**Irving Reiner** was an American mathematician who (with Curtis) produced an important book on group representations.

- Max Reiner was born in Austria and emigrated to the United States in 1907 when he was twenty-two years old.
- Irving attended both elementary school and high school in Brooklyn then, in 1940, he entered Brooklyn College.
- Alex Heller, who was a year younger than Reiner, was, like him, born and brought up in New York.
- Reiner graduated from Brooklyn College with a B.A. in 1944.
- Burton Wadsworth Jones (1902-1983), who had written is own Ph.D. thesis on Representation by positive ternary quadratic forms, was assigned as Reiner's advisor.
- Reiner was awarded a Master's Degree for his thesis on binary quadratic forms in 1945.
- Reiner was awarded his doctorate in June 1947 for his thesis A generalisation of Meyer's theorem, his doctoral advisor being Burton W Jones.
- While at Cornell University, Reiner met Irma Moses who was also a graduate student of mathematics being supervised by Burton W Jones.
- After completing work on his doctoral thesis, Reiner went to the Institute for Advanced Study at Princeton where he spent a year.
- Reiner remained at the University of Illinois for the rest of his career but Loo-Keng Hua was only there for two years before returning to his native China.
- Although Reiner 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, England.
- It was written jointly with Charles W Curtis (1926-) 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.
- Curtis and Reiner produced a completely rewritten book on representation theory in two volumes published in 1981 and 1987, entitled Methods of representation theory.
- Reiner wrote over 100 papers and books in a highly productive career.
- The influence of Reiner's work is most strongly felt by research mathematicians interested in problems related to integral representation theory.
- We have already looked at Reiner's most influential book but he wrote other books: Introduction to matrix theory and linear algebra (1971); Maximal orders (1975); and (with Klaus Roggenkamp) Integral representations (1979).
- Reiner's joint publication with Klaus Roggenkamp is really a two-part book, the first part being a published form of Reiner's lectures Topics in integral representation theory.
- Irving was not an aggressive player; he played in a relaxed, gentle way, sometimes carrying on a conversation with his opponent during the game.
- Lee Albert Rubel (1928-1995) tells of losing such a game to Irving and then attempting to excuse his loss with a remark to the effect that he had not been feeling well earlier that day and was not up to his usual game.

Born 8 February 1924, Brooklyn, New York, USA. Died 28 October 1986, Urbana, Illinois, USA.

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Group Theory, Origin Usa

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