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Irving Kaplansky 1917–2006. (English) Zbl 1174.01014

Irving Kaplansky (1917–2006) was born in Toronto and was the first PhD student of Saunders Mac Lane, in Harvard, 1941. From 1945 through his retirement, in 1984, Kaplansky was Professor of Mathematics at the University of Chicago. He chaired the mathematics department from 1962 to 1967, was the Director of the Mathematical Sciences Research Institute, in Berkeley, from 1984-1992, and was elected President of the American Mathematical Society in 1984. In his long career at the University of Chicago, Kaplansky had 55 students spanning from 1950 to 1978. The first author of this paper, Hyman Bass, took his PhD degree in 1959, from Kap, as Kaplansky became known among friends and colleagues. The second author, T.Y. Lam, received his PhD in Columbia University, in 1967, under Hyman Bass. This justifies Lam calling Kap, “my mathematical grandfather”.
This paper analyzes and relates Kaplansky’s production in several different areas of mathematics and the research areas of the students who took their PhD under him. To do this analysis, Bass groups his publications in four major areas: topological algebra, quadratic and higher forms, commutative and homological algebra, Lie theory, and in other areas to which Kaplansky contributed: ring theory (noncommutative), combinatorics and number theory, module theory, abelian groups, linear algebra, general topology, group theory, game theory, probability and statistics. The recourse of an imaginative colored chronological chart allows Bass to distribute Kaplansky’s production among these areas. Another similar chart relates the research areas of his PhD students with the current research interest of Kaplansky. This is a very significant correlation to illustrate how his role as a professor was integrated with his activities as a researcher. Bass claims that he was a virtuous problem solver and, recurring to citations of Kaplansky himself, shows his mathematical style. Very interesting remarks by Bass and a number of opinions by his students justifies the affirmation that Kaplansky was a gifted teacher, mentor and writer. He was concerned with the preparation of a new generation of researchers and realized that problem solving was an important component of this preparation. This is clearly seen in his numerous contributions to the Problem sections of the American Mathematical Monthly.
In his part of the paper T. Y. Lam, much younger, recalls being hired by Kaplansky when he was chair of the math department in Chicago. His attitude receiving a young faculty is a good lesson of how to be an academic administrator. This quality impressed again Lam when he was a professor at Berkeley and Kaplansky arrived, after retirement from Chicago, to take on “two simultaneous tasks of herculean proportions”: to become the Director of the Mathematical Sciences Research Institute and to be the President of the American Mathematical Society. Much of Lam’s comments are about Kaplansky being a model for young faculty, his advices and broad interest in the classics. He also refers to his excellent lectures and to his notes. Lam praises the assorted, unpublished, short lecture notes, particularly a “fourteen loose-leaf notebooks” which Kaplansky himself mentions in the preface of his Selected Papers and Other Writings [New York, NY: Springer-Verlag. (1995; Zbl 0826.01039)]. Lam wonders “how many more mathematical gems have remained hidden in those unpublished notebooks!” Lam adds interesting episodes of the social life of the Kaplansky family in Berkeley.
Eleven shorter narratives, by colleagues, students and his daughter, Lucy Kaplansky, complement the paper, talking about his family life, his multifaceted research interests, his role as a teacher and mentor and as an administrator. The paper is illustrated with very nice pictures, including his family. This is an exemplary memorial notice of a brilliant mathematician and influential professional, who was also an accomplished musician and highly devoted to a rich personal and family life.

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
18-03 History of category theory
22-03 History of topological groups

Keywords:

Obituary

Biographic References:

Kaplansky, Irving

Citations:

Zbl 0826.01039
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