Murray Gerstenhaber (June 5, 1927 – February 21, 2024) was an American mathematician, physicist, and lawyer. He was a professor of mathematics at the University of Pennsylvania, best known for his contributions to theoretical physics with his discovery of Gerstenhaber algebra. He was also a lecturer in law at the University of Pennsylvania Law School.

Early life and education Murray Gerstenhaber was born in Brooklyn, New York, to Jewish immigrants Pauline (née Rosenzweig; who was born in Romania; died in 1978) and Joseph Gerstenhaber (who was born in 1892 in Romania; died in 1975). His father was trained as a jeweler, "but being unable to find work in this line he [took] employment in a factory making airplane precision instruments”. As to his mother, in 2015 he noted: "For someone born into a minority family without means, I have been exceedingly lucky. The problems faced by talented but disadvantaged children today are preventing many who could be important contributors to the sciences, arts, and society in general, from achieving their potential. They don’t all have mothers like mine, who fought to find a path to education for her child. We have to seek them out but are not doing enough to find them, bring them out of isolation, and give them the opportunities I was so fortunate to have enjoyed."

Gerstenhaber was a child prodigy who was profiled in Leta Hollingworth's book Children Above 180 IQ (1942). In this book, Gerstenhaber was dubbed "Child L," and his prodigious abilities and personality traits were described in great detail. At age 9 years 5 months, a Stanford-Binet test showed him to have a mental age of between 17 and 18 and an IQ between 195 and 198. A second revised Stanford-Binet given a year later found him to have a mental age of 19 years 11 months and an IQ of 199+.

Gerstenhaber attended the now-defunct Speyer School, a school for rapid learners in New York City. Many years later, his daughter-in-law co-founded Speyer Legacy School, naming the new school after the original. After graduating from Speyer School, Gerstenhaber entered the Bronx High School of Science in 1940."The Cyclotron, by Murray Gerstenhaber, 16," Science Talent Research (1944) - Google Books. From 1945 to 1947 he served in the infantry in the United States Army as a corporal assigned to the Office of Military Government for Germany."Our Honored Temple Beth Hillel–Beth El Veterans," Veterans Day Program, November 11, 2017.

Gerstenhaber finished his B.S. in mathematics at Yale University (1948)."C.V." At Yale, he participated in the William Lowell Putnam Mathematical Competition and was on the team representing Yale University (along with Murray Gell-Mann and Henry O. Pollak) that won the second prize in 1947; each of them received a monetary prize of $30 ($ in current dollar terms).G. W. Mackey (August–September 1947). "the William Lowell Putnam Mathematical Competition," The American Mathematical Monthly, Vol. 54, No. 7, Part 1, pp. 400-403. His 1948 participation in the competition earned him a Top 10 ranking.

Gerstenhaber earned an M.A. and a Ph.D. (1951) in mathematics from the University of Chicago, under the instruction of Abraham Adrian Albert. Gerstenhaber's dissertation was entitled Rings of Derivations.

Gerstenhaber earned a J.D. from the University of Pennsylvania Law School in 1973, and was admitted to the Pennsylvania bar in 1974.

Career Gerstenhaber was an assistant professor in the Department of Mathematics at the University of Pennsylvania from 1953 to 1958, rising to associate professor (1958–61), and full professor (1961–2024) and chairman."National Science Board, NSF Staff, Advisory Committees and Panels; Advisory Panel for Mathematical Sciences," NSF 1971 Annual Report. His research interests include: algebraic deformation theory, universal algebra, quantum groups, and statistics for law. He is best known for his contributions to theoretical physics with his discovery of Gerstenhaber algebra.

Among his writings were Algebraic cohomology and deformation theory, with SD Schack, Deformation theory of algebras and structures and applications, 11–264 (1988), "On the deformation of rings and algebras," Annals of Mathematics, Second Series, Vol. 79, No. 1 (Jan., 1964), pp. 59–103, and "The cohomology structure of an associative ring," Annals of Mathematics, Second Series, Vol. 78, 267–288 (1963)."Murray Gerstenhaber," Google Scholar Citations."On the Deformation of Rings and Algebras," Annals of Mathematics, Second Series, Vol. 79, No. 1 (January 1964), pp. 59–103, DOI: 10.2307/1970484. For these last two papers he received in 2021 the Leroy P. Steele Prize for Seminal Contribution to Research.Leroy P. Steele Prize 2021 for Seminal Contribution to Research Gerstenhaber noted in 1990: “The ability to hang in there has a lot to do with scientific productivity, I am convinced. And in mathematics … hanging in there is a solitary accomplishment.”

Gerstenhaber was chairman of the faculty senate at the University of Pennsylvania from 1982 to 1983.

Gerstenhaber was also a lecturer in law at the University of Pennsylvania Law School, teaching a seminar on statistics for law.

In 2012 he became a fellow of the American Mathematical Society, and was a member of its council."List of Fellows of the American Mathematical Society", retrieved January 19, 2013. Gerstenhaber was the managing editor of the Bulletin of the American Mathematical Society. Gerstenhaber was also a Fellow of the American Association for the Advancement of Science.

In 2021 he received the Steele Prize for Seminal Contribution to Research.

Personal life Gerstenhaber married Ruth Priscilla Zager on June 3, 1956, in the Spanish and Portuguese Synagogue in New York City."Dr. Ruth P. Zager becomes Fiancee; Texas Physician Engaged to Dr. Murray Gerstenhaber, Professor at U. of P.", The New York Times, April 29, 1956."Dr. Ruth Zager Wed to U. of P. Teacher," The New York Times, June 4, 1956. They lived in Merion Station, Pennsylvania, and Haverford, Pennsylvania, and had three children: Jeremy M. Gerstenhaber, David Ezra Gerstenhaber (now founder, president, and portfolio manager at Argonaut Management), and Rachel Rebecca Stern (now general counsel and head of strategic resources of FactSet).Deformation Theory of Algebras and Structures and Applications - Google Books"Weddings; Rachel Gerstenhaber, Alexander Stern," The New York Times, June 26, 1994. His son David, a hedge fund manager and Tiger Management alumnus, is married to financier Steven Posner's daughter Kelly.Melanie Grayce West (June 11, 2012). "Guiding Gifted Students," The Wall Street Journal.

Gerstenhaber died on February 21, 2024, at the age of 96.

See also Nilpotent orbit Purely inseparable extension

References

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