# Garrett Birkhoff

Garrett Birkhoff ( born January 19, 1911 in Princeton, New Jersey, USA, † November 22, 1996 in Water Mill, NY, USA) was an American mathematician, with algebra and applied mathematics ( hydrodynamics ) dealt.

## Life and work

Birkhoff was the son of the famous mathematician George David Birkhoff, who had him teach until the age of eight at home. He graduated in 1928 at Harvard University, among others, Oliver Kellogg, Marston Morse, Hassler Whitney. After graduating in 1932 he went on a scholarship to the University of Cambridge in England, where he abstract algebra ( group theory ) turned to and studied with Philip Hall. A joint paper was published 1936. 1933 he was briefly in Munich with Constantin Caratheodory (who drew his attention to van der Waerden algebra textbook ). From 1933 he was a Fellow at Harvard and from 1936 Instructor. From 1937 he held there too algebra lectures, alternating with Saunders MacLane, and it was her well-known textbook Survey of Modern Algebra, which first appeared in 1941 and as an introduction to undergraduate students ( undergraduates ) turned. It contributed much to the early spread of abstract algebra in the USA. At the same time Birkhoff dealt with the lattice theory (in English Lattice Theory), 1940 what his book Lattice Theory appeared.

During the Second World War he worked mathematics, eg in Applied on the Aberdeen Proving Ground ( the Ballistikforschungszentrum the U.S. Army) over grenades explosions, shock waves around projectiles, distance measurement with radar. This two books on hydrodynamics arose ( Hydrodynamics 1950, Jets, Wakes and Cavities 1957). Ever since the days of World War II, he worked in the Committee for Applied Mathematics by John von Neumann.

As a consultant for Westinghouse 1954 he also began work on numerical linear algebra. In consulting work for General Motors from 1959, he campaigned for the use of cubic spline functions for the modeling of bodies.

In 1969 he was George Putnam Professor at Harvard, a position he held until his retirement in 1981. In 1970 he published a more Applied Algebra textbook with Thomas Bartee (Modern Applied Algebra ).

In 1978 he was named after his father Birkhoff Prize for Applied Mathematics. He was six honorary doctorates and a member of the National Academy of Sciences and the American Academy of Arts and Sciences. The set of Poincaré - Birkhoff -Witt and the representation theorem of Birkhoff are associated with his name.

## Selected writings

- Garrett Birkhoff: Lattice Theory. AMS, Providence (RI ) 1940, ISBN 0-8218-1025-1 ( 3rd edition 1973).
- Garrett Birkhoff, Gian- Carlo Rota: Ordinary Differential Equations. Ginn - Blaisdell, Boston ( MA ) 1959, ISBN 0-471-86003-4 ( 4th edition, Wiley, Boston 1989).
- Garrett Birkhoff, Thomas Bartee Creson: Applied Algebra. Oldenbourg, München 1973, ISBN 978-3-4863-4231-4 (formerly: 3-4863-4231-2 ).
- Garrett Birkhoff: Current trends in algebra. In: Amer. Math Monthly. No. 80, 1973, p 760-782 ( for this post, he was in 1974 awarded the Lester Randolph Ford Award, online).