Heinz Hopf

Mathematician, born in Wroc?aw, SW Poland (formerly Breslau, Prussia). After war service he studied at Berlin and Göttingen universities, where he met the Russian topologist Pavel Alexandrov with whom he wrote the influential Topologie (1935). In 1931 he became professor at Zürich. One of Europe's leading topologists, he worked on many aspects of combinatorial topology, including homotopy theory and vector fields.

Heinz Hopf (November 19, 1894 – June 3, 1971) was a mathematician born in Gräbschen, Germany (now Grabiszyn, part of Wrocław, Poland). When World War I broke out in 1914, Hopf eagerly enlisted.

In 1920, Hopf moved to Berlin to continue his mathematical education. He also studied the indices of zeros of vector fields on hypersurfaces, and connected their sum to curvature. Some six months later he gave a new proof that the sum of the indices of the zeros of a vector field on a manifold is independent of the choice of vector field and equal to the Euler characteristic of the manifold.

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

In 1926 Hopf moved back to Berlin, where he gave a course in combinatorial topology. He spent the academic year 1927/28 at Princeton University on a Rockefeller fellowship with Alexandrov. In the summer of 1928 Hopf returned to Berlin and began working with Alexandrov, at the suggestion of Courant, on a book on topology.

In October 1928 Hopf married Anja von Mickwitz (1891 - 1967). The next year he declined a job offer from Princeton. In 1931 Hopf took Hermann Weyl's position at Zürich.

Hopf received another invitation to Princeton in 1940, but he declined it. Two years later, however, he was forced to file for Swiss citizenship after his property was confiscated by Nazi authorities.

In 1946/47 and 1955/56 Hopf visited the United States, staying at Princeton and giving lectures at New York University and Stanford University. He received honorary doctorates from Princeton, Freiburg i.