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

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)