Garrett Birkhoff
| Garrett Birkhoff | |
|---|---|
 |
|
| Born |
January 19, 1911 Princeton, New Jersey, United States |
| Died | November 22, 1996 (aged 85) Water Mill, New York, USA |
| Fields | Mathematics |
| Institutions | Harvard University |
| Alma mater |
Cambridge University Harvard University |
| Academic advisors |
Ralph H. Fowler Philip Hall |
| Doctoral students |
Richard Arens Jerry L. Bona Chandler Davis George Fix George Mostow Peter J. Olver R. Tyrrell Rockafellar Henry C. Wente Philip M. Whitman David M. Young, Jr. Thomas Caywood |
| Other notable students | Richard S. Varga |
| Known for | Lattice theory |
| Influences | Constantin Carathéodory |
| Influenced | Gian-Carlo Rota |
| Notable awards |
National Academy of Sciences American Academy of Arts and Sciences George David Birkhoff Prize (1978) |
Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician. He is best known for his work in lattice theory.
The mathematician George Birkhoff (1884–1944) was his father.
The son of the mathematician George David Birkhoff, Garrett was born in Princeton, New Jersey. He began the Harvard University BA course in 1928 after less than seven years of prior formal education. Upon completing his Harvard BA in 1932, he went to Cambridge University in England to study mathematical physics but switched to studying abstract algebra under Philip Hall. While visiting the University of Munich, he met Carathéodory who pointed him towards two important texts, Van der Waerden on abstract algebra and Speiser on group theory.
Birkhoff held no Ph.D., a qualification British higher education did not emphasize at that time, and did not even bother obtaining an M.A. Nevertheless, after being a member of Harvard's Society of Fellows, 1933–36, he spent the rest of his career teaching at Harvard. From these facts can be inferred the number and quality of Birkhoff's papers published by his 25th year.
During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra. In 1941 he and Mac Lane published A Survey of Modern Algebra, the second undergraduate textbook in English on the subject (Cyrus Colton MacDuffee's An Introduction to Abstract Algebra was published in 1940). Mac Lane and Birkhoff's Algebra (1967) is a more advanced text on abstract algebra. A number of papers he wrote in the 1930s, culminating in his monograph, Lattice Theory (1940; the third edition remains in print), turned lattice theory into a major branch of abstract algebra. His 1935 paper, "On the Structure of Abstract Algebras" founded a new branch of mathematics, universal algebra. Birkhoff's approach to this development of universal algebra and lattice theory acknowledged prior ideas of Charles Sanders Peirce, Ernst Schröder, and Alfred North Whitehead; in fact, Whitehead had written an 1898 monograph entitled Universal Algebra.
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