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Saunders Mac Lane | |
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| Born | Leslie Saunders MacLane (1909-08-04)August 4, 1909 Norwich, Connecticut, U.S. |
| Died | April 14, 2005(2005-04-14) (aged 95)[3] San Francisco, California, U.S. |
| Alma mater | Yale University (BA) University of Chicago (MA) University of Göttingen (PhD) |
| Known for | Acyclic model Category theory Shuffle algebra Standard complex Mac Lane coherence theorem Mac Lane set theory Mac Lane's condition Mac Lane's planarity criterion Eilenberg–MacLane space Steinitz–Mac Lane exchange lemma |
| Spouse | Dorothy Jones (m. 1934) |
| Awards | Chauvenet Prize (1941)[1][2] Leroy P. Steele Prize (1986) National Medal of Science (1989) |
| Scientific career | |
| Fields | Mathematical logic Algebraic number theory Algebraic topology |
| Institutions | Harvard University Cornell University University of Chicago Columbia University |
| Doctoral advisor | Hermann Weyl Paul Bernays |
| Doctoral students | |
Saunders Mac Lane (August 4, 1909 – April 14, 2005), bornLeslie Saunders MacLane, was an American mathematician who co-foundedcategory theory withSamuel Eilenberg.
Mac Lane was born inNorwich, Connecticut, near where his family lived inTaftville.[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 eldest of three brothers; one of his brothers, Gerald MacLane, also became a mathematics professor atRice University andPurdue University. Another sister died as a baby. His father and grandfather were both ministers; his grandfather had been aPresbyterian, but was kicked out of the church for believing inevolution, and his father was aCongregationalist. His mother, Winifred, studied atMount Holyoke College and taught English, Latin, and mathematics.[4]
In high school, Mac Lane's favorite subject waschemistry. 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 toYale 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 fromJesse Beams,Ernest William Brown,Ernest Lawrence,F. S. C. Northrop, andØystein Ore, among others. He graduated from Yale with a B.A. in 1930.[4] During this period, he published his first scientific paper, inphysics and co-authored withIrving Langmuir.
In 1929, at a party of Yale football supporters inMontclair, New Jersey, Mac Lane (there to be presented with a prize for having the best grade point average yet recorded at Yale) had metRobert Maynard Hutchins, the new president of theUniversity 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 includedset theory withE. H. Moore,number theory withLeonard Eugene Dickson, thecalculus of variations withGilbert Ames Bliss, and logic withMortimer 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 theUniversity of Göttingen prior to its decline under the Nazis. His greatest influences there werePaul Bernays andHermann 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 withGustav Herglotz andEmmy Noether. Within days of finishing his degree, he married Dorothy Jones, from Chicago, and soon returned to the U.S.[4][6][7]
From 1934 through 1938, Mac Lane held short-term appointments atYale University,Harvard University,Cornell University, and theUniversity 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 theUniversity of Michigan, he metSamuel Eilenberg and began what would become a fruitful collaboration on the interplay between algebra and topology. In 1944 and 1945, he directed Columbia University's Applied Mathematics Group, which was involved in the war effort as a contractor for theApplied Mathematics Panel; the mathematics he worked on in this group concerneddifferential equations forfire-control systems.[4]
In 1947, he accepted an offer to return to Chicago, where (in part because of the university's involvement in theManhattan Project, and in part because of the administrative efforts ofMarshall Stone) many other famous mathematicians and physicists had also recently moved. He traveled as aGuggenheim Fellow toETH Zurich for the 1947–1948 term, where he worked withHeinz Hopf. Mac Lane succeeded Stone as department chair in 1952, and served for six years.[4]
He was vice president of theNational Academy of Sciences and theAmerican Philosophical Society, and 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 from 1974 to 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 theNational Academy of Sciences in 1949, and received theNational Medal of Science in 1989.[8]
After a thesis inmathematical logic, Mac Lane's early work was infield theory andvaluation theory. He wrote onvaluation rings andWitt vectors, and separability in infinitefield extensions. He started writing ongroup extensions in 1942, and in 1943 began his research on what isnow calledEilenberg–MacLane spaces K(G,n), having a single non-trivialhomotopy groupG in dimensionn. This work opened the way togroup cohomology in general.[citation needed]
After introducing, via theEilenberg–Steenrod axioms, the abstract approach tohomology theory, he and Eilenberg originatedcategory theory in 1945. He is especially known for his work oncoherence theorems. A recurring feature of category theory,abstract algebra, and of some other mathematics as well, is the use ofdiagrams, consisting of arrows (morphisms) linking objects, such asproducts andcoproducts. According to McLarty (2005), this diagrammatic approach to contemporary mathematics largely stems from Mac Lane (1948), who also coined the termYoneda lemma for a lemma which is an essential background to many central concepts of category theory and which was discovered byNobuo Yoneda.[9]
Mac Lane had an exemplary devotion to writing approachable texts, starting with his very influentialA Survey of Modern Algebra, coauthored in 1941 withGarrett Birkhoff. From then on, it was possible to teach elementary modern algebra to undergraduates using an English text. HisCategories for the Working Mathematician remains the definitive introduction to category theory.[citation needed]
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