Born Nov. 19, 1894, in Breslau, Germany. Swiss mathematician.
Hopf became a professor at the Federal Institute of Technology in Zürich in 1931. His principal works deal with topology and topological questions of differential geometry. He proved an important theorem on the algebraic number of fixed points in the mapping of a polyhedron into itself, set forth a homotopic classification of the transformations of a polyhedron of arbitrary dimensionality into a sphere of the same dimensionality, and showed that there are infinitely many mutually nonhomotopic mappings of a three-dimensional sphere into a two-dimensional sphere. In addition, Hopf established new connections between differential geometry and topology.