# Israel Gelfand

Israïl Moiseevich Gelfand | |
---|---|

File:IM Gelfand.jpg | |

Born | Krasniye Okny, Odessa Oblast, Russian Empire |
September 2, 1913

Died | October 5, 2009 New Brunswick, New Jersey, United States |
(aged 96)

Nationality | Soviet Union Russian |

Fields | Mathematician |

Institutions | Moscow State University Rutgers University |

Alma mater | Moscow State University |

Doctoral advisor | Andrey Kolmogorov |

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

Known for | Group Theory, Representation Theory, mathematical analysis |

Notable awards | Order of Lenin (three times) Wolf Prize (1978) Wigner Medal (1980) Kyoto Prize in Mathematical sciences (1989) AMS Steele Prize (2005) |

**Israel Moiseevich Gelfand**, also written **Israïl Moyseyovich Gel'fand**, or **Izrail M. Gelfand** (Yiddish: ישראל געלפֿאַנד, Russian: Изра́иль Моисе́евич Гельфа́нд; 2 September [O.S. 20 August] 1913 – 5 October 2009) was a Soviet mathematician who is regarded to be a prominent mathematician of the 20th century. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of awards, including the Order of Lenin and the Wolf Prize, he was a Fellow of the Royal Society and an academic, serving as a professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at the Busch Campus of New Jersey's Rutgers University.

He taught students through his seminar at Moscow State University. His legacy continues in the mathematicians who were his students, such as Endre Szemerédi, Alexandre Kirillov, Edward Frenkel,^{[1]} Joseph Bernstein, Dmitry Fuchs as well as his own son, Sergei Gelfand.

## Contents

## Early years

A native of Kherson Governorate of the Russian Empire, Gelfand was born into a Jewish family in the small southern Ukrainian town of Okny (subsequently, Krasni Okny). According to his own account, Gelfand was expelled from high school because his father had been a mill owner. Bypassing both high school and college, he proceeded to postgraduate study at Moscow State University, where his advisor was the preeminent mathematician Andrei Kolmogorov. He nevertheless managed to attend lectures at the University and began postgraduate study at the age of 19.^{[2]}

## Work

Gelfand is known for many developments including:

- the book
*Calculus of Variations*(1963), which he co-authored with Sergei Fomin - the Gelfand representation in Banach algebra theory;
- the Gelfand–Mazur theorem in Banach algebra theory;
- the Gelfand–Naimark theorem;
- the Gelfand–Naimark–Segal construction;
- Gelfand–Shilov spaces
- the Gelfand–Pettis integral;
- the representation theory of the complex classical Lie groups;
- contributions to the theory of Verma modules in the representation theory of semisimple Lie algebras (with I. N. Bernstein and S. I. Gelfand);
- contributions to distribution theory and measures on infinite-dimensional spaces;
^{[3]} - the first observation of the connection of automorphic forms with representations (with Sergei Fomin);
- conjectures about the Atiyah–Singer 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;
- general hypergeometric functions;
- Gelfand–Tsetlin patterns;
- and many other results, particularly in the representation theory for the classical groups.

## Influence outside of mathematics

The *Gelfand–Tsetlin basis* (also in the common spelling *Zetlin*) 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.^{[4]} For a long time he took an interest in cell biology and organized a research seminar on the subject.^{[5]}^{[6]}

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

## Family

Gelfand was married to Zorya Shapiro, and their two sons, Sergei and Vladimir both live in the United States. A third son, Aleksandr, died of leukemia. Following the divorce from his first wife, Gelfand married his second wife, Tatiana. Gelfand and Tatiana became the parents of a daughter, Tatiana. The family also includes four grandchildren and three great-grandchildren.^{[7]}^{[8]} The memories about I.Gelfand are collected at the special site^{[9]} handled by his family.

## Honors and awards

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",^{[10]} having exerted a tremendous influence on the field both through his own works and those of his students.

## Death

Israel 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^{[11]} and confirmed a few hours later by an obituary in the Russian online newspaper *Polit.ru*.^{[12]}

