# Mathematician:Garrett Birkhoff

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## Mathematician

American mathematician mainly working in mathematical physics and abstract algebra.

Also wrote plenty of text books: his *Lattice Theory* (1940) is much cited.

The son of George David Birkhoff.

## Nationality

American

## History

- Born: January 19, 1911, Princeton, New Jersey, USA
- Died: November 22, 1996, Water Mill, New York, USA

## Theorems and Definitions

- Birkhoff-Kakutani Theorem (with Shizuo Kakutani)
- Birkhoff-von Neumann Theorem (with John von Neumann)
- Pierce-Birkhoff Conjecture (with Richard Scott Pierce)

Results named for **Garrett Birkhoff** can be found here.

Definitions of concepts named for **Garrett Birkhoff** can be found here.

## Publications

- 1935:
*Orthogonality in linear metric spaces*(*Duke Math. J.***Vol. 1**: pp. 169 – 172) - 1936:
*On the order of groups of automorphisms*(with Philip Hall)

- 1940:
*Lattice Theory, 1st ed.*- 1948:
*Lattice Theory, 2nd ed.* - 1967:
*Lattice Theory, 3rd ed.*

- 1948:

- 1941:
*A Survey of Modern Algebra*(with Saunders Mac Lane)- 1965:
*A Brief Survey of Modern Algebra*(with Saunders Mac Lane) (second revised edition of*A Survey of Modern Algebra*from $1941$)

- 1965:

- 1946:
*Tres observaciones sobre el algebra lineal*(*Univ. Nac. Tucumn Rev***Ser. A****Vol. 5**: pp. 147 – 151) (in which Birkhoff-von Neumann Theorem is presented)

- 1950:
*Hydrodynamics: A study in logic, fact, and similitude* - 1956:
*Lattice-ordered rings*(*Anais da Academia Brasileira de Ciências*28) (with R. Pierce) (in which the Pierce-Birkhoff Conjecture was first posited) - 1957:
*Jets, Wakes, and Cavities*(with E. Zarantello)

- 1959:
*Ordinary Differential Equations*(with Gian-Carlo Rota)- 1962:
*Ordinary Differential Equations, 2nd ed.*(with Gian-Carlo Rota) - 1978:
*Ordinary Differential Equations, 3rd ed.*(with Gian-Carlo Rota)

- 1962:

- 1967:
*Algebra*(with Saunders Mac Lane) - 1970:
*Modern Applied Algebra*(with Thomas C. Bartee) - 1973:
*Source Book in Classical Analysis*