George David Birkhoff

George David Birkhoff ( born March 21, 1884 in Overisel, Michigan, † November 12, 1944 in Cambridge, Massachusetts ) was an American mathematician.

Life

Birkhoff had Dutch ancestry ( his grandfather emigrated in 1869 as a carpenter ), the son of a doctor was in Chicago and went to school ( Lewis Institute). Even before graduating, he corresponded with Harry Vandiver on number theoretical problems, which led to a joint publication in 1904. He studied from 1902 at the University of Chicago from 1903 to 1905 and from Harvard University with William Fogg Osgood maxim Bôcher and where he made his Bachelor 1905 and 1906 his master's degree. In 1905 he went back to the University of Chicago, where he he received his doctorate at Eliakim Hastings Moore with a thesis on differential equations 1907 ( Asymptotic Properties of Certain Ordinary Differential Equations with Applications to Boundary Value and Expansion problem). His greatest influence were the works of Henri Poincaré on differential equations and celestial mechanics. In 1913 he proved a Poincaré left open to problem, a special case of the three-body problem of celestial mechanics. More of his teachers in Chicago were Oskar Bolza and Heinrich Maschke. The problems that arose from his dissertation, occupied him and his students Rudolph Langer and Marshall Stone in the following decades. Birkhoff taught then 1907-1909 at the University of Wisconsin in Madison and Princeton University, where he became professor in 1911. In 1912 he went to Harvard as an assistant professor, where he became professor in 1919 and remained until his death. In 1932 he became a professor there, Perkins and 1936 Dean of the Faculty of Arts and Sciences. After he had suffered for several years from heart failure, he died in 1944 in his sleep.

Birkhoff was at the time a central position in the U.S. mathematics. He maintained close relations with European mathematicians, particularly Tullio Levi -Civita, Niels Erik Nørlund, Jacques Hadamard and Edmund Whittaker. Sometimes anti-Semitism he has been accused in relation to appointments at Harvard, at least the appointment of Oscar Zariski but he does not seem to have worked against.

In 1917 he received the Querini - Stampalia price of the Venetian Academy for The restricted problem- fo three bodies (1915 ), 1926 the price of the American Association for the Advancement of Science and in 1935 awarded every two years the price of the Pontifical Academy of Sciences in Rome. In 1923 he received the first Bôcher Memorial Prize of the American Mathematical Society ( AMS) for Dynamical systems with two degrees of freedom ( Transactions of the American Mathematical Society, 1917). In 1928 he gave a plenary lecture at the International Congress of Mathematicians in Bologna ( Quelques éléments Mathématiques de l'art ) as well as on the 1936 in Oslo ( On the Foundations of Quantum Mechanics ).

He was a member of the National Academy of Sciences, the American Academy of Arts and Sciences, the American Philosophical Society, the French, Danish, Göttingen and Pontifical Academies of Sciences, the Circolo Mathematico di Palermo and the mathematical societies of London ( London Mathematical Society) and Edinburgh (Edinburgh Mathematical Society ). In 1919, he was Vice President of AMS and 1925/6 president. 1921 to 1924 he was editor of the Transactions of the AMS.

He was married to the same age Margaret Elizabeth Graftus since 1908 and had three children. The famous mathematician Garrett Birkhoff (1911-1996) was his son.

Work

Birkhoff is today best known for his formulation of the ergodic theorem (1931 /2), together with his PhD student Bernard Koopman. The ergodic theorem combines insights from physics ( ergodic hypothesis ) with an abstract formulation of the measure theory.

Additional areas of Birkhoff were number theory, the three-body problem and the four- color theorem.

He also dealt with the theory of relativity and wrote in 1923 together with Langer the book " Relativity and Modern Physics".

In addition, Birkhoff did research for a uniform rule for aesthetic evaluation of works of art (where he previously one years traveled the world to study works of art ). With his study "Aesthetic Measure" (1933 ) he came to a formula for the aesthetic dimension:

In the case of the performing arts, the "order" O of geometric contexts depends. Properties such as symmetry and balance are observed. The " complexity " ( Complexity ) C defines the number of points of the work, which attract the attention of the viewer. This approach is similar to the Norbert Wiener and later by Max Bense ( German philosopher) was added with further insights. As the factors are to be determined, Birkhoff had also defined in "Aesthetic Measure".

Publications

  • Collected Mathematical Papers, 3 vols, 1950 (with 3 portraits)
  • Proof of Poincaré 's geometric theoremTrans. Amer. Math Soc. Vol 14, 1913, p.14 - 22nd
  • Dynamical Systems with Two Degrees of Freedom Trans Amer. Math Soc. Bd.18, 1917, p.199 -300.
  • Proof of the ergodic theorem, Proceedings of National Acad. Sci. USA, Vol 17, 1931, S.656 -660, pdf file
  • What is the ergodic theorem? , American Mathematical Monthly, Vol 49, 1942, P.222 -226,
  • Dynamical Systems, AMS, 1927
  • Basic Geometry, 1941, 3rd edition Chelsea Publishing 1959
  • Aesthetic Measure, Harvard University Press 1933
Cambridge (Massachusetts) Marshall Harvey Stone E. T. Whittaker Ergodic theory#Ergodic theorems Birkhoff's theorem (relativity) Integrated Authority File
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