Gerhard Paul Hochschild (April 29, 1915 in

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

– July 8, 2010 in

El Cerrito, California El Cerrito (Spanish language, Spanish for "The Little Hill") is a city in Contra Costa County, California, United States, and forms part of the San Francisco Bay Area. It has a population of 25,962 according to the 2020 United States census, 2 ...

) was a German-born American mathematician who worked on

Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Eucli ...

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...

homological algebra Homological algebra is the branch of mathematics that studies homology (mathematics), homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precurs ...

and

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

Early life

On April 29, 1915, Hochschild was born to a middle-class

Jewish Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...

family in

, Germany, the son of Lilli and Heinrich Hochschild. Hochschild had an older brother. His father was a patent attorney who had an engineering degree. After the rise of the

National Socialist German Workers' Party The Nazi Party, officially the National Socialist German Workers' Party ( or NSDAP), was a far-right politics, far-right political party in Germany active between 1920 and 1945 that created and supported the ideology of Nazism. Its precursor ...

in 1933, his father sent him to South Africa where he was able to enroll in school with funding from the Hochschild Family Foundation established by

Berthold Hochschild Berthold Hochschild (March 6, 1860 – January 24, 1928) was a mining magnate, a founder of the American Metal Company, and a philanthropist. Biography Hochschild was born to a Jewish family in Biblis, Grand Duchy of Hesse, the son of Augus ...

, a cousin of his grandfather.

Education

In 1936, Hochschild earned a BS degree in mathematics from

University of Cape Town The University of Cape Town (UCT) (, ) is a public university, public research university in Cape Town, South Africa. Established in 1829 as the South African College, it was granted full university status in 1918, making it the oldest univer ...

in Union of South Africa. In 1937, Hochschild earned a MS degree in mathematics from

. In 1941, Hochschild earned his PhD in mathematics from

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

. Hochschild completed his thesis in 1941 at

with

Claude Chevalley Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a found ...

on ''Semisimple Algebras and Generalized Derivations''.

Career

In 1956–7 Hochschild was at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

. Hochschild was a professor at

University of Illinois at Urbana-Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...

. In the late 1950s Hochschild was a professor at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

. introduced Hochschild cohomology, a cohomology theory for algebras, which classifies deformations of algebras. introduced cohomology into

class field theory In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credit ...

. Along with

Bertram Kostant Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory, differential geometry, and mathematical physics. Early life and education Kostant grew up in New York City, where he gradua ...

and

Alex F. T. W. Rosenberg Alex F. T. W. Rosenberg (1926–2007) was a German-American mathematician who served as the editor of the ''Proceedings of the American Mathematical Society'' from 1960 to 1965, and of the ''American Mathematical Monthly'' from 1974 to 1976.. H ...

, the Hochschild–Kostant–Rosenberg theorem is named after him. Among his students were Andrzej Białynicki-Birula and

James Ax James Burton Ax (10 January 1937 – 11 June 2006) was an American mathematician who made groundbreaking contributions in algebra and number theory using model theory. He shared, with Simon B. Kochen, the seventh Frank Nelson Cole Prize in ...

. In 1955, Hochschild was a

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon and Olga Hirsh Guggenheim. These awards are bestowed upon individuals who have demonstrated d ...

. In 1979 Hochschild was elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

, and in 1980 he was awarded the

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

of the

AMS AMS or Ams may refer to: Organizations Companies * Alenia Marconi Systems * American Management Systems * AMS (Advanced Music Systems) * ams AG, semiconductor manufacturer * AMS Pictures * Auxiliary Medical Services Educational institutions ...

. In 1982, Hochschild retired but continued teaching part-time until 1985.

Personal life

In July 1950, Hochschild married Ruth Heinsheimer. Ruth was born in Germany and fled with her mother in 1939; the couple met at the University of Illinois where she was earning her M.S. in mathematics and Gerhard was working as an assistant professor. Hochschild's children are Ann Hochschild (b. 1955) and Peter Hochschild (b. 1957).Moscowitz, p. 1087 On July 8, 2010, Hochschild died at his home. Hochschild was 95.

Publications

* * * * * *

References

* * *

External links

*
Pictures of Gerhard Hochschild
from Oberwolfach
Finding Aid to the Gerhard P. Hochschild papers, 1941-2004

The Bancroft Library The Bancroft Library is the primary special-collections library of the University of California, Berkeley. It was acquired from its founder, Hubert Howe Bancroft, in 1905, with the proviso that it retain the name Bancroft Library in perpetuity. ...

Hochschild Family Foundation at foundation center.org
{{DEFAULTSORT:Hochschild, Gerhard 20th-century American mathematicians 21st-century American mathematicians Algebraists 1915 births 2010 deaths Princeton University alumni University of Cape Town alumni University of Illinois Urbana-Champaign faculty University of California, Berkeley College of Letters and Science faculty Members of the United States National Academy of Sciences Mathematicians from Berlin Emigrants from Nazi Germany to the United States Immigrants to South Africa Immigrants to the United States

Gerhard Gerhard is a name of Germanic origin and may refer to: Given name * Gerhard (bishop of Passau) (fl. 932–946), German prelate * Gerhard III, Count of Holstein-Rendsburg (1292–1340), German prince, regent of Denmark * Gerhard Barkhorn (1919� ...