Mathematician:George David Birkhoff

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American mathematician best known for what is now known as the Ergodic Theorem.

The father of Garrett Birkhoff.




  • Born: 21 March 1884, Overisel, Michigan
  • Died: 12 November 1944, Cambridge, Massachusetts

Theorems and Definitions

Results named for George David Birkhoff can be found here.

Definitions of concepts named for George David Birkhoff can be found here.

Axioms named for George David Birkhoff can be found here.


  • July 1904: On the Integral Divisors of $a^n-b^n$ (Ann. Math. Vol. 5: pp. 173 – 180) (with Harry Schultz
  • 1906: General mean value and remainder theorems with applications to mechanical differentiation and quadrature
  • 1907: Asymptotic Properties of Certain Ordinary Differential Equations with Applications to Boundary Value and Expansion Problems (PhD thesis)
  • 1913: Proof of Poincaré's geometric theorem
  • 1917: Dynamical Systems with Two Degrees of Freedom
  • 1923: Relativity and Modern Physics (with R.E. Langer)
  • 1927: Dynamical Systems
  • 1931: Proof of the ergodic theorem
  • 1932: A Set of Postulates for Plane Geometry (Based on Scale and Protractors)
  • 1933: Aesthetic Measure
  • 1937: Representability of Lie algebras and Lie groups by matrices
  • 1938: Electricity as a Fluid
  • 1941: Basic Geometry (which contains Birkhoff's Axioms)