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Ph.D. University of Iowa, Iowa City, 1933
Montgomery's principal appointments were at Smith College, Northampton, Massachusetts (1935-1946) and at the Institute for Advanced Study, Princeton, New Jersey (1947 until his retirement in 1980). He served as president of the International Mathematical Union from 1974-1978. His research interests encompassed algebraic and geometric topology and transformation groups, and he was at the center of activity in topology at the Institute.
Montgomery was known for his efforts in helping young topologists, and for his interest in the careers of those from graduate programs at smaller institutions. He was awarded the AMS Leroy P. Steele Prize for Lifetime Achievement in 1988 for his lasting impact on mathematics, particularly mathematics in America. Montgomery was a member of the American Academy of Arts and Sciences and the U.S. National Academy of Sciences.