Israel Moissejewitsch Gelfand

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Israel Gelfand

Israel Moiseevich Gelfand ( Russian Израиль Моисеевич Гельфанд * August 20 jul. / 2 September  1913 greg. In Okny in Kherson Gubernia , Russian Empire , now Odessa , Ukraine ; † 5. October 2009 in New Brunswick , New Jersey ) was a Soviet mathematician .


Gelfand began studying mathematics at Moscow State University in 1932 under Andrei Kolmogorow in the field of functional analysis , which he completed in 1935 with a thesis on abstract functions and linear operators . During this time he worked with Abraham Plessner and Lasar Aronowitsch Ljusternik . He completed his habilitation in 1938 (also at Moscow State University) as Doctor Scientiae with a thesis on commutative standardized algebras . From 1941 to 1990 he held a professorship at Moscow State University. From 1968 to 1970 Gelfand was President of the Moscow Mathematical Society and subsequently became its honorary member. In 1990 he moved to the USA and has since worked at Rutgers University in New Jersey , where he was professor of mathematics and biology.

In addition to his research activities, Gelfand is also known for his very influential seminar on functional analysis at Moscow State University, which was founded in 1943 and is being continued at Rutgers University. In Gelfand's famous seminar, the Moscow School of Mathematicians he founded, which dealt in particular with representation theory and functional analysis, met regularly. He also directed a distance learning mathematics program, the Gelfand Correspondence Program in Mathematics (GCPM) , after leading similar programs in the Soviet Union.

Various mathematical terms are named after Gelfand, including the Gelfand transformation , the Gelfand-Neumark theorem , the Gelfand-Neumark-Segal construction , the Gelfand-Mazur theorem and the Gelfand space triple . Gelfand's work played a major role in the prehistory of the Atiyah-Singer index theorem and non-commutative geometry . Since the 1960s he has also dealt with applications of mathematics in biology . With Boris Levitan he developed the Gelfand-Levitan theory of the inverse scattering theory of Sturm-Liouville operators (1951).

His son Sergei Gelfand is also a mathematician.


Gelfand was a member of the Soviet and Russian Academy of Sciences (corresponding member since 1953, full member since 1984), the American Academy of Arts and Sciences in Boston since 1964, the London Mathematical Society since 1967, and the Royal Irish Academy in Dublin since 1970 , the National Academy of Sciences of the USA since 1970, the Royal Swedish Academy of Sciences in Stockholm since 1974, the Académie des Sciences de l'Institut der France since 1976, the Royal Society in London since 1977, the Accademia dei Lincei since 1988 and the Japanese Academy of Sciences since 1989, the New York Academy of Sciences since 2000 and the European Academy of Sciences since 2004.

In 1970 he gave a plenary lecture at the ICM in Nice ( The Cohomology of Infinite Dimensional Lie Algebras; Some Questions of Integral Geometry ), as well as in Stockholm in 1962 ( Automorphic functions and the theory of representations ) and in Amsterdam in 1954 ( Some Aspects of Functional Analysis and algebra ).

In 1978 he received the Wolf Prize for Mathematics, which was then first awarded (together with Carl Ludwig Siegel ), in 1980 the Wigner Medal in 1989, the Kyoto Prize , in 1994 a MacArthur Fellowship from the MacArthur Foundation , and in 2005 the Leroy P. Steele Prize from the American Mathematical Society for life's work.

In the Soviet Union , Gelfand received the Stalin Prize (1951 and 1953), the Order of Lenin three times (1954, 1956 and 1973), twice the Order of the Red Banner of Labor (1963 and 1983) and the Order of Friendship between Nations (1975).

Gelfand received honorary doctorates from the Universities of Oxford (1973), Paris VI and VII (1974), Harvard (1976), Uppsala (1977), Lyon (1984), Pisa (1985), New York (1988), Kyoto (1989), Pennsylvania (1990), New York (1992) and Rutgers (1993).


