[22] and the London and Edinburgh Mathematical Societies.
The George David Birkhoff Prize in applied mathematics is awarded jointly by the American Mathematical Society and the Society for Industrial and Applied Mathematics in his honor.
Personal life[edit]
Birkhoff married Margaret Elizabeth Graftus in 1908.[4] The two had three children, Barbara, mathematician Garrett Birkhoff (1911–1996) and Rodney.[4]
