## In Memoriam: Gerhard Paul Hochschild

Gerhard Paul Hochschild, an algebraist of the highest caliber, died July 8, 2010 in El Cerrito, CA. His fields of interest included cohomology theory for algebra, algebraic groups, and Lie algebra. He was on the staff of the University of Illinois at Urbana-Champaign from 1948 to 1958. In 1958 he accepted an offer from the University of California at Berkeley, a position he held until his retirement. In 1979 he was elected to the National Academy of Sciences. In 1980 he was awarded the Leroy P. Steele Prize of the American Mathematical Society.

Gerhard Hochschild was born April 29, 1915 in Berlin, Germany. After the Nazi takeover in the early thirties he suffered considerable harassment from Hitler Youth. Fortunately, his extended family was widely distributed geographically. Thus, in due course he became a student at the University of Capetown in South Africa. From that university he received a B.S. in 1937 and an M.S. in Mathematics in 1938. He then entered the graduate college of Princeton University. In 1941 he produced an outstanding Ph.D. thesis under the supervision of Claude Chevalley. This was entitled “Semisimple Algebras and Generalized Derivations” and was subsequently published in the American Journal of Mathematics vol. 64 (1947) pp. 677-694.

In 1942 Hochschild was drafted into the U.S. Army. He spent three years in the Army, most of it at the Aberdeen Proving Grounds in Maryland. In the Army he found it desirable to use his middle name Paul, rather than the more teutonic name Gerhard. After his military service, Hochschild held a Benjamin Pierce Instructorship at Harvard University from 1946 to 1948. In 1948 Gerhard was appointed to an assistant professorship at Illinois by H. Roy Brahana, the acting department head during the academic year 1947-48.

At Illinois, Hochschild was an assistant professor from 1948 to 1950, an associate professor from 1950 to 1952, and a full professor from 1952 to 1958. During his ten years on the Illinois staff Hochschild had three leaves of absence. He was a visiting professor at Yale for the academic year 1951-52, a visiting professor at Berkeley for the academic year 1955-56, and a member of the Institute for Advanced Study at Princeton for the academic year 1956-57. The Institute membership was supported by a Guggenheim Fellowship and by a sabbatical leave at half pay from the University of Illinois.

During his service at the University of Illinois, Gerhard taught a graduate course every semester. As someone who audited one of these courses, I can report that his lectures were very thoroughly prepared and well presented. Personally I found Hochschild to be a very helpful consultant on matters related to algebra and algebraic number theory. While at Urbana Gerhard supervised the following three Ph.D. dissertations:

George Francis Leger (1951): On cohomology theory for Lie Algebras

Kung-Sing Shih (1953): Cohomology of associative algebras and spectral sequences.

Ronald Alvin Macauley (1955): Analytic group kernels and Lie algebra kernels.

(written by Professor Emeritus Paul Bateman on 11/19/10)