## Publications

- Gelfand, I. M. (1998),
*Lectures on linear algebra*, Courier Dover Publications, ISBN 978-0-486-66082-0<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Gelfand, I. M.; Fomin, Sergei V. (1963), Silverman, Richard A. (ed.),
*Calculus of variations*, Englewood Cliffs, N.J.: Prentice-Hall Inc., ISBN 978-0-486-41448-5, MR 0160139<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Gelfand, I.; Raikov, D.; Shilov, G. (1964) [1960],
*Commutative normed rings*, Translated from the Russian, with a supplementary chapter, New York: Chelsea Publishing Co., ISBN 978-0-8218-2022-3, MR 0205105<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Gel'fand, I. M.; Shilov, G. E. (1964) [1958],
*Generalized functions. Vol. I: Properties and operations*, Translated by Eugene Saletan, Boston, MA: Academic Press, ISBN 978-0-12-279501-5, MR 0166596<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>^{[13]} - Gelfand, I. M.; Shilov, G. E. (1968) [1958],
*Generalized functions. Vol. 2. Spaces of fundamental and generalized functions*, 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<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>^{[13]} - 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: Academic Press, MR 0217416<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>^{[13]} - Gelfand, I. M.; Vilenkin, N. Ya. (1964) [1961],
*Generalized functions. Vol. 4: Applications of harmonic analysis*, Translated by Amiel Feinstein, Boston, MA: Academic Press, ISBN 978-0-12-279504-6, MR 0173945<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>^{[13]} - 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: Academic Press, ISBN 978-0-12-279505-3, MR 0207913<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>^{[13]} - Gelfand, I. M.; Graev, M. I.; Pyatetskii-Shapiro, I. I. (1969),
*Representation theory and automorphic functions*, Translated from the Russian by K. A. Hirsch, Philadelphia, Pa.: W. B. Saunders Co., ISBN 978-0-12-279506-0, MR 0233772<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Gelfand, Izrail M. (1987), Gindikin, S. G.; Guillemin, V. W.; Kirillov, A. A.; Kostant, Bertram; Sternberg, Shlomo (eds.),
*Collected papers. Vol. I*, Berlin, New York: Springer-Verlag, ISBN 978-3-540-13619-4, MR 0929821<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Gelfand, Izrail M. (1988), Gindikin, S. G.; Guillemin, V. W.; Kirillov, A. A.; Kostant, Bertram; Sternberg, Shlomo (eds.),
*Collected papers. Vol. II*, Berlin, New York: Springer-Verlag, ISBN 978-3-540-19035-6, MR 0929821<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Gelfand, Izrail M. (1989), Gindikin, S. G.; Guillemin, V. W.; Kirillov, A. A.; Kostant, Bertram; Sternberg, Shlomo (eds.),
*Collected papers. Vol. III*, Berlin, New York: Springer-Verlag, ISBN 978-3-540-19399-9, MR 0997939<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Gelfand, I. M.; Kapranov, M.M.; Zelevinsky, A.V. (1994),
*Discriminants, resultants, and multidimensional determinants*, Boston: Birkhäuser, ISBN 978-0-8176-3660-9<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>^{[14]} - Gelfand, I. M.; Gindikin, S. G.; Graev, M. I. (2003),
*Selected topics in integral geometry*, Translations of Mathematical Monographs,**220**, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-2932-5, MR 2000133<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Borovik, Alexandre V.; Gelfand, I. M.; White, Neil (2003),
*Coxeter matroids*, Progress in Mathematics,**216**, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3764-4, MR 1989953<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> *Generalized Functions Volumes, 1-6*, American Math Society, (2015)

## See also

## References

### Notes

- ↑ Edward Frenkel (2013). "preface".
*Love and Math: The Heart of Hidden Reality*. Basic Books. ISBN 978-0465050741.One of my teachers, the great Israel Gelfand

<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ "Science Obituaries: Israel Gelfand".
*The Telegraph*. London. 26 Oct 2009. Retrieved 31 May 2013.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ Gel'fand, I.M. (1964),
*Generalized Functions*, Academic Press, p. 375, ISBN 0-12-279504-0 Unknown parameter`|coauthors=`

ignored (help)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ ru:Гельфанд, Израиль Моисеевич
- ↑ V.I. Agol, Notes about I.M. Gelfand’s Seminar,
*Russian Journal Developmental Biology, Volume 39, Number 6, 367-368.* - ↑ L.V. Beloussov, Short notes about Gelfand’s Seminar,
*Russian Journal Developmental Biology, Volume 39, Number 6, 369-370.* - ↑ Chang, Kenneth. "Israel Gelfand, Math Giant, Dies at 96",
*The New York Times*(October 7, 2009) - ↑ Stewart, Ian (November 8, 2009). "Israel Gelfand obituary".
*The Guardian*. London.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ http://israelmgelfand.com/ site dedicated to Israel M. Gelfand
- ↑ Kochman, Marilyn. "In Person: An Equation for Success",
*The New York Times*(October 5, 2003) - ↑ (Russian) "Скончался И.М. Гельфанд" ("I.M. Gelfand has died"), accessed 2009-10-06
- ↑ "5 октября ушел из жизни выдающийся математик Израиль Моисеевич Гельфанд. "Эпоха Гельфанда ушла, но она продолжится в существующих поколениях" {"Renowned Mathematician Israil Moiseyevich Gelfand Departed on October 5. Gelfand's era has gone, but it shall continue in succeeding generations"}
- ↑
^{13.0}^{13.1}^{13.2}^{13.3}^{13.4}Guillemin, Victor (1980). "Review:*Generalized functions*, by I. M. Gel'fand and G. E. Shilov".*Bull. Amer. Math. Soc. (N.S.)*.**3**(1, Part 1): 758–762. doi:10.1090/s0273-0979-1980-14813-2.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ Catanese, Fabrizio (2000). "Review:
*Discriminants, resultants, and multidimensional determinants*, by I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky".*Bull. Amer. Math. Soc. (N.S.)*.**37**(2): 183–198. doi:10.1090/s0273-0979-99-00858-7.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>

### Sources

- Chang, Kenneth. "Israel Gelfand, Math Giant, Dies at 96",
*The New York Times*(October 7, 2009) - "Leading mathematician Israel Gelfand dies in N.J."
*USA Today*(October 9, 2009) - "Israel Gelfand | Top mathematician, 96".
*The Philadelphia Inquirer*(October 10, 2009) - "Israel Gelfand"
*The Daily Telegraph*(October 27, 2009)

## External links

- Israel Moiseevich Gelfand, dedicated site, maintained by Tatiana V. Gelfand and Tatiana I. Gelfand
- Israel Gelfand - Daily Telegraph obituary
- Israel Gelfand - Guardian obituary
- Israel Gelfand at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Israel Gelfand",
*MacTutor History of Mathematics archive*, University of St Andrews<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>. - Web page at Rutgers
- List of publications.
- Steele Prize citation.
- The unity of mathematics – In honor of the ninetieth burthday 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)

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