**Israil Gelfand** was a Ukranian mathematician who made important contributions to many areas including group theory, representation theory and functional analysis.

- There were many different institutes in Moscow where mathematics was taught in evening classes and Gelfand taught elementary mathematics in various of these institutes, then a little later progressing to teach more advanced mathematics.
- In 1932 Gelfand was admitted as a research student under Kolmogorov's supervision.
- Gelfand presented his thesis Abstract functions and linear operators in 1935 which contains important results, but is perhaps even more important for the methods that he used, studying functions on normed spaces by applying linear functionals to them and using classical analysis to study the resulting functions.
- Gelfand's next major achievement was the theory of commutative normed rings which he created and studied in his D.Sc. thesis submitted in 1938.
- Gelfand's theory of normed rings revealed close connections between Banach's general functional analysis and classical analysis.
- During the time that he was carrying out this work for his D.Sc., Gelfand taught at the USSR Academy of Sciences.
- In joint work with Naimark in the early 1940s, Gelfand worked on noncommutative normed rings with an involution.
- It is impossible to do any justice to the range of work covered by Gelfand in this short article.
- Gelfand's work on group representations led him to study integral geometry (a term due to Blaschke) which in turn he was led to by a study of the Radon transform.
- Between 1968 and 1972 Gelfand produced a series of important papers on the cohomology of infinite dimensional Lie algebras.
- From 1958 onwards Gelfand became interested in problems in biology and medicine.
- Gelfand's interests were certainly not confined to research despite his incredible record of having published over 500 papers in mathematics, applied mathematics and biology.
- This is only one of a very large number of honours which have been given to Gelfand over many years of outstanding contributions.
- In 1989-90 Gelfand taught at Harvard University and in 1990 he also taught at Massachusetts Institute of Technology.
- In 1992 Gelfand set up a programme in the United States similar to the correspondence school in mathematics which he had run in Russia.
- In 1994 Gelfand was awarded a MacArthur Fellowship from the John T and Catherine D MacArthur Foundation.
- The award to Gelfand is $375,000, to be paid over five years.
- Let us mention two other honours given to Gelfand.

Born 2 September 1913, Krasnye Okny, Odessa, Ukraine. Died 5 October 2009, New Brunswick, N.J., USA.

View full biography at MacTutor

Origin Ukraine, Prize Wolf

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive