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Israïl Moiseevich Gelfand (Russian: Израиль Моисеевич Гельфанд, Yiddish: ישראל געלפֿאַנד) (born on September 2, 1913) is a mathematician.

He was born into a Jewish family in Okny, Kherson gubernia of the Russian Empire (now Krasnye Okny in Ukraine).

He did postgraduate work at the Moscow State University where his advisor was Andrei Kolmogorov.

He is considered by many to be the leading figure of the Soviet school of mathematics, and has exerted a tremendous influence on the field both through his own works and those of his students. He ran a famous seminar at Moscow State University. In 1990 he emigrated to the U.S. and took up a Distinguished Visiting Professorship at the math department at Rutgers University in New Jersey, where he is now an associate member of the faculty.

The mathematician Sergei Gelfand is his son. The mathematician Endre Szemerédi is one of his students.

He is known for many developments including:

• the Gelfand representation in Banach algebra theory;
• the Gelfand–Naimark theorem;
• the Gelfand-Naimark-Segal construction
• the representation theory of the complex classical Lie groups;
• 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 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;
• generalised hypergeometric series;

and many other results, particularly in the representation theory for the classical groups.

The Gelfand-Tsetlin basis (also in the common spelling Zetlin) 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.

For a long time he took an interest in cell biology.

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

Gelfand 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. He held the presidency of the Moscow Mathematical Society between 1968 and 1970, and has been 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. He holds several honorary degrees.

• Israel Gelfand at the Mathematics Genealogy Project
• O'Connor, John J; Edmund F. Robertson "Israel Gelfand". MacTutor History of Mathematics archive.  
• Faculty appointments at Rutgers Math, Including Gelfand.
• List of publications.
• Steele Prize citation.