Eberhard Frederich Ferdinand Hopf (April 4, 1902 in

Salzburg Salzburg is the List of cities and towns in Austria, fourth-largest city in Austria. In 2020 its population was 156,852. The city lies on the Salzach, Salzach River, near the border with Germany and at the foot of the Austrian Alps, Alps moun ...

Austria-Hungary Austria-Hungary, also referred to as the Austro-Hungarian Empire, the Dual Monarchy or the Habsburg Monarchy, was a multi-national constitutional monarchy in Central Europe#Before World War I, Central Europe between 1867 and 1918. A military ...

– July 24, 1983 in

Bloomington, Indiana Bloomington is a city in Monroe County, Indiana, United States, and its county seat. The population was 79,168 at the 2020 United States census, 2020 census. It is the List of municipalities in Indiana, seventh-most populous city in Indiana and ...

, USA) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

, one of the founding fathers of

ergodic theory Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behav ...

and a pioneer of

bifurcation theory Bifurcation theory is the Mathematics, mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential e ...

who also made significant contributions to the subjects of

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s and

integral equation In mathematical analysis, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,\ldots,x_n ; u(x_1,x_2 ...

fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, and

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

. 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 equation In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are frequently used to model steady states, unlike parabolic PDE and hyperbolic PDE which gene ...

Biography

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 Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

'' in mathematical astronomy from the

University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

in 1929. In 1971, Hopf was the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Gibbs Lecturer.Josiah Willard Gibbs Lectures #42
AMS In 1981, he received the Leroy P. Steele Prize from the American Mathematical Society for seminal contributions to research.

Major publications

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

Notes

External links

* *
Online list of E. Hopf's works from Göttinger Digitalisierungszentrum
{{DEFAULTSORT:Hopf, Eberhard 1902 births 1983 deaths Scientists from Salzburg 20th-century German mathematicians German topologists People from Austria-Hungary Immigrants to Germany Immigrants to the United States