Kaplansky or "Kap" as his friends and colleagues called him was born in Toronto, Ontario, Canada, to Polish-Jewish immigrants;[3][4] his father worked as a tailor, and his mother ran a grocery and, eventually, a chain of bakeries.[5][6][7] He went to Harbord Collegiate Institute receiving the Prince of Wales Scholarship as a teenager. He attended the University of Toronto as an undergraduate and finished first in his class for three consecutive years.[8] 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.[5] Administered by the Mathematical Association of America, the competition is widely considered to be the most difficult mathematics examination in the world and "its difficulty is such that the median score is often zero or one (out of 120) despite being attempted by students specializing in mathematics."[9]
He was professor of mathematics at the University of Chicago from 1945 to 1984, and Chair of the department from 1962 to 1967. In 1968, Kaplansky was presented an honorary doctoral degree from Queen's University with the university noting "we honour as a Canadian whose clarity of lectures, elegance of writing, and profundity of research have won him widespread acclaim as the greatest mathematician this country has so far produced."[15] From 1967 to 1969, Kaplansky wrote the mathematics section of Encyclopædia Britannica.[16][17][18] 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.[19]
Kaplansky was also an accomplished amateur musician. He had perfect pitch, studied piano until the age of 15, earned money in high school as a dance band musician, taught Tom Lehrer,[20] 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.[5] 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.[21]
Kaplansky, Irving (1954). Infinite Abelian groups.[22] revised edn. 1971 with several later reprintings
—— (1955). An introduction to differential algebra. University of Chicago Press. 2nd edn. Paris: Hermann. 1957.
—— (1966). Introdução à teoria de Galois, por I. Kaplansky. Pref. de Elon Lages Lima.
—— (1968). Rings of operators.
—— (1969). Fields and rings. 2nd edn. 1972
—— (1969). Linear algebra and geometry; a second course. revised edn. 1974
—— (1970). Algebraic and analytic aspects of operator algebras. ISBN 9780821816509.
—— (1971). Lie Algebras and Locally Compact Groups. University of Chicago Press. ISBN 0-226-42453-7. several later reprintings
—— (1972). Set theory and metric spaces. 2nd edn. 1977
—— (September 1974). Commutative Rings. Lectures in Mathematics. University of Chicago Press. ISBN 0-226-42454-5. 1st edn. 1966; revised 1974 with several later reprintings
with I. N. Herstein: —— (1974). Matters mathematical. New York, Harper & Row. ISBN 9780060428037. 2nd edn. 1978
Kaplansky, Irving (1995). Selected papers and other writings. ISBN 9780387944067.
Articles
edit
Kaplansky, Irving (1944). "Symbolic solution of certain problems in permutations". Bull. Amer. Math. Soc. 50 (12): 906–914. doi:10.1090/s0002-9904-1944-08261-x. MR 0011393.
Kaplansky, Irving (1945). "A note on groups without isomorphic subgroups". Bull. Amer. Math. Soc. 51 (8): 529–530. doi:10.1090/s0002-9904-1945-08382-7. MR 0012267.
with I. S. Cohen: Cohen, I. S.; Kaplansky, Irving (1946). "Rings with a finite number of primes. I". Trans. Amer. Math. Soc. 60: 468–477. doi:10.1090/s0002-9947-1946-0019595-7. MR 0019595.
Kaplansky, Irving (1946). "On a problem of Kurosch and Jacobson". Bull. Amer. Math. Soc. 52 (6): 496–500. doi:10.1090/s0002-9904-1946-08600-0. MR 0016758.
with Richard F. Arens: Arens, Richard F.; Kaplansky, Irving (1948). "Topological representations of algebras". Trans. Amer. Math. Soc. 63 (3): 457–481. doi:10.1090/s0002-9947-1948-0025453-6. MR 0025453.
Kaplansky, Irving (1948). "Rings with a polynomial identity". Bull. Amer. Math. Soc. 54 (6): 575–580. doi:10.1090/s0002-9904-1948-09049-8. MR 0025451.
Kaplansky, I. (1949). "Primary ideals in group algebras". Proc Natl Acad Sci U S A. 35 (3): 133–136. Bibcode:1949PNAS...35..133K. doi:10.1073/pnas.35.3.133. PMC1062983. PMID 16588871.
Kaplansky, Irving (1950). "The Weierstrass theorem in fields with valuations". Proc. Amer. Math. Soc. 1 (3): 356–357. doi:10.1090/s0002-9939-1950-0035760-3. MR 0035760.
Kaplansky, Irving (1951). "The structure of certain operator algebras". Trans. Amer. Math. Soc. 70 (2): 219–255. doi:10.1090/s0002-9947-1951-0042066-0. MR 0042066.
Kaplansky, Irving (1952). "Modules over Dedekind rings and valuations rings". Trans. Amer. Math. Soc. 72 (2): 327–340. doi:10.1090/s0002-9947-1952-0046349-0. MR 0046349.
Kaplansky, Irving (1952). "Orthogonal similarity in infinite dimensional spaces". Proc. Amer. Math. Soc. 3: 16–25. doi:10.1090/s0002-9939-1952-0046564-1. MR 0046564.
