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Saunders Mac Lane

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Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.

Contents

Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville. He 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. He was the oldest of three brothers; one of his brothers, Gerald MacLane, also became a mathematics professor at Rice University and Purdue University. Another sister died as a baby. His father and grandfather were both ministers; his grandfather had been a Presbyterian, but was kicked out of the church for believing in evolution, and his father was a Congregationalist. His mother, Winifred, studied at Mount Holyoke College and taught English, Latin, and mathematics.

In high school, Mac Lane's favorite subject was chemistry. While in high school, his father died, and he came under his grandfather's care. His half-uncle, a lawyer, was determined to send him to Yale University, where many of his relatives had been educated, and paid his way there beginning in 1926. As a freshman, he became disillusioned with chemistry. His mathematics instructor, Lester S. Hill, coached him for a local mathematics competition which he won, setting the direction for his future work. He went on to study mathematics and physics as a double major, taking courses from Jesse Beams, Ernest William Brown, Ernest Lawrence, F. S. C. Northrop, and Øystein Ore, among others. He graduated from Yale with a B.A. in 1930. During this period, he published his first scientific paper, in physics and co-authored with Irving Langmuir.

In 1929, at a party of Yale football supporters in Montclair, New Jersey, Mac Lane (there to be presented with a prize for having the best grade point average yet recorded at Yale) had met Robert Maynard Hutchins, the new president of the University of Chicago, who encouraged him to go there for his graduate studies and soon afterwards offered him a scholarship. Mac Lane neglected to actually apply to the program, but showed up and was admitted anyway. At Chicago, the subjects he studied included set theory with E. H. Moore, number theory with Leonard Eugene Dickson, the calculus of variations with Gilbert Ames Bliss, and logic with Mortimer J. Adler.

In 1931, having earned his master's degree and feeling restless at Chicago, he earned a fellowship from the Institute of International Education and became one of the last Americans to study at the University of Göttingen prior to its decline under the Nazis. His greatest influences there were Paul Bernays and Hermann Weyl. By the time he finished his doctorate in 1934, Bernays had been forced to leave because he was Jewish, and Weyl became his main examiner. At Göttingen, Mac Lane also studied with Gustav Herglotz and Emmy Noether. Within days of finishing his degree, he married Dorothy Jones, from Chicago, and soon returned to the U.S.

From 1934 through 1938, Mac Lane held short term appointments at Yale University, Harvard University, Cornell University, and the University of Chicago. He then held a tenure track appointment at Harvard from 1938 to 1947. In 1941, while giving a series of visiting lectures at the University of Michigan, he met Samuel Eilenberg and began what would become a fruitful collaboration on the interplay between algebra and topology. 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 mathematics he worked on in this group concerned differential equations for fire-control systems.

In 1947, he accepted an offer to return to Chicago, where (in part because of the university's involvement in the Manhattan Project, and in part because of the administrative efforts of Marshall Stone) many other famous mathematicians and physicists had also recently moved. He traveled as a Guggenheim Fellow to ETH Zurich for the 1947–1948 term, where he worked with Heinz Hopf. Mac Lane succeeded Stone as department chair in 1952, and served for six years.

Mac Lane was vice president of the National Academy of Sciences and the American Philosophical Society, and 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.

Mac Lane and Samuel Eilenberg at a conference in July 1992

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 in 1943 began his research on what are now called Eilenberg–MacLane 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. 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 also coined the term Yoneda lemma for a lemma which is an essential background to many central concepts of category theory and which was discovered by Nobuo Yoneda.

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, and John G. Thompson.

In addition to reviewing a fair amount 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.

  1. Pearce, Jeremy (21 April 2005). "Saunders Mac Lane, 95, Pioneer of Algebra's Category Theory, Dies". The New York Times. Retrieved28 August 2020.
  2. Mac Lane, Saunders (1940). "Modular Fields". Amer. Math. Monthly. 47 (5): 67–84. doi:10.2307/2302685. JSTOR 2302685.
  3. Mac Lane, Saunders (1939). "Some Recent Advances in Algebra". Amer. Math. Monthly. 46 (1): 3–19. doi:10.2307/2302916. JSTOR 2302916.
  4. Albers, Donald J.; Alexanderson, Gerald L.; Reid, Constance, eds. (1990), "Saunders Mac Lane", More Mathematical People, Harcourt Brace Jovanovich, pp. 196–219.
  5. Mac Lane (2005), p. 6.
  6. Mac Lane, Saunders (Oct 1995). "Mathematics at Göttingen under the Nazis"(PDF). Notices of the AMS. 42 (10): 1134–1138.
  7. Segal, Sanford L. (April 1996). "Letters to the Editor: Corrections on Mac Lane's Article"(PDF). Notices of the AMS. 43 (4): 405–406.
  8. Kinoshita, Yoshiki (23 April 1996). "Prof. Nobuo Yoneda passed away". Retrieved21 December 2013.

