# Mathematician:George David Birkhoff

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## Mathematician

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

The father of Garrett Birkhoff.

## Nationality

American

## History

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

## Theorems and Definitions

- Chromatic Polynomial
- Birkhoff's Axioms
- Birkhoff's Theorem (Relativity)
- Birkhoff's Theorem (Electromagnetism)
- Birkhoff's Ergodic Theorem
- Birkhoff-Grothendieck Theorem (with Alexander Grothendieck)
- Poincaré-Birkhoff-Witt Theorem (with Henri Poincaré and Ernst Witt)
- Birkhoff Interpolation
- Equidistribution Theorem

Axioms named for **George David Birkhoff** can be found here.

## Publications

- July 1904:
*On the Integral Divisors of $a^n-b^n$*(*Ann. Math.***Vol. 5**: pp. 173 – 180) (with Harry Schultz Vandiver) www.jstor.org/stable/2007263 - 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)

## Sources

- John J. O'Connor and Edmund F. Robertson: "George David Birkhoff": MacTutor History of Mathematics archive

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**Birkhoff, George David**(1884-1944) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Birkhoff, George David**(1884-1944)