- Saunders Mac Lane
Saunders Mac Lane (
4 August 1909, Taftville, Connecticut– 14 April 2005, San Francisco) was an American mathematicianwho cofounded category theorywith Samuel Eilenberg.
Mac Lane was christened "Leslie Saunders MacLane", but "Leslie" fell into disuse because his parents, Donald MacLane and Winifred Saunders, came to dislike it. He began inserting a space into his surname because his first wife found it difficult to type the name without a space. [Mac Lane (2005), p. 6.]
Mac Lane earned a BA from
Yale Universityin 1930, and an MA from the University of Chicagoin 1931. During this period, he published his first scientific paper, in physicsand 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, Hitlercame 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 Americain 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 Chinato study the conditions affecting mathematics there. Mac Lane was elected to the National Academy of Sciences in 1949, and received the National Medal of Sciencein 1989.
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 Eilenbergin 1943, resulting in 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 cohomologyin general.
After introducing, via the
Eilenberg-Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theoryin 1945. He is especially known for his work on coherence theorems. A recurring feature of category theory, abstract algebra, and of some other mathematics as well, is the use of diagrams, consisting of arrows ( morphisms) linking objects, such as products and coproducts. According to McLarty (2005), this diagrammatic approach to contemporary mathematics largely stems from Mac Lane (1948).
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.
In addition to reviewing a fair bit of his mathematical output, the obituary articles McLarty (2005, 2007) clarify Mac Lane's contributions to the
philosophy of mathematics. Mac Lane (1986) is an approachable introduction to his views on this subject.
Books by Mac Lane
* 1997 (1941). "A Survey of Modern Algebra" (with
Garrett Birkhoff). A K Peters. ISBN 1-56881-068-7
*1948, "Groups, categories and duality," "Proceedings of the Nat. Acad. of Sciences of the USA 34": 263–67.
* 1995 (1963). "Homology", Springer (
Classics in Mathematics) ISBN 978-0387586625 (Originally, Band 114 of Die Grundlehren Der Mathematischen Wissenschaften in Einzeldarstellungen.) [http://www.ams.org/bull/2000-37-01/S0273-0979-99-00847-2/S0273-0979-99-00847-2.pdf AMS review.]
* 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
* McLarty, Colin, 2005, " [http://philmat.oxfordjournals.org/cgi/content/full/13/3/237 Saunders Mac Lane (1909–2005): His Mathematical Life and Philosophical Works,] " "Philosophia Mathematica 13": 237-51. With selected bibliography emphasizing Mac Lane's philosophical writings.
* --------, 2007, " [http://bjps.oxfordjournals.org/cgi/content/short/58/1/77 The Last Mathematician from Hilbert's Göttingen: Saunders Mac Lane as Philosopher of Mathematics,] ", "British Journal for the Philosophy of Science 58(1)": 77-112.
From Action to Mathematics per Mac Lane
* [http://www-news.uchicago.edu/releases/05/050421.maclane.shtml Obituary press release] from the
University of Chicago.
* [http://www.iti.cs.tu-bs.de/~koslowj/cgi-bin/p0454?MacLane-0/idx&256 Photographs of Mac Lane,] 1984–99.
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Saunders MacLane — Saunders Mac Lane Saunders MacLane. Saunders MacLane (4 août 1909 14 avril 2005) est un mathématicien américain. Ses travaux portent principalement sur la logique et la topologie algébrique. Il est l un des créateurs de la théo … Wikipédia en Français
Saunders MacLane — Saunders Mac Lane (4 de agosto de 1909, Taftville, Connecticut – 14 de abril de 2005, San Francisco) fue un matemático estadounidense cofundador con Samuel Eilenberg de la teoría de categorías Categorías: Nacidos en 1909Fallecidos en 2005 … Wikipedia Español
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