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Irving Reiner attended school in Brooklyn then, in 1940, he entered Brooklyn College. His first paper on formulae for primes was published while he was still an undergraduate. Reiner graduated in 1944 and became a graduate student at Cornell. He was awarded a Master's Degree for a thesis on binary quadratic forms in 1945 and his doctorate in 1949 for a thesis on a generalisation of Meyer's theorem. His doctoral supervisor was Burton Jones.
After completing work on his doctoral thesis Reiner went to the Institute for Advanced Study at Princeton. After a year at Princeton he was appointed to the University of Illinois. Although he was to remain at the University of Illinois throughout his career, he held various visiting appointments in particular in London and at the University of Warwick.
G J Janusz wrote in [1]:-
[Reiner lived] a life dedicated to mathematics. He gave encouragement to everyone in whom he saw some mathematical talent and, in return, he was stimulated by the success of other mathematicians with whom he had contact. ... He would often work in streaks, putting in long hours on many consecutive days and nights. In order to refresh himself after such periods of intensive work, he would like to relax by attending a concert. ... During the summers, the vacation of his choice would be a couple of weeks in the mountains.
After his doctoral thesis Reiner worked on classical subgroups of GL(n,Z). He solved problems concerning minimal generating sets. He then found generators for the automorphism group of GL(n,Z) and of related groups. In 1955 he wrote his first paper on representations of groups. His most famous book, Representation theory of finite groups and associative algebras was published in 1962. It was written jointly with C Curtis who was based at the University of Wisconsin, Madison and Reiner claimed it was the only mathematics book written in a museum and a hotel lobby.
Since Chicago was approximately half way between Madison and Urbana, Curtis and Reiner would make day trips there, about once a month, to discuss the progress of the book, meeting first at the Art Institute (which was between their train stations) where the day's work was planned during a stroll through the galleries. When it was time to work on their manuscript... they usually found a congenial place in some out-of-the-way corner of the lobby of the Palmer House to spread out their papers.
Curtis and Reiner produced a completely rewritten book on representation theory in two volumes published in 1981 and 1987. Reiner wrote over 100 papers and books in a highly productive career.
Article by: J J O'Connor and E F Robertson
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