Birkhoff, George David (1884–1944)

US mathematician. He made fundamental contributions to the study of dynamical systems such as the Solar System. He formulated the ‘weak form’ of the ergodic theorem.

Birkhoff was born at Overisel, Michigan, and studied at the University of Chicago and at Harvard. From 1912 he taught at Harvard, and was appointed professor in 1919.

Birkhoff developed a system of differential equations which is still inspiring research. His work on difference equations was notable for the prominence he gave to the use of matrix algebra.

Birkhoff notably investigated the theory of dynamical systems and Jules Poincaré's celestial mechanics. He began to examine the motion of bodies in the light of his work on asymptotic expansions and boundary value problems of linear differential equations. In 1913 he proved Poincaré's last geometric theorem on the three-body problem.

With John Von Neumann, Birkhoff was chiefly responsible for establishing, in the 1930s, the modern science of ergodics. He arrived at the statement of his ‘positive ergodic theorem’, or what is known as the ‘weak form’ of ergodic theory, just before Von Neumann published his ‘strong form’ of it. Birkhoff also transformed the Maxwell–Boltzmann hypothesis of the kinetic theory of gases, which was undermined by the number of exceptions found to it, into a vigorous principle.

Throughout his life Birkhoff argued that Einstein's general relativity was an unhelpful theory.