Irving Kaplansky

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

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-Jewish immigrants; 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, becoming one of the first five recipients of the Putnam Fellowship, which paid for graduate studies at Harvard University. After receiving his Ph.D. from Harvard in 1941 as Saunders Mac Lane's first student, he remained at Harvard as a Benjamin Pierce 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. Kaplansky's many doctoral students included Hyman Bass, Donald Ornstein, and Harold Widom. Kaplansky 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 was also an accomplished amateur musician. He studied piano until the age of 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 two decades, but then returned to music as an accompanist for student-run Gilbert and Sullivan productions and as a calliope player in football game 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 more than 150 papers and worked with at least 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 (1974). Commutative Rings. Lectures in Mathematics. University of Chicago Press. ISBN 0-226-42454-5. {{cite book}}: Unknown parameter |month= ignored (help)
• 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. {{cite journal}}: Cite journal requires |journal= (help)
• Freund, Peter G. O. Irving Kaplansky and Supersymmetry. arXiv:physics/0703037
• Bass, Hyman (2007). "Irving Kaplansky (1917–2006)" (PDF). Notices of the American Mathematical Society. 54 (11): pp.1477–1493. Retrieved 2008-01-05. {{cite journal}}: |pages= has extra text (help); Unknown parameter |coauthors= ignored (|author= suggested) (help); Unknown parameter |month= ignored (help)
• Kadison, Richard V. (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. {{cite journal}}: |pages= has extra text (help); Unknown parameter |month= ignored (help)

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