Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of dynamical systems, topology and geometry.

[3][4] Hopf attended Karl Mittelhaus higher boys' school from 1901 to 1904, and then entered the König-Wilhelm-Gymnasium in Breslau.

In 1913 he entered the Silesian Friedrich Wilhelm University where he attended lectures by Ernst Steinitz, Adolf Kneser, Max Dehn, Erhard Schmidt, and Rudolf Sturm.

In his dissertation, Connections between topology and metric of manifolds (German: Über Zusammenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten), he proved that any simply connected complete Riemannian 3-manifold of constant sectional curvature is globally isometric to Euclidean, spherical, or hyperbolic space.

He also studied the indices of zeros of vector fields on hypersurfaces, and connected their sum to curvature.

Hopf spent the year after his doctorate at the University of Göttingen, where David Hilbert, Richard Courant, Carl Runge, and Emmy Noether were working.

In the summer of 1928 Hopf returned to Berlin and began working with Pavel Alexandrov, at the suggestion of Courant, on a book on topology.

Two years later, however, he was forced to file for Swiss citizenship after his property was confiscated by Nazis, his father's conversion to Christianity having failed to convince German authorities that he was an "Aryan".