- Saunders Mac Lane
**Saunders Mac Lane**(4 August 1909 ,Taftville ,Connecticut –14 April 2005 ,San Francisco ) was an Americanmathematician who cofoundedcategory theory withSamuel Eilenberg .**Career**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 University in 1930, and an MA from theUniversity of Chicago in 1931. During this period, he published his first scientific paper, inphysics and co-authored withIrving Langmuir . He attended theUniversity of Göttingen , 1931–1933, studying logic and mathematics underPaul Bernays ,Emmy Noether , andHermann 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 theUniversity 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 theApplied Mathematics Panel .Mac Lane served as vice president of the National Academy of Sciences and the

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

mathematical logic , his early work was in field theory and valuation theory. He wrote onvaluation ring s andWitt vector s, and separability in infinitefield extension s. He started writing ongroup extension s in 1942, and began his epochal collaboration withSamuel Eilenberg in 1943, resulting in what are now called Eilenberg–Mac Lane spaces K("G","n"), having a single non-trivialhomotopy group "G" in dimension "n". This work opened the way togroup cohomology in general.After introducing, via the

Eilenberg-Steenrod axioms , the abstract approach tohomology theory , he and Eilenberg originatedcategory theory in 1945. He is especially known for his work oncoherence theorem s. A recurring feature of category theory,abstract algebra , and of some other mathematics as well, is the use of diagrams, consisting of arrows (morphism s) linking objects, such as products andcoproduct s. 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.Mac Lane supervised the Ph.Ds of, among many others,

David Eisenbud , William Howard,Irving Kaplansky , Michael Morley,Anil Nerode ,Robert Solovay , andJohn G. Thompson .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" (withGarrett 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" (withIeke Moerdijk ). ISBN 0-387-97710-4

* 2005. "Saunders Mac Lane: A Mathematical Autobiography". A K Peters. ISBN 1-56881-150-0**Biographical*** 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.**ee also***

Category theory

*From Action to Mathematics per Mac Lane **Footnotes****External links***

* [*http://www-news.uchicago.edu/releases/05/050421.maclane.shtml Obituary press release*] from theUniversity 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 Mac Lane**— Nacimiento 4 de agosto de 1909 Taftville, Connecticut … Wikipedia Español**Saunders Mac Lane**— (* 4. August 1909 in Taftville, Connecticut; † 14. April 2005 in San Francisco, Kalifornien) war ein US amerikanischer Mathematiker. Er gilt zusammen mit Samuel Eilenberg als der Begründer der Kategorientheor … Deutsch Wikipedia**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 théorie des catégories et l auteur de l… … Wikipédia en Français**Mac Lane**— McLane, MacLane oder Mac Lane ist der Familienname folgender Personen: Barton MacLane (1902–1969), US amerikanischer Schauspieler James McLane (* 1930), US amerikanischer Schwimmer Louis McLane (1786–1856), US amerikanischer Politiker Robert… … Deutsch Wikipedia**Mac Lane's planarity criterion**— In graph theory, Mac Lane s planarity criterion is a characterisation of planar graphs in terms of their cycle spaces. It states that a finite graph G is planar if and only if the cycle space C ( G ), which in topologists terms is the space of 1… … Wikipedia**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… … Universalium**Saunders MacLane**— Saunders Mac Lane Saunders Mac Lane (* 4. August 1909 in Taftville, Connecticut; † 14. April 2005 in San Francisco, Kalifornien) war ein US amerikanischer Mathematiker. Er gilt zusammen mit Samuel Eilenberg als der Begründer der Kategorientheorie … Deutsch Wikipedia**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**Liste der Biografien/Mac**— Biografien: A B C D E F G H I J K L M N O P Q … Deutsch Wikipedia