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Junior Prize Fellow, Harvard University, Cambridge, Massachusetts, 1950
Gleason's principal academic appointment has been at Harvard University, starting in 1950. His areas of research are Banach spaces and classical geometry. He is known for his contribution to the solution of Hilbert's 5th problem, and in 1959 chaired the advisory committee of the School Mathematics Study Group (which formulated the "New Math"). Gleason is a member of the American Academy of Arts and Sciences and of the U.S. National Academy of Sciences.