Kaplansky loved solving ‘quirky mathematical problems’

Irving Kaplansky, the George Herbert Mead Distinguished Service Professor Emeritus in Mathematics and the College and a leading authority on algebra, died Sunday, June 25 at his home in Sherman Oaks, Calif. He was 89.

Kaplansky loved working with young people, and he served as the Ph.D. adviser to 55 graduate students, the most of any mathematics professor ever to have taught at the University, said J. Peter May, Professor in Mathematics.

“He published close to 150 papers, the earliest appearing in 1939 and the last in 2003, an astonishing span of activity for a mathematician,” May said. “Kaplansky had a great sense of humor, or perhaps more accurately fun. He enjoyed life and lit up any room he was in. He liked quirky mathematical problems with a real-life twist. For example, a 1943 paper gave an elegant solution to the problem of finding the number of ways that a given number of married couples may be seated at a round table, men alternating with women, so that no wife sits next to her own husband.”

Kaplansky received the prestigious Steele Prize in 1989 from the American Mathematical Society for his career-long influence on mathematics. The citation said he received the honor “for his lasting impact on mathematics, particularly mathematics in America. By his energetic example, his enthusiastic exposition and his overall generosity, he has made striking changes in mathematics and has inspired generations of younger mathematicians.”

His research was devoted primarily to algebra and functional analysis. He contributed many basic results on the structure of Banach algebras, on locally compact groups and on group representations.

He also did fundamental work on ring theory and wrote important books, among them, Commutative Rings (1970), Infinite Abelian Groups (1969) and Lie Algebras and Locally Compact Groups (1971).

From 1957 to 1961, he was editor of the Proceedings of the American Mathematical Society.

In 1966 he was elected to the National Academy of Sciences and to the American Academy of Arts and Sciences in 1967. He was chairman of the Board of Trustees of the American Mathematical Society in 1971 and the organization’s president from 1985 to 1986.

Kaplansky, a native of Toronto, Canada, received a B.A. in 1938 and an M.A. in 1939, both from the University of Toronto. He received a Ph.D. in 1941 from Harvard University.

At the University of Toronto as an undergraduate, he was on the winning team of the first William Lowell Putnam competition, a mathematical contest for students from the United States and Canada. He was also the first individual winner of that contest which earned him a fellowship to Harvard.

After teaching at Harvard and Columbia universities, Kaplansky joined the Chicago faculty in 1945. He was made a full professor in 1956. He served from 1962 to 1967 as Chairman of Mathematics, and received his appointment as the George Herbert Mead Distinguished Service Professor in Mathematics in 1969.

Kaplansky’s teaching was honored in 1961 when he received the University’s Lewellyn John and Harriet Manchester Quantrell Award for Excellence in Undergraduate Teaching. The citation read: “Students at the University have always found his treatment of mathematics original and illuminating to an extraordinary degree, and his teaching at once thorough, vivid and inspiring.”

In 1984 he became director of the Mathematical Sciences Research Institute in Berkeley, California, a post he held until 1992.

David Eisenbud, the institute’s current director and a former student of Kaplansky’s said, “I remember well his highly entertaining and beautifully polished lectures from my student days in Chicago. Whatever he taught, I signed up for the course, it was such a pleasure to listen to him.

As an avid musician and pianist, Kaplansky played in or directed many University musical and theater productions, including its annual productions of the works of Gilbert & Sullivan.

Kaplansky’s wife of 55 years, Chellie, two sons, Steven, of Sherman Oaks, Calif. and Alex of Hillsborough, NJ, a daughter, Lucy, of New York City, and two grandchildren survive him.