# Birkhoff, Garrett

**Birkhoff, Garrett**gâr´ət bûr´kôf [key], 1911–96, American mathematician, b. Princeton, N.J.; son of George David Birkhoff . He was educated at Harvard (B.A., 1932) where he was elected a fellow in 1933 and taught until his retirement in 1981. Birkoff has made several important contributions to abstract mathematics, the teaching of mathematics, and mathematical physics. From 1934 on he developed the concept of a lattice, a generalized algebra with two operators, and showed how a number of subjects, e.g., Boolean algebra, projective geometry, and affine geometry, could be treated as special types of lattices. His text

*A Survey of Modern Algebra*(with Saunders MacLane, 1941, 4th ed. 1977) became a standard undergraduate textbook, as did several other books he wrote.

See his * Lattice Theory * (1940, 3d ed. 1967).

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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