**George Birkhoff** was an American mathematician who was educated at Chicago and Harvard. He became a Professor at Harvard. His most important work was the Ergodic Theorem he discovered in 1931.

- George was educated in Chicago where he was a student at the Lewis Institute from 1896 to 1902.
- Graduating from the Lewis Institute in 1902, Birkhoff began his university education.
- Birkhoff was awarded his A.B. by Harvard in 1905 and his A.M. in 1906.
- Birkhoff returned to the University of Chicago in 1905 to study for his doctorate.
- His research concentrated on asymptotic expansions, boundary value problems, and Sturm-Liouville type problems but his thesis advisor Eliakim Moore appears to have been a less influential guide to Birkhoff than was Poincaré.
- Birkhoff read Poincaré's works on differential equations and celestial mechanics and he learnt more, and was more strongly influenced in the direction his research was taking, by Poincaré than from his supervisor.
- The doctoral thesis which Birkhoff submitted was entitled Asymptotic Properties of Certain Ordinary Differential Equations with Applications to Boundary Value and Expansion Problems and it led to the award of his Ph.D. in 1907.
- Birkhoff himself developed the ideas further in the following years, as did two of his students, Rudolph Langer and Marshall Stone.
- For example Birkhoff and Langer published an important extension in 1923.
- Birkhoff's work on linear differential equations, difference equations and the generalised Riemann problem mostly all arose from the basis he laid in his thesis.
- Birkhoff taught at the University of Wisconsin at Madison as an instructor from 1907 to 1909.
- Because Birkhoff worked on so many different mathematical topics it is difficult to do justice to the range of his contributions in a biography of this length.
- It is, of course, not only the ergodic theorem that made Birkhoff the most famous mathematician in America in his day.
- The foundations of relativity and quantum mechanics were also topics which Birkhoff studied.
- 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.
- Perhaps this high level of involvement with the American Mathematical Society already suggest that Birkhoff worked tirelessly to advance mathematics in America.
- 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.
- Other honours which Birkhoff received include the Querini-Stampalia prize from the Royal Venice Institute of Science in 1917 for his paper The restricted problem of three bodies published in 1915, the annual prize from the American Association for the Advancement of Science in 1926, and the biennial prize from the Accademia dei Lincei in Rome in 1935.
- This is remarkable world-wide recognition for Birkhoff's outstanding contribution.
- There was, however, a negative side to Birkhoff's character which we should comment on.

Born 21 March 1884, Overisel, Michigan, USA. Died 12 November 1944, Cambridge, Massachusetts, USA.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive