George David Birkhoff

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

Birkhoff had a central position in US mathematics in his time. He maintained close relationships with European mathematicians, especially Tullio Levi-Civita , Niels Erik Nørlund , Jacques Hadamard and Edmund Whittaker . Occasionally he has been accused of anti-Semitism in relation to positions at Harvard , but at least he does not seem to have worked against the appointment of Oscar Zariski .

In 1917 he received the Querini Stampalia Prize of the Venetian Academy for The restricted problem fo three bodies (1915), in 1926 the Prize of the American Association for the Advancement of Science, and in 1935 the biannual prize 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 at 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 (1913), the American Philosophical Society , the Académie des Sciences , the Danish Academy of Sciences , the Academy of Sciences in Göttingen , the Royal Society of Edinburgh and the Pontifical Academy 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 the AMS and President in 1925/6. From 1921 to 1924 he was editor of the Transactions of the AMS.

In 1970 the lunar crater Birkhoff was named after him.

He had been married to Margaret Elisabeth Graftus of the same age since 1908 and had three children. The well-known mathematician Garrett Birkhoff (1911–1996) was his son.

His PhD students include Clarence Raymond Adams , Robert Daniel Carmichael , Marston Morse , Charles Morrey , Bernard Koopman , David Widder , Marshall Stone , Hyman Ettlinger, and Hassler Whitney .

plant

Birkhoff is best known today for his formulation of the individual ergodic set (1931/2) together with his doctoral student Bernard Koopman . The ergodic theorem combines findings from physics ( ergodic hypothesis ) with an abstract formulation from measurement theory . The set partly bears his name and is called the Ergodic set by Birkhoff .

Birkhoff's other areas of work were number theory , the three-body problem and the four-color theorem .

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

In addition, Birkhoff researched a uniform rule for the aesthetic assessment of works of art (although he had previously traveled the world for a year to study works of art). With his investigation "Aesthetic Measure" (1933) he came up with a formula for the aesthetic measure:

In the case of the performing arts, the “order” O depends on geometric relationships. Properties such as symmetry and balance must be taken into account. The “Complexity” C defines the number of all points in the work that attract the viewer's attention. This approach is comparable to that of Norbert Wiener and was later also taken up by Max Bense (German philosopher) with further insights. Birkhoff also defined how the individual factors are to be determined in “Aesthetic Measure”.

Publications

  • Collected Mathematical Papers , 3 vols., 1950 (with 3 portraits)
  • Proof of Poincaré's geometric theorem Trans. Amer. Math. Soc. Vol. 14, 1913, pp. 14-22.
  • Dynamical Systems with Two Degrees of Freedom Trans. Amer. Math. Soc. Vol. 18, 1917, pp. 199-300.
  • Proof of the ergodic theorem , Proceedings National Acad. Sci. USA, Vol. 17, 1931, pp.656-660, PDF file
  • What is the ergodic theorem? , American Mathematical Monthly, Vol. 49, 1942, pp. 222-226.
  • Dynamical Systems , AMS, 1927
  • Basic Geometry , 1941, 3rd edition, Chelsea Publishing 1959
  • Aesthetic Measure , Harvard University Press 1933

See also

Web links

Individual evidence

  1. ^ Biographical Index: Former RSE Fellows 1783–2002. Royal Society of Edinburgh, accessed October 9, 2019 .
  2. ↑ George David Birkhoff in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
personal data
SURNAME Birkhoff, George David
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH March 21, 1884
PLACE OF BIRTH Overisel , Michigan
DATE OF DEATH November 12, 1944
Place of death Cambridge , Massachusetts