Katana VentraIP

Israel Gelfand

Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (Yiddish: ישראל געלפֿאַנד, Russian: Изра́иль Моисе́евич Гельфа́нд, Ukrainian: Ізраїль Мойсейович Гельфанд; 2 September [O.S. 20 August] 1913 – 5 October 2009) was a prominent Soviet-American mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow.

Not to be confused with Alexander Gelfond.

Israel Gelfand

(1913-09-02)September 2, 1913

Okny, Kherson Governorate, Russian Empire

October 5, 2009(2009-10-05) (aged 96)

New Brunswick, New Jersey, United States

Soviet Union American

Moscow State University

Group theory
Integral geometry
Mathematical analysis
Representation theory
Gelfand–Levitan–Marchenko integral equation
Gelfand–Pettis integral
Gelfand representation
Gelfand–Naimark theorem
Liouville–Bratu–Gelfand equation

Order of Lenin (three times)
ForMemRS (1977)
Wolf Prize (1978)
Wigner Medal (1980)
Kyoto Prize in Mathematical Sciences (1989)
AMS Steele Prize (2005)

Mathematician

Moscow State University
Rutgers University

Andrey Kolmogorov

Georgy Adelson-Velsky
Felix Berezin
Joseph Bernstein
Victor Ginzburg
Alexander Goncharov
Tanya Khovanova
Alexandre Kirillov
Georgiy Shilov
Endre Szemerédi
Andrei Zelevinsky
Vitalii Ditkin

His legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel,[1] Joseph Bernstein, David Kazhdan, as well as his own son, Sergei Gelfand.

Early years[edit]

A native of Kherson Governorate, Russian Empire (now, Odesa Oblast, Ukraine), Gelfand was born into a Jewish family in the small southern Ukrainian town of Okny. According to his own account, Gelfand was expelled from high school under the Soviets because his father had been a mill owner. Bypassing both high school and college, he proceeded to postgraduate study at the age of 19 at Moscow State University, where his advisor was the preeminent mathematician Andrei Kolmogorov.[2] He received his PhD in 1935.[3]


Gelfand immigrated to the United States in 1989.[4]

the book Calculus of Variations (1963), which he co-authored with ;

Sergei Fomin

which expresses the spectral radius as a limit of matrix norms.

Gelfand's formula

the in Banach algebra theory;

Gelfand representation

the in Banach algebra theory;

Gelfand–Mazur theorem

the ;

Gelfand–Naimark theorem

the ;

Gelfand–Naimark–Segal construction

;

Gelfand–Shilov spaces

the ;

Gelfand–Pettis integral

the of the complex classical Lie groups;

representation theory

contributions to the theory of in the representation theory of semisimple Lie algebras (with I. N. Bernstein and S. I. Gelfand);

Verma modules

contributions to theory and measures on infinite-dimensional spaces;[5]

distribution

the first observation of the connection of with representations (with Sergei Fomin);

automorphic forms

conjectures about the ;

Atiyah–Singer index theorem

(Gelfand–Levitan theory);

ordinary differential equations

work on and soliton theory (Gelfand–Dikii equations);

calculus of variations

contributions to the ;

philosophy of cusp forms

Gelfand– cohomology of Lie algebras;

Fuchs

;

Gelfand–Kirillov dimension

;

integral geometry

combinatorial definition of the ;

Pontryagin class

;

Coxeter functors

;

general hypergeometric functions

Gelfand– patterns;

Tsetlin

Gelfand–Lokutsievski method;

and many other results, particularly in the representation theory of .

classical groups

Gelfand is known for many developments including:


Gelfand ran a seminar at Moscow State University from 1943[1] until May 1989 (when it continued at Rutgers University), which covered a wide range of topics and was an important school for many mathematicians.[6][7][8]

Influence outside mathematics[edit]

The Gelfand–Tsetlin (also spelled Zetlin) basis 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.


Gelfand also published works on biology and medicine.[9] For a long time he took an interest in cell biology and organized a research seminar on the subject.[10][11]


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

Personal life[edit]

Gelfand was married to Zorya Shapiro, and their two sons, Sergei and Vladimir both live in the United States. The third son, Aleksandr, died of leukemia. Following the divorce from his first wife, Gelfand married his second wife, Tatiana; together they had a daughter, Tatiana. The family also includes four grandchildren and three great-grandchildren.[12][13] Memories about I. Gelfand are collected at a dedicated website handled by his family.[14]


Gelfand was an advocate of animal rights.[15] He became a vegetarian in 1994 and vegan in 2000.[15][16]

Honors and awards[edit]

Gelfand held several honorary degrees and 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, Kyoto Prize in 1989 and MacArthur Foundation Fellowship in 1994. He held the presidency of the Moscow Mathematical Society between 1968 and 1970, and was 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.


In an October 2003 article in The New York Times, written on the occasion of his 90th birthday, Gelfand is described as a scholar who is considered "among the greatest mathematicians of the 20th century",[17] having exerted a tremendous influence on the field both through his own works and those of his students.

Death[edit]

Gelfand died at the Robert Wood Johnson University Hospital near his home in Highland Park, New Jersey. He was less than five weeks past his 96th birthday. His death was first reported on the blog of his former collaborator Andrei Zelevinsky[18] and confirmed a few hours later by an obituary in the Russian online newspaper Polit.ru.[19]

Gelfand, I. M. (1998), , Courier Dover Publications, ISBN 978-0-486-66082-0

Lectures on linear algebra

Gelfand, I. M.; Fomin, Sergei V. (1963), Silverman, Richard A. (ed.), , Englewood Cliffs, N.J.: Prentice-Hall Inc., ISBN 978-0-486-41448-5, MR 0160139

Calculus of variations

Gelfand, I.; Raikov, D.; Shilov, G. (1964) [1960], , Translated from the Russian, with a supplementary chapter, New York: Chelsea Publishing Co., ISBN 978-0-8218-2022-3, MR 0205105

Commutative normed rings

Gel'fand, I. M.; Shilov, G. E. (1964) [1958], , Translated by Eugene Saletan, Boston, MA: Academic Press, ISBN 978-0-12-279501-5, MR 0166596[20]

Generalized functions. Vol. I: Properties and operations

Gelfand, I. M.; Shilov, G. E. (1968) [1958], , Translated from the Russian by Morris D. Friedman, Amiel Feinstein and Christian P. Peltzer, Boston, MA: Academic Press, ISBN 978-0-12-279502-2, MR 0230128[20]

Generalized functions. Vol. 2. Spaces of fundamental and generalized functions

Gelfand, I. M.; Shilov, G. E. (1967) [1958], Generalized functions. Vol. 3: Theory of differential equations, Translated from the Russian by Meinhard E. Mayer, Boston, MA: , MR 0217416[20]

Academic Press

Gelfand, I. M.; Vilenkin, N. Ya. (1964) [1961], , Translated by Amiel Feinstein, Boston, MA: Academic Press, ISBN 978-0-12-279504-6, MR 0173945[20]

Generalized functions. Vol. 4: Applications of harmonic analysis

Gelfand, I. M.; Graev, M. I.; Vilenkin, N. Ya. (1966) [1962], Generalized functions. Vol. 5: Integral geometry and representation theory, Translated from the Russian by Eugene Saletan, Boston, MA: , ISBN 978-0-12-279505-3, MR 0207913[20]

Academic Press

Gelfand, I. M.; Graev, M. I.; Pyatetskii-Shapiro, I. I. (1969), , Translated from the Russian by K. A. Hirsch, Philadelphia, Pa.: W. B. Saunders Co., ISBN 978-0-12-279506-0, MR 0233772

Representation theory and automorphic functions

Gelfand, Izrail M. (1987), Gindikin, S. G.; Guillemin, V. W.; Kirillov, A. A.; Kostant, Bertram; (eds.), Collected papers. Vol. I, Berlin, New York: Springer-Verlag, ISBN 978-3-540-13619-4, MR 0929821

Sternberg, Shlomo

Gelfand, Izrail M. (1988), Gindikin, S. G.; Guillemin, V. W.; Kirillov, A. A.; Kostant, Bertram; (eds.), Collected papers. Vol. II, Berlin, New York: Springer-Verlag, ISBN 978-3-540-19035-6, MR 0929821

Sternberg, Shlomo

Gelfand, I. M.; Shen, A. (1993), , Boston: Birkhäuser, ISBN 978-0-8176-3677-7

Algebra

Gelfand, Izrail M. (1989), Gindikin, S. G.; Guillemin, V. W.; Kirillov, A. A.; Kostant, Bertram; (eds.), Collected papers. Vol. III, Berlin, New York: Springer-Verlag, ISBN 978-3-540-19399-9, MR 0997939

Sternberg, Shlomo

Gelfand, I. M.; Kapranov, M.M.; Zelevinsky, A.V. (1994), Discriminants, resultants, and multidimensional determinants, Boston: Birkhäuser,  978-0-8176-3660-9[21][22]

ISBN

Gelfand, I. M.; Saul, M. (2001), , Boston: Birkhäuser, doi:10.1007/978-1-4612-0149-6, ISBN 978-0-8176-3914-3

Trigonometry

Gelfand, I. M.; Gindikin, S. G.; Graev, M. I. (2003), Selected topics in integral geometry, Translations of Mathematical Monographs, vol. 220, Providence, R.I.: , ISBN 978-0-8218-2932-5, MR 2000133

American Mathematical Society

Borovik, Alexandre V.; Gelfand, I. M.; White, Neil (2003), , Progress in Mathematics, vol. 216, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3764-4, MR 1989953

Coxeter matroids

American Math Society, (2015)

Generalized Functions Volumes, 1-6

Gelfand duality

Gelfand–Levitan–Marchenko equation

Gelfand pair

Gelfand mapping

Gelfand ring

Gelfand triple

[23]

Anti-cosmopolitan campaign

dedicated site, maintained by Tatiana V. Gelfand and Tatiana I. Gelfand

Israel Moiseevich Gelfand

– Daily Telegraph obituary

Israel Gelfand

– Guardian obituary

Israel Gelfand

at the Mathematics Genealogy Project

Israel Gelfand

O'Connor, John J.; , "Israel Gelfand", MacTutor History of Mathematics Archive, University of St Andrews

Robertson, Edmund F.

Web page at Rutgers

.

List of publications

.

Steele Prize citation

The unity of mathematics – In honor of the ninetieth birthday of I. M. Gelfand

Interview: "A talk with professor I. M. Gelfand.", recorded by V. Retakh and A. Sosinsky, Kvant (1989), no. 1, 3–12 (in Russian). English translation in: Quantum (1991), no. 1, 20–26. ()

Link