Gelfand has published over 800 papers and 30 books. The works were mainly published in Russian, but most of them have been translated into English, and some books also into German. Some important works are

  • Generalized functions (Volumes I to IV: University books for mathematics . Vol. 47–50):
    • Volume I, Generalized functions and calculating with them , Berlin, Deutscher Verlag der Wissenschaften 1960 with Schilow
    • Volume II, linear topological spaces, spaces of basic functions and generalized functions , with Schilow, Berlin, Deutscher Verlag der Wissenschaften 1962
    • Volume III, Some questions on the theory of differential equations , Berlin, Deutscher Verlag der Wissenschaften 1964, with Schilow
    • Volume IV, Some Applications of Harmonic Analysis: Gelfandsche Raumtripel , Berlin, Deutscher Verlag der Wissenschaften 1964 with Naum Wilenkin
    • Volume V Integralgeometrie and representation theory , Moscow, 1962 with MI Graev and Naum Wilenkin (russ.) (English translation: "Integral geometry and representation theory", Academic Press 1966)
    • Volume VI Representation Theory and automorphic functions with Ilja Pjatetskij-Shapiro , MI Graev, Academic Press 1990
  • with D. Raikov , G. Shilov Commutative standardized algebras , Berlin, Deutscher Verlag der Wissenschaften 1964 (English: Commutative Normed Rings , Chelsea Publ. 1964, AMS / Chelsea 2003)
  • Calculus of Variations , Prentice Hall 1963 (with Fomin )
  • Collected papers , Volumes I – III (1987, 1988, 1989), Springer-Verlag

In addition, Gelfand published a number of other mathematical textbooks and monographs such as:

  • with A. Shen Algebra , Birkhäuser 1993
  • with Michail Kapranow , Andrei Zelevinsky Discriminants, resultants, and multidimensional determinants , Birkhäuser 2008
  • Functions and their graphic representation , Teubner 1971, Harri Deutsch 1972
  • Lectures on Linear Algebra , Dover 1989
  • with EG Glagoleva, Alexander Kirillow Method of coordinates , Birkhäuser 1990
  • with Gindikin , M. Graev Selected topics in Integral Geometry , American Mathematical Society 2003
  • with RA Minlos , Z. Shapiro Representations of the rotation and Lorentz groups and their application , Pergamon Press 1963
  • with Mark Naimark Unitary representations of the classical groups , Berlin, Akademie Verlag 1957
  • with Mark Saul Trigonometry , Birkhäuser 2001

Important works by Gelfand include

  • On the embedding of a normed ring into a ring of operators in a Hilbert space (with Neumark ), Mat. Sbornik 12 (54, 1943), 197-217
  • Irreducible unitary representations of locally compact groups (with Raikow), Mat. Sbornik 13 (55, 1943), 301-316
  • Eigenfunction expansions of differential and other operators (with Kostjutschenko), Dokl. Akad Nauk SSSR 103: 349-352 (1955)
  • with DB Fairlie: The algebra of Weyl symmetrized polynomials and its quantum extension, Comm. Math. Phys. Vol. 136, 1992, pp. 487-499, Project Euclid


  • Izrail 'Moiseevich Gel'fand (on his fiftieth birthday), Russ. Math. Surveys 19 (3, 1964), 163-180
  • Decree conferring the Order of Lenin on Gelfand, Russ. Math. Surveys 29 (1, 1974), 1
  • Izrail 'Moiseevich Gel'fand (on his sixtieth birthday), Russ. Math. Surveys 29 (1, 1974), 3-61
  • Izrail 'Moiseevich Gel'fand (on his seventieth birthday), Russ. Math. Surveys 38 (6, 1983), 145-153
  • Semen G. Gindikin (Editor) Functional analysis on the eve of the twenty-first century. In honor of the 80th birthday of Israel Gelfand , Volumes I and II, Boston, Birkhäuser, 1995
  • Pavel Etingof, Vladimir Retakh, Isadore M. Singer (editors): The unity of mathematics - In Honor of the 90th Birthday of IM Gelfand , Birkhäuser, 2006 (with Gelfand's contribution Mathematics as an adequate language )
  • Vladimir Retakh (Editor) Israel Moiseevich Gelfand , Part I , Notices AMS, January 2013, Part II, Notices AMS, February 2013

Web links

Individual evidence

  1. As he said in the anthology by Etingof et al. a. According to The Unity of Mathematics , he never got a formal degree
  2. Gelfand Correspondence Program in Mathematics (GCPM) ( Memento of the original dated August 11, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot /
  3. ^ Wolf Prize for Gelfand