Israel Gelfand

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Image:IMGelfand.jpg Israïl (Israel) Moiseevich Gelfand (Template:Lang-ru) (born on September 2, 1913) is a prolific mathematician in the field of functional analysis, which he interprets in a broad sense as the mathematics of quantum mechanics.

He was born into a Jewish family in Okny, Kherson region in Ukraine then part of the Russian Empire. He studied at the Moscow State University where his advisor was Andrei Kolmogorov.

He has collaborated on papers with many mathematicians in Moscow, where he ran a seminar. In 1990 he emigrated to the USA and took up a Distinguished Visiting Professorship at Rutgers University in New Jersey. He also for a long time took an interest in cell biology.

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.

He also worked extensively in mathematics education, particularly with correspondence education. He was awarded a MacArthur fellowship for this work.

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