**Irving Kaplansky** was a Canadian mathematician who made major contributions to ring theory, group theory and field theory.

- Although he is recorded on official documents as Samuel and Anna's son, and later gave his name sometimes as Max Kaplansky sometimes Max Copeland, in fact on his marriage certificate he gives his parents as Monchay and Sarah Copeland.
- The surprise in this census data is that Irving, who is four years old at this time, is recorded as Isaac.
- This is not the only surprise with Irving Kaplansky's name and we note the complications here.
- When he graduated in 1938 his name appears as Irving Kaplansky, but when he first travelled to United States on 12 September 1940 he gave his name as Izidor Kaplansky.
- Irving's early interest was music, an interest which he has kept all his life.
- However Irving knew from a very young age that mathematics, and not music, was to be his life.
- Kaplansky's secondary education was at the Harbord Collegiate Institute, founded in 1892, where he was very involved in both mathematics and music, singing in Gilbert and Sullivan productions.
- In many ways Kaplansky was lucky in entering the University of Toronto when he did, for the Mathematics Department was very much on the up.
- In 1938 Kaplansky graduated with a B.A. from the University of Toronto.
- Kaplansky was a Putnam fellow in the individual competition and Toronto won the team competition.
- The summer of 1938 was, in many ways, a vital step in Kaplansky's development as a mathematician.
- Richard Brauer who was attending the Chicago summer of algebra and was giving lectures, advised his student Kaplansky to attend.
- Nathan Jacobson gave a course on 'Continuous Groups' which Kaplansky attended and he also learnt much from Albert's lectures.
- In 1940 Kaplansky received his M.A. from Toronto, and continued his studies at Harvard University.
- His thesis supervisor at Harvard was Saunders Mac Lane and Kaplansky's thesis was entitled Maximal Fields with Valuations.
- Kaplansky was appointed a Benjamin Peirce Instructor in Harvard that year and he continued to hold that post there until 1944.
- The year 1944-45 Kaplansky spent in the Applied Mathematics Group of the National Defense Council at Columbia University working on aerial photography.
- During the years 1962-67 Kaplansky was chairman of the department in Chicago.
- After he retired in 1984, Kaplansky went to California where he became director of the Mathematical Sciences Research Institute at the University of California, Berkeley.
- Kaplansky's work in mathematics was wide ranging although mostly it was in areas of algebra.
- Asked what his own favourite paper was, Kaplansky said it was Any Orthocomplemented Complete Modular Lattice is a Continuous Geometry (1955).
- Many students were inspired by Kaplansky's remarkable lectures.
- Kaplansky received numerous awards.
- There were many other ways in which Kaplansky served the Society, particularly with respect to the publications of the American Mathematical Society.
- Despite this remarkable record of service to the Society, there were still further ways in which Kaplansky used his many talents to its benefit.
- Kaplansky was awarded a Guggenheim Fellowship and elected to the National Academy of Sciences and the American Academy of Arts and Sciences.
- Two years later, in 1989, the American Mathematical Society awarded Kaplansky their Steele Prize.
- The citation for the prize gives an excellent summary of Kaplansky's many achievements.
- Kaplansky could not be present at the Summer Meeting of the American Mathematical Society in 1989 to reply in person to this citation.

Born 22 March 1917, Toronto, Ontario, Canada. Died 25 June 2006, Sherman Oaks, Los Angeles, California, USA.

View full biography at MacTutor

Group Theory, Origin Canada

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive