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Saunders Mac Lane
Saunders Mac Lane

Saunders Mac Lane (4 August 1909, Taftville, Connecticut – 14 April 2005, San Francisco) was an American mathematician who cofounded category theory with Samuel Eilenberg. Events 70 - The Destruction of the Second Temple in Jerusalem by the Romans. Year 1909 ( MCMIX) was a Common year starting on Friday (link will display full calendar of the Gregorian calendar (or a Common year starting Taftville is a small village in eastern Connecticut. It is a neighborhood of Norwich CT but has its own post office ( ZIP Code 06380 Connecticut ( is a state located in the New England region of the northeastern United States of America. Events 43 BC - Battle of Forum Gallorum: Mark Antony, besieging Julius Caesar 's assassin Decimus Junius Brutus in Year 2005 ( MMV) was a Common year starting on Saturday (link displays full calendar of the Gregorian calendar. The City and County of San Francisco is the fourth most populous city The United States of America —commonly referred to as the A mathematician is a person whose primary area of study and research is the field of Mathematics. In Mathematics, category theory deals in an abstract way with mathematical Structures and relationships between them it abstracts from sets Samuel Eilenberg ( September 30, 1913 — January 30, 1998) was a Polish and American Mathematician of

Contents

Career

Mac Lane (2005) is the autobiography. Also see McLarty (2005, 2007).

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. [1]

Mac Lane earned a BA from Yale University in 1930, and an MA from the University of Chicago in 1931. The University of Chicago is a Private university located principally in the Hyde Park neighborhood of Chicago. During this period, he published his first scientific paper, in physics and co-authored with Irving Langmuir. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Irving Langmuir ( January 31, 1881 in Brooklyn New York – August 16, 1957 in Woods Hole Massachusetts) was an He attended the University of Göttingen, 1931–1933, studying logic and mathematics under Paul Bernays, Emmy Noether, and Hermann Weyl. The University of Göttingen ( German: Georg-August-Universität Göttingen) is a University in the city of Göttingen, Germany. Paul Bernays ( 17 October 1888 London – 18 September 1977 Zurich) was a Swiss mathematician who made significant Amalie Emmy Noether, ˈnøːtɐ (23 March 1882 – 14 April 1935 was a German Mathematician known for her groundbreaking contributions to Abstract algebra and Hermann Klaus Hugo Weyl ( 9 November 1885 – 8 December 1955) was a German Mathematician. 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. Hi and welcome to Wikipedia! Please understand that this article is frequently vandalized and vandalism is reverted immediately Antisemitism (alternatively spelled anti-semitism or anti-Semitism; also rarely known as judeophobia) is the Prejudice against or hostility

From 1934 through 1938, Mac Lane held short term appointments at Harvard University, Cornell University, and the University of Chicago. The University of Chicago is a Private university located principally in the Hyde Park neighborhood 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. The Applied Mathematics Panel (AMP was created at the end of 1942 as a division of the National Defense Research Committee (NDRC within the Office of Scientific Research

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. The National Academy of Sciences (NAS is a corporation in the United States whose members serve Pro bono as "advisers to the nation on science The American Philosophical Society is a discussion group founded in 1743 by Benjamin Franklin as an offshoot of his earlier club the Junto. The American Mathematical Society (AMS is an association of professional Mathematicians dedicated to the interests of mathematical research and scholarship which While presiding over the Mathematical Association of America in the 1950s, he initiated its activities aimed at improving the teaching of modern mathematics. The Mathematical Association of America ( MAA) is a professional society that focuses on Mathematics accessible at the undergraduate level He was a member of the National Science Board, 1974–1980, advising the American government. The National Science Foundation (NSF is a United States Government agency that supports fundamental Research and Education in all the non-medical In 1976, he led a delegation of mathematicians to China to study the conditions affecting mathematics there. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National Mac Lane was elected to the National Academy of Sciences in 1949, and received the National Medal of Science in 1989. The National Academy of Sciences (NAS is a corporation in the United States whose members serve Pro bono as "advisers to the nation on science The National Medal of Science is an honor bestowed by the President of the United States to individuals in Science and Engineering who have made important