Kaplansky, Irving (1952). "Symmetry of Banach algebras". Proc. Amer. Math. Soc. 3 (3): 396–399. doi:10.1090/s0002-9939-1952-0048711-4. MR 0048711.
Kaplansky, I. (1952). "Some results on abelian groups". Proc Natl Acad Sci U S A. 38 (6): 538–540. Bibcode:1952PNAS...38..538K. doi:10.1073/pnas.38.6.538. PMC1063607. PMID 16589142.
Kaplansky, Irving (1953). "Infinite dimensional quadratic forms admitting composition". Proc. Amer. Math. Soc. 4 (6): 956–960. doi:10.1090/s0002-9939-1953-0059895-7. MR 0059895.
Kaplansky, Irving (1953). "Dual modules over a valuation ring. I". Proc. Amer. Math. Soc. 4 (2): 213–219. doi:10.1090/s0002-9939-1953-0053092-7. MR 0053092.
Kaplansky, Irving (1994). "A quasi-commutative ring that is not neo-commutative". Proc. Amer. Math. Soc. 122: 321. doi:10.1090/s0002-9939-1994-1257114-3. MR 1257114.
"The forms x+32y2 and x+64y2 ". Proc. Amer. Math. Soc. 131: 2299–2300. 2003. doi:10.1090/s0002-9939-03-07022-9. MR 1963780.
^ abO'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St Andrews. http://www-history.mcs.st-andrews.ac.uk/Biographies/Kaplansky.html.
^"Irving Kaplansky Memoir by Nancy E. Albert" (PDF). Archived from the original (PDF) on 2010-06-18. Retrieved 2012-11-27.
^December 4; Rothman, 2012 Ellen K. "Making Family Stories into Art". Jewish Women's Archive. Retrieved 2022-10-07.{{cite web}}: CS1 maint: numeric names: authors list (link)
^ abcAlbers, Donald J.; Alexanderson, Gerald L.; Reid, Constance, eds. (1990), "Irving Kaplansky", More Mathematical People, Harcourt Brace Jovanovich, pp. 118–136, ISBN 9780120482511.
^"In memoriam: Irving Kaplansky". Archived from the original on 2014-01-06. Retrieved 2014-01-05.
^"Irving Kaplansky discovered in Canada, Selected School Yearbooks, 1901-2010". Ancestry.com. Retrieved 2022-10-07.
^The Putnam Competition from 1938-2015 by Joseph A. Gallian
^MacLane, Saunders. "The Applied Mathematics Group at Columbia in World War II" in A Century of Mathematics in America, vol. 3 (ed. Peter Duren). Providence: American Mathematical Society, 1989.
^Defense Technical Information Center. http://www.dtic.mil/dtic/tr/fulltext/u2/b809137.pdf
^Kaplansky, Irving. "Abraham Adrian Albert" 1972. http://www.ams.org/samplings/math-history/hmath1-kaplansky17.pdf
^ ab"Irving Kaplansky - Biography". Maths History. Retrieved 2022-10-07.
^"Irving Kaplansky - Scholars | Institute for Advanced Study". 9 December 2019.
^ abBass, Hyman and Lam, T.Y., (December, 2007) "Irving Kaplansky (1917-2007)." Notices of the American Mathematical Society. (54)11,1477-1493. http://www.ams.org/notices/200711/tx071101477p.pdf
^Kaplansky, I. (1967). Mathematics. In: Book of the Year: Events of 1966, 9th ed. Chicago, Toronto, London, Geneva, Sydney, Tokyo, Manila: William Benton, pp.502-503.
^Kaplansky, I. (1968). Mathematics. In: Book of the Year: Events of 1967, 9th ed. Chicago, Toronto, London, Geneva, Sydney, Tokyo, Manila: William Benton, pp.502.
^Kaplansky, I. (1969). Mathematics. In: Book of the Year: Events of 1968, 9th ed. Chicago, Toronto, London, Geneva, Sydney, Tokyo, Manila: William Benton, pp.488-489.
^Tourist, Math (2013-09-22). "MTArchive: A Song about Pi". MTArchive. Retrieved 2022-10-07.
^Pearce, Jeremy "Irving Kaplansky, 89, a Pioneer in Mathematical Exploration" https://www.nytimes.com/2006/07/13/us/13kaplansky.html_r=1&oref=slogin
^Baer, Reinhold (1955). "Review: Infinite abelian groups by I. Kaplansky" (PDF). Bull. Amer. Math. Soc. 61 (1): 88–89. doi:10.1090/s0002-9904-1955-09877-x.
References
edit
Albert, Nancy E. (2007). "Irving Kaplansky: Some Reflections on His Early Years" (PDF). Retrieved 2008-06-27. {{cite journal}}: Cite journal requires |journal= (help)
Peterson, Ivars. (2013). "A Song about Pi" http://mtarchive.blogspot.com/2013/09/a-song-about-pi.html?m=1
Freund, Peter G. O. Irving Kaplansky and Supersymmetry. arXiv:physics/0703037
Kadison, Richard V. (February 2008). "Irving Kaplansky's Role in Mid-Twentieth Century Functional Analysis" (PDF). Notices of the AMS. 55 (2): 216–225. Retrieved 2008-01-05.