Mathematician:Garrett Birkhoff

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 Polytope

• Birkhoff's HSP Theorem
• Birkhoff's Representation Theorem

• Birkhoff-James Orthogonality (with Robert Clarke James)

• 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.

• 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 $1941$)

• 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)
• 1962: Ordinary Differential Equations (with Gian-Carlo Rota)
• 1967: Algebra (with Saunders Mac Lane)
• 1970: Modern Applied Algebra (with Thomas C. Bartee)
• 1973: Source Book in Classical Analysis

Sources

• John J. O'Connor and Edmund F. Robertson: "Garrett Birkhoff": MacTutor History of Mathematics archive