Eberhard Hopf
Eberhard Hopf.jpg
Born(1902-04-04)4 April 1902
Died24 July 1983(1983-07-24) (aged 81)
Bloomington, Indiana, United States
Alma materUniversity of Berlin
Known forErgodic theory
Partial differential equation
Differential geometry
Scientific career
InstitutionsMIT (1931-36)
University of Leipzig (1936-42)
University of Munich (1944-47)
Indiana Univ. Bloomington (1949-83)
Doctoral advisorErhard Schmidt
Issai Schur
Doctoral studentsAlbert Schaeffer

Eberhard Frederich Ferdinand Hopf (April 4, 1902 in Salzburg, Austria-Hungary – July 24, 1983 in Bloomington, Indiana, USA) was a mathematician and astronomer, one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who also made significant contributions to the subjects of partial differential equations and integral equations, fluid dynamics, and differential geometry. The Hopf maximum principle is an early result of his (1927) that is one of the most important techniques in the theory of elliptic partial differential equations.


Hopf was born in Salzburg, Austria-Hungary, but his scientific career was divided between Germany and the United States. He received his Ph.D. in mathematics in 1926 and his Habilitation in mathematical astronomy from the University of Berlin in 1929.

In 1971, Hopf was the American Mathematical Society Gibbs Lecturer.[1] In 1981, he received the Leroy P. Steele Prize from the American Mathematical Society for seminal contributions to research.

See also

Major publications

A non-comprehensive selection of his work was published in 2002: