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Israel Moiseevich Gelfand. I. (English) Zbl 1290.01027

Israel Gelfand is one of the most distinguished mathematicians of the twentieth century. He was born in Odessa (Ukraine) in 1913, did his research in Moscow (1930–1990) and later at Rutgers University (New Jersey, USA). Several mathematical theorems and formulas carry his name. During his life he wrote about 530 papers and 65 books (quoted in zbMATH). He received numerous awards and honours.
The present volume 60 of the Notices of the AMS contains 12 papers by different mathematicians about Gelfand’s life and work. The articles are divided into two parts (for Part II see [ibid. 60, No. 2, 162–171 (2013; Zbl 1290.01026)]).
(1) The coordinating editor, Vladimir Retakh, gives the curriculum vitae of Gelfand. I would like to mention only three facts which seem most notable to me: Gelfand did not pursue his career as it was common. Until his return to Moscow in 1930 he basically learned alone with the aid of books. He had no assistance of teachers, colleagues or examinations. As soon as he arrived in Moscow, he became acquainted with modern mathematics and the mathematical community. In 1935, Gelfand defended his “candidate” (Ph.D.) thesis, and in 1940 he obtained the higher degree of Doctor of Science. In the fifties he lost his job at Moscow University temporarily because of two reasons. First of all there was an anti-Semitic campaign in the Soviet Union at that time, secondly he was a son of a “bourgeois element”. But after Stalin’s death he was allowed to continue his famous seminar, and to work at the Steklov Institute and the Institute of Applied Mathematics. One of the projects of the institutes was secret work for a Soviet atomic bomb. Andrej Sakharov mentioned this in a talk in 1991.
(2) Isadore M. Singer ranks Gelfand as one of the most influential mathematicians of the twentieth century. He lists all the main mathematical fields in which Gelfand plays a prominent role. A little story indicates Gelfand’s reputation: About 1970, Gelfand should receive an honorary degree at Oxford. It was unclear whether he would be allowed to leave the Soviet Union. At the end of the conference, Sir Michael Atiyah received a telegram: Gelfand is coming. The Queen had asked the Russian ambassador to intercede.
(3) David Kazhdan reports in detail Gelfand’s work on the theory of representations. It was the centre of his interest, because this field combines analysis, algebra and topology. Several results were obtained in joint work with colleagues such as Dimitrij Rajkov, Mark Graev, Mikhail Tsetlin, Aleksandr Kirillov, Arnold Shapiro, Simon Ginikin, and others. This shows not only Gelfand’s ability in generating new mathematical ideas, but also his openness concerning ideas of others.
(4) As well as the authors of the previous chapters, Anatoly Vershik considers Gelfand as an extraordinary phenomenon of twentieth-century mathematics. “His name must be included on any short list of those who formed the mathematics of that century.” And also, “his most important quality of this wonderful mathematician was his ability to inspire others”. Vershik divides his article into seven paragraphs: (a) Gelfand and Leningrad mathematics. (b) My first acquaintance with Gelfand’s work. (c) A few comments on Gelfand’s work of the 1950s and 1960s. (d) My first meeting with Gelfand. (e) Our collaboration. (f) The seminar. (g) Life in the USSR. These paragraphs include Gelfand’s comprehensive work in functional analysis, his position in the mathematical community in the USSR, and again his teamwork with colleagues.
(5) Bertram Kostant first became acquainted with Gelfand during a summer school in Budapest in 1970. The next meeting took place in 1972. Kostant realises that Gelfand “seemed to have created an environment where he was involved with both the personal as well as the professional lives of the many people around him.” Afterwards, Gelfand and Kostant met at different occasions even though some of their mathematical interests did not correspond.
(6) Simon Gindikin gives an article about another important part of Gelfand’s work. His subject is “50 years of Gelfand’s integral geometry”. The titles of the paragraphs are:
(a) First presentation. (b) Prehistory. (c) Complexes of planes. (d) Integral geometry of lines and curves. (f) Complexes of planes. (g) Nonlocal problems and integral geometry for discrete series. These paragraphs include Gelfand’s comprehensive work in functional analysis, his position in the mathematical community in the USSR, and again his teamwork with colleagues.
(7) Peter Lax refers to some of Gelfand’s great theorems, which Gelfand solved when he was young. Lax states “that these spectacular early results are viewed today as merely a small part of his total work”. Lax ends his contribution with “The world shall not see the like of Israel M. Gelfand for a long, long time.”
(8) Andrei Zelevinsky was student at the “School by Correspondence” since 1970. He tells us of the first impression he had at that school: “The organizational matters took only some minutes, but the first meeting with Gelfand lasted for several hours \(\dots\) Gelfand declared that we had done everything wrong, and were almost lost for mathematics, but there was still some little hope for us, if we started to attend his seminar at once.” Zelevinsky further writes: “I never met a person with such personal magnetism and such an ability to ignite enthusiasm about mathematics.” Zelevinsky attended the seminar and worked with Gelfand for about a decade. He concludes his chapter with the sentence “I feel very fortunate for having known Israel Moiseevich, and for being given a chance to be close to this gigantic, complex, wise, inspiring and infinitely fascinating personality.”

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
01A60 History of mathematics in the 20th century
46-03 History of functional analysis
47-03 History of operator theory

Biographic References:

Gel’fand, Izrail’ Moiseevich

Citations:

Zbl 1290.01026
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