Israel Gelfand | |
---|---|

Израиль Гельфанд | |

Born | |

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

Citizenship | Soviet Union American |

Alma mater | Moscow State University |

Known for | 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 |

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 |

**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.

- Early years
- Work
- Influence outside mathematics
- Personal life
- Honors and awards
- Death
- Publications
- See also
- References
- Citations
- Sources
- External links

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.

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] }

Gelfand is known for many developments including:

- the book
*Calculus of Variations*(1963), which he co-authored with Sergei Fomin; - Gelfand's formula, which expresses the spectral radius as a limit of matrix norms.
- 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;
^{ [5] } - 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–Fuchs cohomology of Lie algebras;
- 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 of classical groups.

Gelfand ran a seminar at Moscow State University from 1943 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] }

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.

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] }

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.

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),
*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^{ [20] } - 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^{ [20] } - 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^{ [20] } - 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^{ [20] } - 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^{ [20] } - 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, I. M.; Shen, A. (1993),
*Algebra*, Boston: Birkhäuser, ISBN 978-0-8176-3677-7 - 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^{ [21] }^{ [22] } - Gelfand, I. M.; Saul, M. (2001),
*Trigonometry*, Boston: Birkhäuser, doi:10.1007/978-1-4612-0149-6, ISBN 978-0-8176-3914-3 - Gelfand, I. M.; Gindikin, S. G.; Graev, M. I. (2003),
*Selected topics in integral geometry*, Translations of Mathematical Monographs, vol. 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, vol. 216, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3764-4, MR 1989953 -
*Generalized Functions Volumes, 1-6*, American Math Society, (2015)

In representation theory and algebraic number theory, the **Langlands program** is a web of far-reaching and consequential conjectures about connections between number theory and geometry. Proposed by Robert Langlands, it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics."

In mathematics, especially representation theory, a **quiver** is another name for a multidigraph; that is, a directed graph where loops and multiple arrows between two vertices are allowed. Quivers are commonly used in representation theory: a representation V of a quiver assigns a vector space *V*(*x*) to each vertex x of the quiver and a linear map *V*(*a*) to each arrow a.

**Ilya Piatetski-Shapiro** was a Soviet-born Israeli mathematician. During a career that spanned 60 years he made major contributions to applied science as well as pure mathematics. In his last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions.

In mathematics, the **Selberg trace formula**, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group G on the space *L*^{2}(Γ\*G*) of square-integrable functions, where Γ is a cofinite discrete group. The character is given by the trace of certain functions on G.

In mathematics, **generalized functions** are objects extending the notion of functions. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges. They are applied extensively, especially in physics and engineering.

**Alexandre Aleksandrovich Kirilloff** is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups and Lie groups. In particular he introduced the orbit method into representation theory. He is an emeritus professor at the University of Pennsylvania.

In mathematics, the **orbit method** establishes a correspondence between irreducible unitary representations of a Lie group and its coadjoint orbits: orbits of the action of the group on the dual space of its Lie algebra. The theory was introduced by Kirillov for nilpotent groups and later extended by Bertram Kostant, Louis Auslander, Lajos Pukánszky and others to the case of solvable groups. Roger Howe found a version of the orbit method that applies to *p*-adic Lie groups. David Vogan proposed that the orbit method should serve as a unifying principle in the description of the unitary duals of real reductive Lie groups.

**Naum Yakovlevich Vilenkin** was a Soviet mathematician, an expert in representation theory, the theory of special functions, functional analysis, and combinatorics. He is best known as the author of many books in recreational mathematics aimed at middle and high school students.

In algebra, the **hyperdeterminant** is a generalization of the determinant. Whereas a determinant is a scalar valued function defined on an *n* × *n* square matrix, a hyperdeterminant is defined on a multidimensional array of numbers or tensor. Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor. Many other properties of determinants generalize in some way to hyperdeterminants, but unlike a determinant, the hyperdeterminant does not have a simple geometric interpretation in terms of volumes.

In the mathematical field of functional analysis, a **Gelfand–Shilov space** is a space of test functions for the theory of generalized functions, introduced by Gelfand and Shilov.

In mathematics, specifically representation theory, **tilting theory** describes a way to relate the module categories of two algebras using so-called **tilting modules** and associated **tilting functors**. Here, the second algebra is the endomorphism algebra of a tilting module over the first algebra.

In representation theory, a **Jantzen filtration** is a filtration of a Verma module of a semisimple Lie algebra, or a Weyl module of a reductive algebraic group of positive characteristic. Jantzen filtrations were introduced by Jantzen.

**Andrei Vladlenovich Zelevinsky** was a Russian-American mathematician who made important contributions to algebra, combinatorics, and representation theory, among other areas.

**Sergey Vladimirovich Fomin** is a Russian American mathematician who has made important contributions in combinatorics and its relations with algebra, geometry, and representation theory. Together with Andrei Zelevinsky, he introduced cluster algebras.

**Vera Vladimirovna Serganova** is a professor of mathematics at the University of California, Berkeley who researches superalgebras and their representations.

** Vladimir Solomonovich Retakh ** is a Russian-American mathematician who made important contributions to Noncommutative algebra and combinatorics among other areas.

**Dmitry Borisovich Fuchs** is a Russian-American mathematician, specializing in the representation theory of infinite-dimensional Lie groups and in topology.

**Mark Iosifovich Graev** was a Russian mathematician. He is known as one of the namesakes in the Gelfand–Graev representation.

**Mikhail Kapranov**, is a Russian mathematician, specializing in algebraic geometry, representation theory, mathematical physics, and category theory. He is currently a professor of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo.

**Dmitrii Abramovich Raikov** was a Russian mathematician who studied functional analysis.

- ↑ 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 October 2009. Retrieved 31 May 2013. - ↑ "Israel Moiseevich Gelfand".
*The Mathematics Genealogy Project*. Retrieved 4 October 2022. - ↑ "Israel Gelfand, Math Giant, Dies at 96".
*New York Times*. 7 October 2009. Retrieved 12 November 2022. - ↑ 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 (8 November 2009). "Israel Gelfand obituary".
*The Guardian*. London. - ↑ http://israelmgelfand.com/ site dedicated to Israel M. Gelfand
- 1 2 "Interview with Israel Gelfand and Tatiana V. Gelfand". vita.org.ru. Retrieved 25 February 2023.
- ↑ "Israel Gelfand". telegraph.co.uk. Retrieved 25 February 2023.
- ↑ 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"}
- 1 2 3 4 5 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 . - ↑ Roberts, David P. (2009). "Review: Discriminants, Resultants, and Multidimensional Determinants, by I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky".
*Mathematical Association of America*. Retrieved 1 July 2020. - ↑ Rosenfeld (Розенфельд), Boris Abramowitsch (Борис Абрамович) [in German] (2003). "Math.ru" Об Исааке Моисеевиче Ягломе [About Isaac Moiseevich Yaglom].
*Мат. просвещение (Mat. enlightenment)*(in Russian): 25–28. Archived from the original on 12 January 2022. Retrieved 12 January 2022– via math.ru. […] во время антисемитской кампании, известной как «борьба с космополитизмом», был уволен вместе с И.М. Гельфандом и И. С. Градштейном […][during the antisemitic campaign known as the "fight against cosmopolitanism", he was fired along with I. M. Gelfand and I. S. Gradstein.]

- 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)

- 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 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)

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