George David Birkhoff

George David Birkhoff (March21, 1884November12, 1944) was an American mathematician. He is considered 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. The George D. Birkhoff House, his residence in Cambridge, Massachusetts, has been designated a National Historic Landmark.

Early life He was born in Overisel Township, Michigan, the son of two Dutch immigrants, David Birkhoff, who arrived in the United States in 1870, and Jane Gertrude Droppers. Birkhoff's father worked as a physician in Chicago while he was a child. a special case of the three-body problem, a result that made him world-famous and improved the international recognition of American mathematics.

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. 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.

Influence on selection process Birkhoff believed that fellowships from foreign nations would improve the mathematic standards in the United States, though he wanted to raise the standards for fellowships, believing that the qualifications in less-developed countries were different and that access should be limited. He also was adamant that foreign fellows be able to meet language requirements.

Albert Einstein and Norbert Wiener, among others, accused Birkhoff of advocating antisemitic selection processes. During the 1930s, when many Jewish mathematicians fled Europe and tried to obtain positions in the United States, Birkhoff is alleged to have influenced the selection process at American institutions to exclude Jews. Mac Lane also stated that Birkhoff's efforts were motivated less by animus towards Jews than by a desire to find jobs for home-grown American mathematicians. However, in some of the correspondence that came to light in the book A History in Sum: 150 Years of Mathematics at Harvard (1825-1975), it is obvious that his views of Jews were antisemitic and he regarded them as suspicious elements of the American society.

Birkhoff was, on the other hand, close to a Jewish mathematician Stanislaw Ulam. Gian-Carlo Rota 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."

Summarizing Birkhoff's selection process, fellow mathematician Oswald Veblen would write:

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, 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 Birkhoff married Margaret Elizabeth Graftus in 1908. They had three children, Barbara, mathematician Garrett Birkhoff (1911–1996) and Rodney.

Selected publications

Birkhoff, George David and Ralph Beatley. 1959. Basic Geometry, 3rd ed. Chelsea Publishing Co. [Reprint: American Mathematical Society, 2000. ]