Israel Gelfand

Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (, ;  – 5 October 2009) was a prominent Soviet mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis.  The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow.

His legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel, Joseph Bernstein, David Kazhdan, as well as his own son, Sergei Gelfand.

Early years
A native of Kherson Governorate of the Russian Empire, Gelfand was born into a Jewish family in the small southern  Ukrainian town of Okny.  According to his own account, Gelfand was expelled from high school because his father had been a mill owner. Bypassing both high school and college, he proceeded to postgraduate study at the age of 19 at Moscow State University, where his advisor was the preeminent mathematician Andrei Kolmogorov.

Work

Gelfand is known for many developments including:
 the book Calculus of Variations (1963), which he co-authored with Sergei Fomin
 the Gelfand representation in Banach algebra theory;
 the Gelfand–Mazur theorem in Banach algebra theory;
 the Gelfand–Naimark theorem;
 the Gelfand–Naimark–Segal construction;
 Gelfand–Shilov spaces
 the Gelfand–Pettis integral;
 the representation theory of the complex classical Lie groups;
 contributions to the theory of Verma modules in the representation theory of semisimple Lie algebras (with I. N. Bernstein and S. I. Gelfand);
 contributions to distribution theory and measures on infinite-dimensional spaces;
 the first observation of the connection of automorphic forms with representations (with Sergei Fomin);
 conjectures about the Atiyah–Singer index theorem;
 Ordinary differential equations (Gelfand–Levitan theory);
 work on calculus of variations and soliton theory (Gelfand–Dikii equations);
 contributions to the philosophy of cusp forms;
 Gelfand–Fuks cohomology of foliations;
 Gelfand–Kirillov dimension;
 integral geometry;
 combinatorial definition of the Pontryagin class;
 Coxeter functors;
 general hypergeometric functions;
 Gelfand–Tsetlin patterns;
 Gelfand-Lokutsievski method
 and many other results, particularly in the representation theory for the classical groups.

I.M. Gelfand's seminar at Moscow State University
was running from 1945(?) until May 1989 (then it continued at Rutgers University), covered a wide range of topics,
and was an important school for many mathematicians.

Influence outside mathematics
The Gelfand–Tsetlin (also spelled Zetlin) basis is a widely used tool in theoretical physics and the result of Gelfand's work on the representation theory of the unitary group and Lie groups in general.

Gelfand also published works on biology and medicine. For a long time he took an interest in cell biology and organized a research seminar on the subject.

He worked extensively in mathematics education, particularly with correspondence education. In 1994, he was awarded a MacArthur Fellowship for this work.

Family
Gelfand was married to , and their two sons, Sergei and Vladimir both live in the United States.  The third son, Aleksandr, died of leukemia.  Following the divorce from his first wife, Gelfand married his second wife, Tatiana; together they had a daughter, Tatiana. The family also includes four grandchildren and three great-grandchildren.
Memories about I. Gelfand are collected at a dedicated website handled by his family.

Honors and awards
Gelfand held several honorary degrees and was awarded the Order of Lenin three times for his research.  In 1977 he was elected a Foreign Member of the Royal Society. He won the Wolf Prize in 1978, Kyoto Prize in 1989 and MacArthur Foundation Fellowship in 1994. He held the presidency of the Moscow Mathematical Society between 1968 and 1970, and was elected a foreign member of the U.S. National Academy of Science, the American Academy of Arts and Sciences, the Royal Irish Academy, the American Mathematical Society and the London Mathematical Society.

In an October 2003 article in The New York Times, written on the occasion of his 90th birthday, Gelfand is described as a scholar who is considered "among the greatest mathematicians of the 20th century", having exerted a tremendous influence on the field both through his own works and those of his students.

Death
Israel Gelfand died at the Robert Wood Johnson University Hospital near his home in Highland Park, New Jersey.  He was less than five weeks past his 96th birthday.  His death was first reported on the blog of his former collaborator Andrei Zelevinsky and confirmed a few hours later by an obituary in the Russian online newspaper Polit.ru.

Publications

Generalized Functions Volumes, 1-6, American Math Society, (2015)

See also

Gelfand duality
Gelfand pair
Gelfand ring
Gelfand triple

References

Citations

Sources 

Chang, Kenneth. "Israel Gelfand, Math Giant, Dies at 96", The New York Times (October 7, 2009)
"Leading mathematician Israel Gelfand dies in N.J." USA Today (October 9, 2009)
"Israel Gelfand | Top mathematician, 96". The Philadelphia Inquirer (October 10, 2009)
"Israel Gelfand" The Daily Telegraph (October 27, 2009)

External links
Israel Moiseevich Gelfand, dedicated site, maintained by Tatiana V. Gelfand and Tatiana I. Gelfand
Israel Gelfand - Daily Telegraph obituary
Israel Gelfand - Guardian obituary

Web page at Rutgers
List of publications.
Steele Prize citation.
The unity of mathematics – In honor of the ninetieth burthday of I. M. Gelfand
Interview: "A talk with professor I. M. Gelfand.", recorded by V. Retakh and A. Sosinsky, Kvant (1989), no. 1, 3–12 (in Russian). English translation in: Quantum (1991), no. 1, 20–26. (Link)

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