George David Birkhoff

Born: 21 March 1884 in Overisel, Michigan, USA
Died: 12 Nov 1944 in Cambridge, Massachusetts, USA

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George Birkhoff was a student at the Lewis Institute in Chicago from 1896 to 1902. He attended the University of Chicago in 1902-3, then moving to Harvard University from 1903 to 1905. He was awarded his A.B. by Harvard in 1905 and his A.M. in 1906.

Birkhoff returned to Chicago in 1905 to study for his doctorate which was awarded in 1907. Archibald writes in [5]:-

During his two years at Harvard, one in college and one in the graduate school, Bôcher and Osgood were in their prime; but during the next two years [at Chicago] he worked under Eliakim Moore, Bolza and Maschke, in the most inspiring mathematical center in the United States at that time. His dissertation was done quite independently however.
Birkhoff taught at Wisconsin Madison at an instructor from 1907 to 1909 when he went to Princeton, becoming a professor there in 1911. In 1912 he moved to Harvard as an assistant professor and he was promoted to full professor there in 1919. In 1936 he became Dean of the Faculty of Arts and Science at Harvard.

His main work was on dynamics and ergodic theory. His ergodic theorem transformed the Maxwell-Boltzmann kinetic theory of gases into a rigorous principle through the use of Lebesgue measure. He also worked on linear differential equations and difference equations.

Birkhoff proved Poincaré's Last Geometric Theorem , a special case of the 3-body problem, in 1913. He also studied the foundations of relativity and quantum mechanics. Birkhoff also did important work on the four colour theorem. He developed a mathematical theory of aesthetics which he applied to art, music and poetry. This is refered to in [5]:-

He has told us that the formal structure of western music, the riddle of melody, began to interest him in undergraduate days; somewhat intense consideration of the mathematical elements here involved led him to apply his theory also to aesthetic objects such as polygons, tilings, vases, and even poetry.
Among his works are Relativity and Modern Physics (1923), Dynamical Systems (1928), Aesthetic Measure (1933), and Basic Geometry (1941).

In 1923 the American Mathematical Society made the first award of the Bôcher Memorial Prize to Birkhoff for his memoir, Dynamical systems with two degrees of freedom which he had published in the Transactions of the American Mathematical Society in 1917. He had a long association with the American Mathematical Society being Vice-President in 1919, Colloquium lecturer in 1920 when he lectured on Dynamical Systems , he edited the Transactions of the American Mathematical Society from 1921 to 1924 and was President from 1925 to 1926.

Of local interest in St Andrews is the fact that Birkhoff was one of the main speakers at the 1926 St Andrews Colloquium and was elected an honorary member of the Edinburgh Mathematical Society in 1927. He gave four lectures at the Gregory Tercentenary celebrations by the Edinburgh Mathematical Society in July 1938 and was awarded an honorary LL.D. by the University of St Andrews during his 1938 visit.

The article [5], written shortly before his death, describes him as:-

... by nature intensely social; through many trips to Europe, and circumnavigation of the globe, he has been extensively in contact with scholars throughout the world; he is a constant attendant and participant at meetings and congresses, and has been frequently in demand as a writer and speaker on popular themes. In recent administrative gatherings the originality and breadth of his views have been noteworthy.

References (16 books/articles)

References elsewhere in this archive:

Tell me about Birkhoff's work on the four colour theorem and on orbits and gravitation

G D Birkhoff was the President of the American Mathematical Society in 1925 - 1926. You can see a history of the AMS and a list of AMS presidents.
He was the American Mathematical Society Colloquium Lecturer in 1920. You can see a history of the AMS Colloquium and a list of the lecturers.
He was the Bocher Prize winner in 1923. You can see a history of the AMS Bocher Prize and a list of the winners.

George D Birkhoff was elected an honorary member of the Edinburgh Mathematical Society in 1926. You can see a history of the EMS and a list of the honorary fellows.

There is a Crater Birkhoff on the moon. You can see a list of lunar features named after mathematicians.

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JOC/EFR October 1997