Deane Montgomery Quotes

American mathematician (1909–1992)

Deane Montgomery (2 September 1909 – 15 March 1992) was an American 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.

From: Wikiquote (CC BY-SA 4.0)

Showing quotes in randomized order to avoid selection bias. Click Popular for most popular 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 <sup>3</sup>, are far from completely known.

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.