George David Birkhoff

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Lore & Background

Birkhoff was born in Overisel Township, Michigan, the son of two Dutch immigrants, David Birkhoff and Jane Gertrude Droppers. His father worked as a physician in Chicago while he was a child. From 1896 to 1902, he attended the Lewis Institute as a teenager. He then spent a year at the University of Chicago, obtained his A.B. and A.M. from Harvard University, returned to the University of Chicago in 1905, and at age twenty-three graduated summa cum laude with his Ph.D. in 1907 in differential equations. While E. H. Moore was his supervisor, he was most influenced by the writings of Henri Poincaré. After teaching at the University of Wisconsin–Madison from 1907 to 1909 and at Princeton University from 1909 to 1912, he taught at Harvard from 1912 until his death. He was the only American familiar with the three main mathematical institutions within the United States—Chicago, Harvard and Princeton. In 1912, attempting to solve the four color problem, Birkhoff introduced the chromatic polynomial. In 1913, he proved Poincaré's 'Last Geometric Theorem,' a special case of the three-body problem, a result that made him world-famous and improved the international recognition of American mathematics. In 1923, Birkhoff proved that the Schwarzschild geometry is the unique spherically symmetric solution of the Einstein field equations, a consequence being that black holes could result from any spherical star having sufficient mass. His 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. He also proposed an axiomatization of Euclidean geometry different from Hilbert's (see Birkhoff's axioms), culminating in his text Basic Geometry (1941). His 1933 Aesthetic Measure proposed a mathematical theory of aesthetics.

Reader's Guide

Birkhoff's significance lies in his foundational contributions across multiple areas of mathematics and physics. His ergodic theorem solved, at least in principle, a fundamental problem of statistical mechanics and has had repercussions for dynamics, probability theory, group theory, and functional analysis. His proof of Poincaré's last geometric theorem advanced the three-body problem and raised the international recognition of American mathematics. In general relativity, his uniqueness theorem for the Schwarzschild solution was later used to develop the Oppenheimer–Snyder model. He served as president of the American Mathematical Society from 1925 to 1926 and as president of the American Association for the Advancement of Science in 1937, a rare occurrence for mathematicians. His legacy includes the George David Birkhoff Prize in applied mathematics, awarded jointly by the American Mathematical Society and the Society for Industrial and Applied Mathematics. However, his career is also marked by controversy: Albert Einstein and Norbert Wiener accused Birkhoff of advocating antisemitic selection processes during the 1930s. Saunders Mac Lane called Einstein's allegations 'worthless' and stated Birkhoff's efforts were motivated by a desire to find jobs for home-grown American mathematicians, but correspondence later revealed that his views of Jews were antisemitic. Yet he was close to Jewish mathematician Stanislaw Ulam, and Gian-Carlo Rota wrote that Birkhoff 'would occasionally feel the urge to shower his protective instincts on some good-looking young Jew.'

Did You Know?

• Birkhoff graduated summa cum laude with his Ph.D. at age twenty-three in 1907.
• He proved Poincaré's 'Last Geometric Theorem' in 1913, a special case of the three-body problem, which made him world-famous.
• In 1923, Birkhoff proved that the Schwarzschild geometry is the unique spherically symmetric solution of the Einstein field equations.
• He served as president of the American Association for the Advancement of Science in 1937, a rare occurrence for mathematicians.
• Birkhoff's 1933 book Aesthetic Measure proposed a mathematical theory of aesthetics, for which he spent a year studying art, music, and poetry.