Biographical references

Saunders Mac Lane
Saunders Mac Lane Language Watch Edit This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Saunders Mac Lane news newspapers books scholar JSTOR March 2013 Learn how and when to remove this template message Saunders Mac Lane 4 August 1909 14 April 2005 was an American mathematician who co founded category theory with Samuel Eilenberg Saunders Mac LaneBorn 1909 08 04 4 August 1909 Taftville Connecticut U S Died14 April 2005 2005 04 14 aged 95 1 San Francisco California U S NationalityUnited StatesAlma materYale University University of Chicago University of GottingenKnown forCategory theory Mac Lane set theoryAwardsChauvenet Prize 1941 2 3 Leroy P Steele Prize 1986 National Medal of Science 1989 Scientific careerFieldsMathematics Mathematical logic Algebraic number theory Algebraic topology InstitutionsHarvard University Cornell University University of Chicago Columbia UniversityDoctoral advisorHermann Weyl Paul BernaysDoctoral studentsSteve Awodey David Eisenbud William Howard Irving Kaplansky Roger Lyndon Michael D Morley Anil Nerode Robert Solovay John G Thompson Contents 1 Early life and education 2 Career 3 Contributions 4 Selected works 5 See also 6 Notes 7 References 7 1 Biographical references 8 External linksEarly life and education EditMac Lane was born in Norwich Connecticut near where his family lived in Taftville 4 He 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 5 He was the oldest of three brothers one of his brothers Gerald MacLane also became a mathematics professor at Rice University and Purdue University Another sister died as a baby His father and grandfather were both ministers his grandfather had been a Presbyterian but was kicked out of the church for believing in evolution and his father was a Congregationalist His mother Winifred studied at Mount Holyoke College and taught English Latin and mathematics 4 In high school Mac Lane s favorite subject was chemistry While in high school his father died and he came under his grandfather s care His half uncle a lawyer was determined to send him to Yale University where many of his relatives had been educated and paid his way there beginning in 1926 As a freshman he became disillusioned with chemistry His mathematics instructor Lester S Hill coached him for a local mathematics competition which he won setting the direction for his future work He went on to study mathematics and physics as a double major taking courses from Jesse Beams Ernest William Brown Ernest Lawrence F S C Northrop and Oystein Ore among others He graduated from Yale with a B A in 1930 4 During this period he published his first scientific paper in physics and co authored with Irving Langmuir In 1929 at a party of Yale football supporters in Montclair New Jersey Mac Lane there to be presented with a prize for having the best grade point average yet recorded at Yale had met Robert Maynard Hutchins the new president of the University of Chicago who encouraged him to go there for his graduate studies and soon afterwards offered him a scholarship Mac Lane neglected to actually apply to the program but showed up and was admitted anyway At Chicago the subjects he studied included set theory with E H Moore number theory with Leonard Eugene Dickson the calculus of variations with Gilbert Ames Bliss and logic with Mortimer J Adler 4 In 1931 having earned his master s degree and feeling restless at Chicago he earned a fellowship from the Institute of International Education and became one of the last Americans to study at the University of Gottingen prior to its decline under the Nazis His greatest influences there were Paul Bernays and Hermann Weyl By the time he finished his doctorate in 1934 Bernays had been forced to leave because he was Jewish and Weyl became his main examiner At Gottingen Mac Lane also studied with Gustav Herglotz and Emmy Noether Within days of finishing his degree he married Dorothy Jones from Chicago and soon returned to the U S 4 6 7 Career EditFrom 1934 through 1938 Mac Lane held short term appointments at Yale University Harvard University Cornell University and the University of Chicago He then held a tenure track appointment at Harvard from 1938 to 1947 In 1941 while giving a series of visiting lectures at the University of Michigan he met Samuel Eilenberg and began what would become