The first William Lowell Putnam Mathematical Competition saw Irving Kaplansky emerge as one of its initial five fellowship recipients in 1938. This early academic distinction facilitated his graduate studies at Harvard University, setting a professional trajectory that would define significant developments in algebra, ring theory, group theory, and functional analysis throughout the twentieth century.
Academic Foundation
Born in Toronto in 1917, Kaplansky attended Harbord Collegiate Institute before enrolling at the University of Toronto. He maintained top-class rankings for three consecutive years during his undergraduate tenure. Following his success in the Putnam competition, he moved to Harvard University, where he completed his doctoral studies in 1941 under the supervision of Saunders Mac Lane.
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During World War II, Kaplansky transitioned from a Benjamin Peirce instructorship at Harvard to join the National Defense Research Committee. From 1944 to 1945, he engaged in applied mathematics research related to aerial gunnery, rocketry, and fire control. Following the war, he held a long-term tenure as a mathematics professor at the University of Chicago, serving from 1945 until 1984.
Mathematical Contributions and Leadership
His research portfolio includes the Kaplansky density theorem, the Erdős–Kaplansky theorem, and various findings regarding projective modules and quadratic forms. Beyond his individual research, he contributed to the broader field as the director of the Mathematical Sciences Research Institute from 1984 to 1992 and as president of the American Mathematical Society during the 1985–1986 term.
Musical Pursuits
Beyond his mathematical work, Kaplansky was an active musician who possessed perfect pitch. He played in a jazz band at Harvard and later served as an accompanist for Gilbert and Sullivan productions. His compositions included A Song About Pi, which assigned musical notes to the decimal expansion of the mathematical constant.
Fast facts
- Born: 1917, Toronto
- Died: 2006, Sherman Oaks
- Education: University of Toronto, Harvard University
- Professional tenure: University of Chicago (1945-1984)
- Notable honors: Putnam Fellow (1938), Guggenheim Fellowship (1948)
- Professional leadership: President of the American Mathematical Society (1985-1986)
- Academic supervision: Doctoral advisor to 55 students
Questions readers ask
What subjects did Kaplansky specialize in?
He focused on algebra, ring theory, group theory, and functional analysis.
Did Kaplansky have interests outside of mathematics?
Yes, he was an accomplished amateur musician who played piano, performed in jazz bands, and composed music based on mathematical themes.
Achievements
- Notable work: Kaplansky density theorem
- Notable work: Kaplansky's theorem on quadratic forms
- Notable work: Kaplansky's theorem
- Affiliated with University of Chicago and Harvard University
- Educated at University of Toronto and Harvard University
- Worked as mathematician and university teacher
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