The greatest American mathematician of the early 20th century. Birkhoff was educated at the University of Chicago,
where he received his Ph.D. in 1907. He then taught at University of Wisconsin (1907-1909), Princeton (1909-1912),
and Harward (1912-1939). He served as president of the American Mathematical Society (1924-26), as dean of the
Harvard Faculty of Arts and Sciences (1935-39), and as president of the American Association for the Advancement of
Science (1936-37). He was also editor of Annals of Mathematics (1911-13), Transactions of the American
Mathematical Society (1920-25), and the American Journal of Mathematics (1943-44). Over the course of his
career, Birkhoff was honored with numerous prizes and awards.
Birkhoff conducted research mainly in mathematical analysis and analysis applied to dynamics. He formulated the ergodic
theorem, which transformed the Maxwell-Boltzmann ergodic hypothesis of the kinetic theory of gases into a rigorous
principle. He also investigated linear differential equations and theory of difference equations. He studied periodic
orbits and three-body problems within general theory of dynamic systems and ergodic theory, and found the existence of
an infinite number of periodic solutions to the restricted three-body problem. 
Birkhoff also studied
regularization in a 1915 paper. In topology, Birkhoff proved Poincaré's last geometric theorem, a
special case of the three-body problem (1913) and also did important work on the four-color
theorem 
. He studied mechanics of fluids in connection with mathematical treatment of viscosity. He also studied the
foundations of relativity and quantum mechanics, developed a theory of gravitation, and constructed a mathematical
theory of aesthetics, which he applied to art, music, and poetry.
Birkhoff, G. D. "General Theory of Linear Difference Equations." Trans. Amer. Math. Soc. 12, 243-284, 1911.
Birkhoff, G. D. "A Determinant Formula for the Number of Ways of Coloring a Map." Ann. Math. Harvard Coll. 14, 1912/13.
Birkhoff, G. D. "Proof of Poincaré's Geometric Theorem." Trans. Amer. Math. Soc. 14 14-22, 1913.
Birkhoff, G. D. "The Generalized Riemann Problem for Linear Differential Equations and the Allied Problem for Linear Difference Equations."
Amer. Acad. Proc. (Boston) 49, 1914.
Birkhoff, G. D. "Dynamical Systems with Two Degrees of Freedom." Trans. Amer. Math. Soc. 18, 199-300, 1917.
Birkhoff, G. D. and Kellogg, O. D. "Invariants Points in Function Space." Trans. Amer. Math. Soc. 23, 96-115, 1922.
Birkhoff, G. D. and Langer R. E. "The Boundary Problems and Developments Associated with a System of Ordinary Differential Equations of First Order."
Proc. Amer. Acad. Arts and Sci. 58, 49-128, 1923.
Birkhoff, G. D. Relativity and Modern Physics. Cambridge, MA: Harvard University Press, 1923.
Birkhoff, G. D. The Origin, Nature and Influence of Relativity. 1925.
Birkhoff, G. D. Dynamical Systems, rev. ed. Providence, RI: Amer. Math. Soc., 1966.
Birkhoff, G. D. "On the Number of Ways of Coloring a Map." Proc. Edinburgh Math. Soc. 2, 83-91, 1930.
Birkhoff, G. D. "Proof of the Ergodic Theorem." Proc. Nat. Acad. Sci. USA. 1931.
Birkhoff, G. D. Aesthetic Measure. Cambridge, MA: Harvard University Press, 1933.
Birkhoff, G. D. "On the Polynomial Expressions for the Number of Ways of Coloring a Map." Ann. R. Scuola norm. sup. Pisa 3, 85-103, 1934.
Birkhoff, G. D. "Sur le problème restreint des trois corps. 1." Ann. R. Scuola norm. sup. Pisa 4, 267-306, 1935.
Birkhoff, G. D. "Sur le problème restreint des trois corps. 2." Ann. R. Scuola norm. sup. Pisa 5, 9-50, 1936.
Birkhoff, G. D. and Beatley, R. Basic Geometry. New York: Chelsea, 1959.
Birkhoff, G. D. Collected Mathematical Papers, 3 vols. New York: Dover, 1968.
Birkhoff, G. D. and Trjitzinsky, W. J. "Analytic Theory of Singular Difference Equations." Acta Math. 60, 1-89, 1933.
Birkhoff, G. D. et al. "On Birkhoff's New Theory of Gravitation." Phys. Rev. 66, 138-143, 1944.
