# Saunders MacLane

**Saunders Mac Lane**(4 August 1909, Taftville, Connecticut – 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg.

## Career

Mac Lane earned a BA from Yale University in 1930, and an MA from the University of Chicago in 1931. During this period, he published his first scientific paper, in physics and co-authored with Irving Langmuir. He attended the University of Göttingen, 1931–1933, studying logic and mathematics under Paul Bernays, Emmy Noether, and Hermann Weyl. Göttingen's Mathematisches Institut awarded him the Ph.D. in 1934. While he was at Göttingen, Hitler came to power and implemented the anti-Semitic policies that destroyed Göttingen's excellence in mathematics, science, and philosophy.From 1934 through 1938, Mac Lane held short term appointments at Harvard University, Cornell University, and the University of Chicago. He then held a tenure track appointment at Harvard, 1938–1947, before spending the rest of his career at the University of Chicago. In 1944 and 1945, he also directed Columbia University's Applied Mathematics Group, which was involved in the war effort as a contractor for the Applied Mathematics Panel.

Mac Lane served as vice president of the National Academy of Sciences and the American Philosophical Society, and as president of the American Mathematical Society. While presiding over the Mathematical Association of America in the 1950s, he initiated its activities aimed at improving the teaching of modern mathematics. He was a member of the National Science Board, 1974–1980, advising the American government. In 1976, he led a delegation of mathematicians to China to study the conditions affecting mathematics there. Mac Lane was elected to the National Academy of Sciences in 1949, and received the National Medal of Science in 1989.

## Contributions

After a thesis in mathematical logic, his early work was in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions. He started writing on group extensions in 1942, and began his epochal collaboration with Samuel Eilenberg in 1943, on what are now called Eilenberg–Mac Lane spaces K(*G*,

*n*), having a single non-trivial homotopy group

*G*in dimension

*n*. This work opened the way to group cohomology in general.

After introducing, via the Eilenberg-Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theory in 1945. He is especially known for his work on coherence theorems.

Mac Lane had an exemplary devotion to writing approachable texts, starting with his very influential

*A Survey of Modern Algebra*, coauthored in 1941 with Garrett Birkhoff. From then on, it was possible to teach elementary modern algebra to undergraduates using an English text. His

*Categories for the Working Mathematician*remains the definitive introduction to category theory.

He supervised the Ph.Ds of, among others, David Eisenbud, Irving Kaplansky, Anil Nerode, Robert Solovay, and John G. Thompson.

## Books by Mac Lane

- 1997 (1941).
*A Survey of Modern Algebra*(with Garrett Birkhoff). A K Peters. ISBN 1-56881-068-7 - 1995 (1963).
*Homology*, Springer (Classics in Mathematics) ISBN 978-0387586625 (Originally, Band 114 of Die Grundlehren Der Mathematischen Wissenschaften in Einzeldarstellungen.) AMS review http://www.ams.org/bull/2000-37-01/S0273-0979-99-00847-2/S0273-0979-99-00847-2.pdf. - 1999 (1967).
*Algebra*(with Garrett Birkhoff). Chelsea. ISBN 0-8218-1646-2 - 1998 (1972).
*Categories for the Working Mathematician*, Springer (Graduate Texts in Mathematics) ISBN 0-387-98403-8 - 1986.
*Mathematics, Form and Function*. Springer-Verlag. ISBN 0-387-96217-4 - 1992.
*Sheaves in Geometry and Logic: A First Introduction to Topos Theory*(with Ieke Moerdijk). ISBN 0-387-97710-4 - 2005.
*Saunders Mac Lane: A Mathematical Autobiography*. A K Peters. ISBN 1-56881-150-0

## External links

- McLarty, Colin, 2005, "Saunders Mac Lane (1909–2005): His Mathematical Life and Philosophical Works,"
*Philosophia Mathematica 13*: 237-51. With selected bibliography. - O'Connor, John J; Edmund F. Robertson "Saunders Mac Lane".
*MacTutor History of Mathematics archive*. - Obituary press release from the University of Chicago
- Photographs of Mac Lane,1984–99.

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**1909**(**MCMIX****.....**Click the link for more information.**Taftville**is a small village in eastern Connecticut. It is a neighborhood of Norwich, CT but has its own post office (ZIP Code 06380). It was established in 1866 as site for the large Taftville Mill, later Ponemah Mill.

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**mathematician**is a person whose primary area of study and research is the field of mathematics.

## Problems in mathematics

Some people incorrectly believe that mathematics has been fully understood, but the publication of new discoveries in mathematics continues at an immense**.....**Click the link for more information.

In mathematics,

**category theory**deals in an abstract way with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and have been a unifying notion.**.....**Click the link for more information.**Samuel Eilenberg**(September 30, 1913—January 30, 1998) was a Polish mathematician. He was born in Warsaw, Russian Empire (now Poland) and died in New York, USA where he had spent much of his career as a professor at Columbia University.

He earned his Ph.D.

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**Irving Langmuir**

Irving Langmuir at home (c. 1900)

Born January 31 1881

Brooklyn, New York

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**Hermann Klaus Hugo Weyl**(November 9 1885 – December 9 1955) was a German mathematician. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is closely identified with the University of Göttingen tradition of mathematics, represented by

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