Gerhard Paul Hochschild (April 29, 1915 in

Berlin Berlin ( , ) is the capital and List of cities in Germany by population, largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's List of cities in the European Union by population within ci ...

– July 8, 2010 in

El Cerrito, California El Cerrito ( 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 census. El Cerrito was founded by refugee ...

) was a German-born American mathematician who worked on Lie groups,

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

s, homological algebra and algebraic number theory.

Early life

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

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

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 (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right political party in Germany active between 1920 and 1945 that created and supported th ...

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 American Metal Company was an American nonferrous metal trading and production company. History The origin of the America ...

, 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) ( af, Universiteit van Kaapstad, xh, Yunibesithi ya yaseKapa) is a public research university in Cape Town, South Africa. Established in 1829 as the South African College, it was granted full university statu ...

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 research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

. 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 foun ...

on ''Semisimple Algebras and Generalized Derivations''.

Career

In 1956–7 Hochschild was at the

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

. Hochschild was a professor at

University of Illinois at Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univ ...

. 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 land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. introduced

Hochschild cohomology In mathematics, Hochschild homology (and cohomology) is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain functors. Hochschild cohomology was introduced by for algebras over a field, ...

, 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, the Hochschild–Kostant–Rosenberg theorem is named after him. Among his students were Andrzej Białynicki-Birula and James Ax. In 1955, Hochschild was a

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the a ...

. In 1979 Hochschild was elected to the National Academy of Sciences, 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. 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

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References

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External links

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

The Bancroft Library The Bancroft Library in the center of the campus of the University of California, Berkeley, is the university's primary special-collections library. It was acquired from its founder, Hubert Howe Bancroft, in 1905, with the proviso that it retai ...

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 People from Berlin German emigrants 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 (1919–19 ...