Garrett Birkhoff

Harvard University

January 10, 1911 - November 22, 1996

Election Year: 1968
Scientific Discipline: Mathematics
Membership Type: Member

Garrett Birkhoff made major contributions in the area of abstract algebra.  His 1940 book, Lattice Theory, on abstract questions of structure and relative magnitude, opened new lines of inquiry and led to a now fertile area of algebraic research. His work with Saunders Mac Lane, Survey of Modern Algebra, was the first American textbook to address questions in advanced algebra for undergraduates and advanced the teaching of mathematics throughout the country.   His other algebraic contributions included the improvement of the theory of Lie groups and group representations, the topology of transformations, combinatorial analysis, and projective geometries.  After working with hydrodynamics during World War II, Birkhoff’s field of interest shifted to fluid mechanics and mathematical engineering for the remainder of his career.  He advanced our modern understanding of hydrodynamics with studies on the theory of vortices, homogeneous turbulence, and the theory of Taylor instability.

Birkhoff received his A.B. degree from Harvard University in 1932 and did additional work at Cambridge University from 1932 to 1933.  He returned to Harvard as a junior fellow of the Society of Fellows and in 1936, joined the faculty as an instructor of mathematics.  He was promoted to full professorship in 1947 and then to George Putnam Professor of Pure and Applied Mathematics in 1969, a position he would keep until his retirement in 1981.  Along with his educational career, Birkhoff served as a consultant for Los Alamos Scientific Laboratory and for the Westinghouse Atomic Power Division.  He was president of the Society of Industrial and Applied Mathematics from 1967 to 1968 and was a vice president of the Mathematical Association of America. He was also a member of the American Mathematical Society, and the American Academy of Arts and Sciences. 

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