Mac Lane, Saunders

▪ 2006

      American mathematician (b. Aug. 4, 1909, Taftville, Conn.—d. April 14, 2005, San Francisco, Calif.), made significant contributions to modern algebra and topology and, with Samuel Eilenberg, was a cofounder of category theory, which established a general framework for understanding how mathematical structures, and systems of structures, relate to one another. After graduating (1930) from Yale University, Mac Lane earned (1931) a master's degree in mathematics from the University of Chicago. He moved to the University of Göttingen, Ger., where he studied under Paul Bernays, Emmy Noether, and Hermann Weyl. In 1933 Mac Lane was awarded a Ph.D. for a thesis on mathematical logic. Returning to the U.S., Mac Lane taught at Yale, Harvard University, the University of Chicago, and Cornell University, Ithaca, N.Y., before returning to Harvard, where he taught until 1946. In 1947 he moved to Chicago, where he spent the remainder of his career, serving (1952–58) as chairman of the mathematics department. In 1982 he became professor emeritus. While Mac Lane was at Harvard, his interest shifted from logic to the modern, abstract algebra developed by Noether and others. In 1941 Mac Lane and Garrett Birkhoff published A Survey of Modern Algebra, for many years the leading English-language textbook in the field. While conducting research in homological algebra (an algebraic study of topological spaces), Mac Lane and Eilenberg, later of Columbia University, New York City, felt the need for a general theory for moving between domains of mathematics. This led to their creation of category theory, which was later applied in many areas of mathematics, computer science, and theoretical physics. Among Mac Lane's publications were Homology (1963), Algebra (1967; with Birkhoff), Categories for the Working Mathematician (1971), and Mathematics, Form and Function (1986). In 1989 Mac Lane was awarded the National Medal of Science.

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▪ American mathematician
born August 4, 1909, Taftville, Connecticut, U.S.
died April 14, 2005, San Francisco, California

      American mathematician who was a cocreator of category theory (mathematics, foundations of), an architect of homological algebra, and an advocate of categorical foundations for mathematics (mathematics, foundations of).

      Mac Lane graduated from Yale University in 1930 and then began graduate work at the University of Chicago. He soon moved to Germany, where he, with a dissertation on mathematical logic (logic), received a doctorate degree in 1933 from the University of Göttingen. While in Germany, he stayed in the homes of Hermann Weyl (Weyl, Hermann) and Richard Courant (Courant, Richard), and he saw his dissertation adviser Paul Bernays (Bernays, Paul Isaak) barred from teaching by the Nazis. Mac Lane returned home and taught at various universities before settling permanently at the University of Chicago in 1947.

      About 1940 Mac Lane made some purely algebraic calculations in group theory, and the Polish American mathematician Samuel Eilenberg noticed that they applied to the topology of infinitely coiled curves called solenoids. To understand and generalize this link between algebra and topology, the two men created category theory, the general cohomology of groups, and the basis for the Eilenberg-Steenrod axioms for homology of topological spaces (topological space). Mac Lane worked with categorical duality and defined categorical universal properties. He defined and named Abelian categories, further developed by Alexandre Grothendieck (Grothendieck, Alexandre) to become central to homological algebra.

      From the 1960s Mac Lane pursued aspects of category theory, including the work of the American mathematician F. William Lawvere on categorical foundations for mathematics. Mac Lane served as president of the Mathematical Association of America (1951–52), the American Philosophical Society (1968–71), and the American Mathematical Society (1973–74). He served as vice president of the National Academy of Sciences (1973–81). His works include A Survey of Modern Algebra (1941; with Garrett Birkhoff), Homology (1963), Categories for the Working Mathematician (1971), and Sheaves in Geometry and Logic: A First Introduction to Topos Theory (1992; with Ieke Moerdijk).

Colin McLarty
 

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Universalium. 2010.

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