Birkhoff, George David

Birkhoff, George David

▪ American mathematician
born March 21, 1884, Overisel, Michigan, U.S.
died November 12, 1944, Cambridge, Massachusetts

      foremost American mathematician of the early 20th century, who formulated the ergodic theorem.

      Birkhoff attended the Lewis Institute (now the Illinois Institute of Technology) in Chicago from 1896 to 1902 and then spent a year at the University of Chicago (Chicago, University of) before switching to Harvard University in 1903 (A.B., 1905; A.M., 1906). He returned to Chicago in 1905 and received a doctorate there in 1907.

      Birkhoff taught at the University of Wisconsin (Wisconsin, University of) (1907–09), Princeton University (1909–12), and Harvard (1912–44). He was an extraordinarily stimulating lecturer and director of research. By the mid 20th century many of the leading American mathematicians either had written their doctoral dissertations under his direction or had done postdoctoral research with him. He edited the Transactions of the American Mathematical Society from 1921 to 1924 and served as the organization's president from 1925 to 1926.

      Birkhoff conducted research mainly in mathematical analysis and its application to dynamics. In the latter he was especially influenced by the work of the French mathematician Henri Poincaré (Poincaré, Henri). His dissertation and much of his later work dealt with the solutions of ordinary differential equations (differential equation) and the associated expansions of arbitrary functions. Using matrix methods, he also contributed fundamentally to the theory of difference equations (difference equation).

      In 1913 Birkhoff proved Poincaré's “last geometric theorem.” The theorem, which Poincaré announced without proof in 1912 shortly before he died, confirms the existence of an infinite number of periodic solutions for the restricted three-body problem—i.e., stable orbits involving three (solar) bodies. Birkhoff's proof was a striking achievement and one that brought him immediate worldwide acclaim. In 1931, stimulated by the recent work of John von Neumann (von Neumann, John) and others, he published his formulation of the ergodic theorem. The theorem, which transformed the Maxwell-Boltzmann ergodic hypothesis of the kinetic theory of gases into a rigorous principle through the use of Lebesgue measure theory (see analysis: Measure theory (analysis)), has important applications to modern analysis. Birkhoff developed his own theory of gravitation which was published shortly before he died, and he constructed a mathematical theory of aesthetics, which he applied to art, music, and poetry. All this internationally renowned creative work stimulated further scientific discoveries.

      Birkhoff's works include Relativity and Modern Physics (1923), Dynamical Systems (1928), Aesthetic Measure (1933), and a textbook on elementary geometry, Basic Geometry (1941; with Ralph Beatley).

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Universalium. 2010.

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  • George David Birkhoff — (* 21. März 1884 in Overisel, Michigan; † 12. November 1944 in Cambridge, Massachusetts) galt zu seiner Zeit als führender US amerikanischer Mathematiker …   Deutsch Wikipedia

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  • George Birkhoff — George David Birkhoff George David Birkhoff (* 21. März 1884 in Overisel, Michigan; † 12. November 1944 in Cambridge, Massachusetts) war ein US amerikanischer Mathematiker. Er galt zu seiner Zeit als führender US Mathematiker …   Deutsch Wikipedia

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  • Prix George David Birkhoff — Le Prix George David Birkhoff en mathématiques appliquées est une récompense décernée conjointement par l American Mathematical Society (AMS) et la Society for Industrial and Applied Mathematics (SIAM) – en l honneur de George David Birkhoff… …   Wikipédia en Français

  • BIRKHOFF (G. D.) — BIRKHOFF GEORGE DAVID (1884 1944) Après des études à Chicago, Birkhoff enseigna à l’université du Wisconsin (1907 1909), à celle de Princeton (1909 1912) et enfin à l’université Harvard, de 1912 jusqu’à sa mort. Il fut un brillant enseignant et… …   Encyclopédie Universelle

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