# Israel Gelfand

**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 prominent Soviet 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.

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

Born | |

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

Nationality | Soviet Union Russian |

Alma mater | Moscow State University |

Known for | Group Theory, Representation Theory, mathematical analysis Gelfand–Levitan–Marchenko integral equation Liouville–Bratu–Gelfand equation Integral geometry Gelfand-Pettis integral Gelfand representation Gelfand-Naimark theorem |

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

Scientific career | |

Fields | Mathematician |

Institutions | Moscow State University Rutgers University |

Doctoral advisor | Andrey Kolmogorov |

Doctoral students | 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

A native of Kherson Governorate of the Russian Empire, 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 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]

## 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;
- Gelfand-Lokutsievski method
- and many other results, particularly in the representation theory for the classical groups.

I.M. Gelfand's seminar at Moscow State University was running from 1945(?) until May 1989 (then it continued at Rutgers University), covered a wide range of topics, and was an important school for many mathematicians.[4][5][6]

## Influence outside mathematics

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.[7] For a long time he took an interest in cell biology and organized a research seminar on the subject.[8][9]

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. 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.[10][11] Memories about I.Gelfand are collected at a dedicated website handled by his family.[12]

## 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",[13] 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[14] and confirmed a few hours later by an obituary in the Russian online newspaper *Polit.ru*.[15]

## Publications

- Gelfand, I. M. (1998),
*Lectures on linear algebra*, Courier Dover Publications, ISBN 978-0-486-66082-0 - 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 - 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 - 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[16] - 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[16] - 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[16] - 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[16] - 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[16] - 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 - 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 - 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 - 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 - Gelfand, I. M.; Kapranov, M.M.; Zelevinsky, A.V. (1994),
*Discriminants, resultants, and multidimensional determinants*, Boston: Birkhäuser, ISBN 978-0-8176-3660-9[17] - 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 - 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 *Generalized Functions Volumes, 1-6*, American Math Society, (2015)

## References

### Citations

- 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

- "Science Obituaries: Israel Gelfand".
*The Telegraph*. London. 26 Oct 2009. Retrieved 31 May 2013. - Gel'fand, I.M.; N.Ya.Vilenkin (1964),
*Generalized Functions*, Academic Press, p. 375, ISBN 0-12-279504-0 - M.I. Vishik, G.E. Shilov, I.M. Gel'fand Seminar on Functional Analysis and Mathematical Physics in Moscow State University (in Russian),
*Uspekhi Mat. Nauk, 13:2(80) (1958), 253-263.* - Конспекты М.А. Шубина с семинаров И.М. Гельфанда
- Александр Бейлинсон, И. М. Гельфанд и его семинар (I. M. Gelfand and his seminar — a presence)
- ru:Гельфанд, Израиль Моисеевич
- V.I. Agol, Notes about I.M. Gelfand’s Seminar,
*Russian Journal Developmental Biology, Volume 39 (2008), Number 6, 367-368.* - L.V. Beloussov, Short notes about Gelfand’s Seminar,
*Russian Journal Developmental Biology, Volume 39 (2008), 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. - http://israelmgelfand.com/ site dedicated to Israel M. Gelfand
- Kochman, Marilyn. "In Person: An Equation for Success",
*The New York Times*(October 5, 2003) - (in 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"}
- 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. - 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.

### 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. - 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)