Contributions

After a thesis in mathematical logic, his early work was in field theory and valuation theory. Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. Valuation in mathematics may refer to Valuation (algebra Valuation (logic Valuation (measure theory He wrote on valuation rings and Witt vectors, and separability in infinite field extensions. In Abstract algebra, a valuation ring is an Integral domain D such that for every element x of its Field of fractions F In Mathematics, a Witt vector is an Infinite sequence of elements of a Commutative ring. In Mathematics, more specifically in Abstract algebra, field extensions are the main object of study in field theory. He started writing on group extensions in 1942, and began his epochal collaboration with Samuel Eilenberg in 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. In Mathematics, a group extension is a general means of describing a group in terms of a particular Normal subgroup and Quotient group. Samuel Eilenberg ( September 30, 1913 — January 30, 1998) was a Polish and American Mathematician of Year 1943 ( MCMXLIII) was a Common year starting on Friday (the link will display full 1943 calendar of the Gregorian calendar. In Mathematics, an Eilenberg-MacLane space is a special kind of Topological space that can be regarded as a building block for Homotopy theory. In Mathematics, homotopy groups are used in Algebraic topology to classify Topological spaces The base point preserving maps from an n -dimensional This work opened the way to group cohomology in general. In Abstract algebra, Homological algebra, Algebraic topology and Algebraic number theory, as well as in applications to Group theory proper

After introducing, via the Eilenberg-Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theory in 1945. In Mathematics, specifically in Algebraic topology, the Eilenberg-Steenrod axioms are properties that homology theories of Topological spaces In Mathematics, homology theory is the Axiomatic study of the intuitive geometric idea of homology of cycles on Topological spaces It can be broadly In Mathematics, category theory deals in an abstract way with mathematical Structures and relationships between them it abstracts from sets He is especially known for his work on coherence theorems. In Mathematics, a coherence condition or coherence theorem expresses the statement that two or more Morphisms between two given objects the existence 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. Abstract algebra is the subject area of Mathematics that studies Algebraic structures such as groups, rings, fields, modules In mathematics and especially in Category theory a commutative diagram is a Diagram of objects also known as vertices, and Morphisms also In Mathematics, a morphism is an abstraction derived from structure-preserving mappings between two Mathematical structures The study of morphisms and In Category theory, the product of two (or more objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as In Category theory, the coproduct, or categorical sum, is the category-theoretic construction which subsumes the disjoint union of sets and of topological 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. Garrett Birkhoff ( January 19, 1911, Princeton, New Jersey, USA – November 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. Categories for the Working Mathematician is a textbook in Category theory written by American Mathematician Saunders Mac Lane, who

Mac Lane supervised the Ph. Ds of, among others, David Eisenbud, Irving Kaplansky, Anil Nerode, Robert Solovay, and John G. Thompson. David Eisenbud (born 8 April, 1947) is an American Mathematician. Irving Kaplansky ( March 22, 1917 &ndash June 25, 2006) was a Canadian Mathematician. Anil Nerode is a US mathematician. He received his PhD in mathematics from the University of Chicago under Saunders Mac Lane and is at present John Griggs Thompson (born October 13 1932 in Ottawa Kansas, USA) is a Mathematician noted for his work in the field of Finite

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. The philosophy of mathematics is the branch of Philosophy that studies the philosophical assumptions foundations and implications of Mathematics. Mac Lane (1986) is an approachable introduction to his views on this subject.

See also

Footnotes

  1. ^ Mac Lane (2005), p. In Mathematics, category theory deals in an abstract way with mathematical Structures and relationships between them it abstracts from sets 6.

Books by Mac Lane

Biographical

External links

The Mathematics Genealogy Project is a web-based Database that gives an Academic genealogy based on Dissertation supervision relations
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