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- Brief scientific biography
- Contributions to Education
- Relevant bibliography
- Publications on the teaching of mathematics

Saunders Mac Lane was born in Norwich, Connecticut, on 4 August 1909.

He graduated from high school at the age of 15 and entered Yale University that year, receiving his B.A from Yale in 1930 and his master's degree from the University of Chicago in 1931. At the urging of E. H. Moore at Chicago, who was retired but still teaching, Mac Lane went to Göttingen, Germany, for his Ph.D., which he obtained in 1934 after studying logic and mathematics with Paul Bernays, Emmy Noether, and Hermann Weyl. In his dissertation, he gave a formal means of abbreviating proofs, arguing that every mathematical proof has a leading idea that determines its steps and provides a plan.

Once back in the United States,

Mac Lane found it difficult to get a job in logic, so he turned his attention to algebra. From 1934 to 1938, he was a mathematics instructor at Harvard University, Cornell University, and the University of Chicago. He returned to Harvard in 1938, holding a tenure-track position there until 1947. In 1944 and 1945, he also directed Columbia University's Applied Mathematics Group, which was one of the largest groups of mathematicians involved in the war effort. In 1947, he went back to Chicago, where he spent the rest of his career. He chaired the Mathematics Department from 1952 to 1958. He was appointed the Max Mason Distinguished Service Professor in Mathematics in 1963, and became Professor Emeritus in 1982. He moved to San Francisco in 2002, where he died on 14 April 2005 after a long illness. He was survived by his second wife, two children, three stepchildren, one grandchild, and five step-grandchildren.

Mac Lane did his early mathematical work in field theory and valuation theory. In 1943, he began his influential collaboration with Samuel Eilenberg on what are now termed Eilenberg-Mac Lane spaces K(G,n), which have a single nontrivial homotopy group G in dimension n and which are building blocks of homotopy theory. Mac Lane's central achievement, with Eilenberg, was the creation of category theory in 1945. Best known of Mac Lane's many publications is the famous introductory textbook written with Garrett Birkhoff in 1941, A Survey of Modern Algebra, a book that was for years the leading textbook in its field.

Mac Lane was one of only four people to have been elected president of both the Mathematical Association of America and the American Mathematical Society. He was elected to the National Academy of Sciences in 1949. In 1989, he received the nation's highest award for scientific achievement, the National Medal of Science. He received two Guggenheim Fellowships and visited Australia as a Fulbright Scholar. He also received honorary degrees from Purdue University, Yale University and the University of Glasgow, among others. Other honors include both the Chauvenet Prize and the Distinguished Service award of the Mathematical Association of America, the Steele Career Prize of the American Mathematical Society, and honorary fellowship in the Royal Society of Edinburgh.

From 1952 to 1954, Mac Lane was a vice-president of the International Commission on Mathematical Instruction. He served on the Executive Committee of the International Mathematical Union from 1955 to 1958.

We must contrive ever anew to expose our students — be they general students or specialized students — to the beauty and excitement and relevance of mathematical ideas. We must set forth the extraordinary way in which mathematics, springing from the soil of basic human experience with numbers and data and space and motion, builds up a far-flung architectural structure composed of theorems which reveal insights into the reasons behind appearances and of concepts which relate totally disparate concrete ideas. (MAC LANE, 1954, p. 152)He proceeded to describe in some detail the curriculum in mathematics at the University of Chicago as an illustration of the integrated structure he sought for college mathematics courses.

Writing in the Bulletin of the National Association of Secondary-School Principals in May 1954, Mac Lane argued that "the lively modern development of mathematics has had no impact on the content or on the presentation of secondary-school mathematics" (p. 66). He noted how the growing applications of mathematics in science and technology together with the severe shortage of new mathematical talent demanded both an improved school mathematics curriculum but also a new generation of teachers trained in modern mathematics. He proceeded to sketch some of the ideas of modern mathematics that should be dealt with in secondary school, concluding with a call for change:

The mathematical subjects now taught [in secondary school] need drastic overhauling. It no longer suffices to continue to teach the old ideas; rather, one must start afresh to determine which ideas should be taught and in what perspective. In this way, school mathematics could become fully relevant to the modern world. (p. 70)Mac Lane (1994) offered intuition, trial, error, speculation, conjecture, proof as the sequence in which we come to understand mathematics. His point was that although mathematicians may do mathematics in many different ways, the path to understanding it always ends in rigorous proof. In his own teaching and in his writings on education, he advocated careful attention to abstraction and proof treated carefully and in recognition of the soil from which mathematics springs.

G. BIRKHOFF, S. MAC LANE 1941, A survey of modern algebra, New York: Macmillan

S. MAC LANE, G. BIRKHOFF 1967, Algebra, New York: Macmillan

S. MAC LANE 1971, Categories for the working mathematician, Berlin: Springer-Verlag

S. MAC LANE 1986, Mathematics: Form and function, Berlin: Springer-Verlag

S. MAC LANE 1994, Response to "Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics",by A. Jaffe and F. Quinn , Bulletin of the American Mathematical Society (New Series), 30, 190-193

S. MAC LANE 2005, A mathematical autobiography, Wellesley, MA: AK Peters

G. ALEXANDERSON, S. MAC LANE 1989, A conversation with Saunders Mac Lane, College Mathematics Journal, 20, 2-25

R.P. Jr. BOAS 1975, Award for Distinguished Service to Professor Saunders Mac Lane, American Mathematical Monthly, 82, 107-108

J.J. O'CONNOR, E.F. ROBERTSON 1997, Saunders Mac Lane, retrieved from the MacTutor History of Mathematics Archive web site:

http://www-history.mcs.st-andrews.ac.uk/Biographies/MacLane.html

I. KAPLANSKY (edited by) 1979, Saunders Mac Lane: Selected papers, New York & Berlin: Springer-Verlag

C. MC LARTY 2005, Saunders Mac Lane (1909-2005): His mathematical life and philosophical works, Philosophia Mathematica, 13(3), 237-251

J. PEARCE 2005, Saunders Mac Lane, 95, pioneer of algebra's category theory, The New York Times, A21

S. MAC LANE 1954, Of course and courses, American Mathematical Monthly, 61, 151-157

S. MAC LANE 1954 (May), The impact of modern mathematics on secondary schools, Bulletin of the National Association of Secondary-School Principals, 38, 66-70, reprinted in 1956 in the Mathematics Teacher, 49, 66-69

S. MAC LANE 1957, Algebra, in F.L. Wren (edited by), Insights into modern mathematics (23rd Yearbook of the National Council of Teachers of Mathematics, Washington, DC: The Council, pp. 100-144)

S. MAC LANE 1989, The education of Ph.D.s in mathematics, in P. Duren (edited by), A century of mathematics in America, Providence, RI: American Mathematical Society, Part 3, 517-523

Author

Jeremy Kilpatrick

University of Georgia

jkilpat@uga.edu