Deane Montgomery Quotes

Deane Montgomery was a mathematician specializing in topology who was one of the contributors to the final resolution of Hilbert's fifth problem in the 1950s. He served as President of the American Mathematical Society from 1961 to 1962.

Born in the small town of Weaver, Minnesota, he received his B.S. from Hamline University in St. Paul, MN and his Masters and Ph.D. from the University of Iowa in 1933; his dissertation advisor was Edward Chittenden.In 1941 Montgomery was awarded a Guggenheim Fellowship. In 1988, he was awarded the American Mathematical Society Leroy P. Steele Prize for Lifetime Achievement.

He was a member of the United States National Academy of Sciences and of the American Academy of Arts and Sciences. Wikipedia

✵ 2. September 1909 – 15. March 1992

Deane Montgomery: 2 quotes 0 likes

Deane Montgomery Quotes

“A group which has a simple structure may offer difficult questions when operating as a transformation group. For example, the ways in which a cyclic group of order 2 can operate on a manifold, even on E 3, are far from completely known.”

Deane Montgomery

[Properties of finite-dimensional groups, Proceedings of the International Mathematical Congress held in Cambridge, Mass. in 1950, 442–446, University of Toronto Press, 1952, http://www.mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0442.0446.ocr.pdf] (quote from p. 442)

Way , Question

“THEOREM: if G is a locally euclidean, connected, simply connected topological group of dimension n greater than one, then G contains a closed proper subgroup of positive dimension.”

Deane Montgomery

[A theorem on locally euclidean groups, Annals of Mathematics, 1947, 650–658, 10.2307/1969132]