a fruitful collaboration on the interplay between algebra and topology 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 mathematics he worked on in this group concerned differential equations for fire control systems 4 In 1947 he accepted an offer to return to Chicago where in part because of the university s involvement in the Manhattan Project and in part because of the administrative efforts of Marshall Stone many other famous mathematicians and physicists had also recently moved He traveled as a Guggenheim Fellow to ETH Zurich for the 1947 1948 term where he worked with Heinz Hopf Mac Lane succeeded Stone as department chair in 1952 and served for six years 4 Mac Lane was vice president of the National Academy of Sciences and the American Philosophical Society and 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 Edit Mac Lane and Samuel Eilenberg at a conference in July 1992 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 in 1943 began his research on what are now called Eilenberg MacLane 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 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 also coined the term Yoneda lemma for a lemma which is an essential background to many central concepts of category theory and which was discovered by Nobuo Yoneda 8 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 and John G Thompson In addition to reviewing a fair amount 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 Selected works Edit1997 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 0 387 58662 5 Originally Band 114 of Die Grundlehren Der Mathematischen Wissenschaften in Einzeldarstellungen AMS review by David Buchsbaum 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 1995 Mathematics at Gottingen under the Nazis PDF Notices of the AMS 42 10 1134 38 2005 Saunders Mac Lane A Mathematical Autobiography A K Peters ISBN 1 56881 150 0See also EditFoundations of geometryNotes Edit Pearce Jeremy 21 April 2005 Saunders Mac Lane 95 Pioneer of Algebra s Category Theory Dies The New York Times Retrieved 28 August 2020 Mac Lane Saunders 1940 Modular Fields Amer Math Monthly 47 5 67 84 doi 10 2307 2302685 JSTOR 2302685 Mac Lane Saunders 1939 Some Recent Advances in Algebra Amer Math Monthly 46 1 3 19 doi 10 2307 2302916 JSTOR 2302916 a b c d e f g Albers Donald J Alexanderson Gerald L Reid Constance eds 1990 Saunders Mac Lane More Mathematical People Harcourt Brace Jovanovich pp 196 219 Mac Lane 2005 p 6 Mac Lane Saunders Oct 1995 Mathematics at Gottingen under the Nazis PDF Notices of the AMS 42 10 1134 1138 Segal Sanford L April 1996 Letters to the Editor Corrections on Mac Lane s Article PDF Notices of the AMS 43 4 405 406 Kinoshita Yoshiki 23 April 1996 Prof Nobuo Yoneda passed away Retrieved 21 December 2013 References EditNadis Steve Yau Shing Tung 2013 Chapter 4 Analysis and Algebra Meet Topology Marston Morse Hassler Whitney and Saunders Mac Lane A History in Sum Cambridge MA Harvard University Press pp 86 115 ISBN 978 0 674 72500 3 JSTOR j ctt6wpqft MR 3100544 Zbl 1290 01005 e book ISBN 978 0 674 72655 0 Biographical references Edit McLarty Colin 2005 Saunders Mac Lane 1909 2005 His Mathematical Life and Philosophical Works Philosophia Mathematica Series III 13 3 237 251 doi 10 1093 philmat nki038 MR 2192173 Zbl 1094 01010 archived from the original on 2013 01 13 With selected bibliography emphasizing Mac Lane s philosophical writings McLarty Colin 2007 The Last Mathematician from Hilbert s Gottingen Saunders Mac Lane as Philosopher of Mathematics The British Journal for the Philosophy of Science 58 1 77 112 CiteSeerX 10 1 1 828 5753 doi 10 1093 bjps axl030 MR 2301283 S2CID 53561655 Zbl 1122 01017 Lawvere William 2007 Saunders Mac Lane New Dictionary of Scientific Biography New York Charles Scribners amp Sons pp 237 251 ISBN 978 0684315591 External links EditO Connor John J Robertson Edmund F Saunders Mac Lane MacTutor History of Mathematics archive University of St Andrews Obituary press release from the University of Chicago Photographs of Mac Lane 1984 99 Kutateladze S S Saunders Mac Lane the Knight of Mathematics https mathshistory st andrews ac uk Biographies MacLane Saunders Mac Lane at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Saunders Mac Lane amp oldid 1029690002, wikipedia, wiki, book,

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