Irving Kaplansky

Irving Kaplansky
Born	March 22, 1917 Toronto
Died	June 25, 2006 Los Angeles
Nationality	Canada, American
Fields	Mathematics
Institutions	University of Chicago
Alma mater	Harvard University
Doctoral advisor	Saunders Mac Lane
Doctoral students	Hyman Bass H. Arlen Brown Jacob Feldman Donald Ornstein Alex Rosenberg Fred Wright, Jr.
Known for	group theory ring theory operator algebras field theory

Irving Kaplansky (March 22, 1917 – June 25, 2006) was a Canadian mathematician.

Biography

Kaplansky (or "Kap," as his friends and colleagues called him) was born in Toronto, Ontario, Canada, to Polish parents who emigrated from Poland; his father worked as a tailor, and his mother ran a grocery and, eventually, a chain of bakeries. He attended the University of Toronto as an undergraduate. In his senior year, he competed in the first William Lowell Putnam Mathematical Competition, and Kaplansky was among the first five recipients of the Putnam Fellowship, which paid for him to go to graduate school at Harvard University. After receiving his Ph.D. from Harvard in 1941 as Saunders Mac Lane's first student, he stayed at Harvard as a Benjamin Peirce Instructor, and in 1944 moved with Mac Lane to Columbia University for a year. He was professor of mathematics at the University of Chicago from 1945 to 1984, and chair of the department from 1962 to 1967. His many doctoral students there include Hyman Bass, Donald Ornstein, and Harold Widom. He was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986.

Kaplansky also was a accomplished amateur musician. He studied piano from approximately the ages of four to 15, earned money in high school as a dance band musician, taught Tom Lehrer, and played in Harvard's jazz band in graduate school. He also had a regular program on Harvard's student radio station. After moving to the University of Chicago, he stopped playing for approximately 20 years, but returned to music as an accompanist to Gilbert and Sullivan productions there, and played a calliope in football parades. He often composed music based on mathematical themes. One of those compositions, A Song About Pi, is a melody based on assigning notes to the first 14 decimal places of pi, and has occasionally been performed by his daughter, singer-songwriter Lucy Kaplansky.

Mathematical contributions

Kaplansky made major contributions to group theory, ring theory, the theory of operator algebras and field theory. He published over 150 papers with over 20 co-authors.

Awards and honors

Kaplansky was a member of the National Academy of Sciences and the American Academy of Arts and Sciences.

Selected publications

• Kaplansky, Irving (September 1974). Commutative Rings. Lectures in Mathematics. University of Chicago Press. ISBN 0-226-42454-5. 
• Fun with Mathematics: Some Thoughts from Seven Decades, a video lecture of Kaplansky's advice on writing mathematical papers

See also

• Kaplansky conjecture
• Kaplansky density theorem
• Kaplansky's theorem on quadratic forms

References

• Albert, Nancy E. (2007). Irving Kaplansky: Some Reflections on His Early Years (PDF). Retrieved 2008-06-27. 
• Freund, Peter G. O. Irving Kaplansky and Supersymmetry. arXiv:physics/0703037
• Bass, Hyman; Lam, T.Y. (December 2007). "Irving Kaplansky (1917–2006)" (PDF). Notices of the American Mathematical Society 54 (11): pp.1477–1493. Retrieved 2008-01-05. 
• Kadison, Richard V. (February 2008). "Irving Kaplansky's Role in Mid-Twentieth Century Functional Analysis" (PDF). Notices of the AMS 55 (2): pp.216–225. Retrieved 2008-01-05. 

External links

• O'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St Andrews .
• Pearce, Jeremy (July 13, 2006). "Irving Kaplansky, 89, a Pioneer in Mathematical Exploration". The New York Times. p. C15. Retrieved 2008-01-05. 
• Irving Kaplansky + Ternary Quadratic Forms
• Irving Kaplansky + Lie Superalgebras