Mac Lane, 95, helped transform 20th-century mathematics

Saunders Mac Lane, one of the most influential American mathematicians of the 20th century and a recipient of the National Medal of Science, died Thursday, April 14, in San Francisco after a long illness. He was 95.

“He was one of the most important figures in the University of Chicago Mathematics Department, or indeed in American mathematics,” David Eisenbud wrote of Mac Lane in the preface of the latter’s autobiography, which will be published in late May by A K Peters Ltd.

Eisenbud, who received his Ph.D. in Mathematics under Mac Lane’s supervision in 1970, is the president of the American Mathematical Society and director of the Mathematical Sciences Research Institute in Berkeley, Calif.

In his research,  Mac Lane “was extraordinarily perceptive and original, and he was especially strong as a philosopher of mathematics,” said Peter May, Professor in Mathematics and the College.

“With Sammy Eilenberg he created a new way of thinking about mathematics. In a landmark 1945 paper, they introduced and named the concepts of ‘categories,’ ‘functors’ and ‘natural transformations.’ The language they introduced there transformed modern mathematics,” he said. “In fact, a very great deal of mathematics since then would quite literally have been unthinkable without that language.”

F. William Lawvere of the State University of New York at Buffalo said, “Category theory is still exploding in its influence after 60 years, illuminating and guiding the development of practically every one of the many varied fields of mathematics.”

Category theory was first developed as a language to describe transformations from one area of mathematics into another, although it was later developed into a field of study in its own right. Said May, “Mac Lane was one of the pioneers of algebraic topology, a subject in which one transforms, or describes, spatial structures, which one first sees in terms of shapes—spaces with holes, like a doughnut, say—into algebraic structures … in which one can do calculations.”

The development of category theory and algebraic topology was accompanied by the development of another subject, homological algebra, a kind of algebra that plays a prominent role in algebraic topology and other branches of mathematics, May said.

Mac Lane also steered national science and mathematics policy through his work on numerous boards and guided dozens of students to mathematical careers. He served as president of the Mathematical Association of America and the American Mathematical Society. He was a member of the National Science Board from 1974 to 1980, providing science policy advice to the U.S. government.

For a time there were a few members of the Department of Mathematics who had received their Ph.D.s under Mac Lane’s supervision. One of them was John Thompson (Ph.D.,’59), who received in 1970 the Fields Medal, sometimes referred to as the Nobel Prize of mathematics.

Irving Kaplansky, who served on the Chicago faculty and was Chairman of Mathematics, was Mac Lane’s first Ph.D. student.

Mac Lane was born in Norwich, Conn., Aug. 4, 1909. He earned his bachelor’s degree from Yale College in 1930, and his master’s from Chicago in 1931. He earned his Ph.D. in 1934 from the Mathematisches Institut of Göttingen, Germany, which at the time was the world’s center of mathematical research.

Mac Lane worked as a mathematics instructor at Harvard and Cornell universities and at Chicago between 1934 and 1938. He served again on the Harvard faculty from 1938 to 1947, and at Chicago beginning in 1947.

Mac Lane was Chairman of Mathematics from 1952 to 1958, taking the reins from Marshall Stone at a time that many consider the high point in the department’s history. He was appointed the Max Mason Distinguished Service Professor in Mathematics in 1963, and became Professor Emeritus in 1982.

He was the author or co-author of more than 100 research papers and six books, including A Survey of Modern Algebra (1941, republished in 1997); Homology (1963); Algebra (1967); and Categories for the Working Mathematician (1971).

Among his many honors, Mac Lane was elected to the National Academy of Sciences in 1949. He received the nation’s highest award for scientific achievement, the National Medal of Science, in 1989.

Mac Lane is survived by his widow, Osa, of San Francisco, and two daughters, Gretchen Mac Lane of New York City and Cynthia Hay of London; one grandson, William Hay, of London; three stepchildren, William Segal of Washington, D.C.; Andrew Segal of Santa Fe, N.M.; and Karen Segal of San Francisco; and five step-grandchildren. Mac Lane’s first wife, Dorothy Jones Mac Lane, died in 1985.

Services for the family were held in San Francisco Tuesday, April 19. The Mathematical Sciences Research Institute in Berkeley will hold a memorial at 4:30 p.m. Wednesday, May 4.