Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (, , ; – 5 October 2009) was a prominent Soviet and American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, one of the greatest mathematicians of the 20th century, biologist, teacher and organizer of mathematical education. He made significant contributions to many branches of mathematics, including

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

and

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...

. The recipient of many awards, including the

Order of Lenin The Order of Lenin (, ) was an award named after Vladimir Lenin, the leader of the October Revolution. It was established by the Central Executive Committee on 6 April 1930. The order was the highest civilian decoration bestowed by the Soviet ...

and the first

Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...

, he was a Foreign

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

and professor at

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

and, after immigrating to the United States shortly before his 76th birthday, at

Rutgers University Rutgers University ( ), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of three campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's C ...

. Gelfand is also a 1994 MacArthur Fellow. His legacy continues through his students, who include

Endre Szemerédi Endre Szemerédi (; born August 21, 1940) is a Hungarian-American mathematician and computer scientist, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science a ...

Alexandre Kirillov Alexandre Aleksandrovich Kirilloff (, born 1936) 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 representa ...

Edward Frenkel Edward Vladimirovich Frenkel (; born May 2, 1968) is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics. He is a professor of mathematics at the University of California, Berkeley. E ...

Joseph Bernstein Joseph Bernstein (sometimes spelled I. N. Bernshtein; ; ; born 18 April 1945) is a Soviet-born Israeli mathematician working at Tel Aviv University. He works in algebraic geometry, representation theory, and number theory. Biography Bernstein ...

David Kazhdan David Kazhdan (), born Dmitry Aleksandrovich Kazhdan (), is a Soviet and Israeli mathematician known for work in representation theory. Kazhdan is a 1990 MacArthur Fellow. Biography Kazhdan was born on 20 June 1946 in Moscow, USSR. His father ...

, as well as his own son, Sergei Gelfand.

Early years

A native of

Kherson Governorate Kherson Governorate, known until 1803 as Nikolayev Governorate, was an administrative-territorial unit ('' guberniya'') of the Russian Empire, with its capital in Kherson. It encompassed in area and had a population of 2,733,612 inhabitants. At t ...

Russian Empire The Russian Empire was an empire that spanned most of northern Eurasia from its establishment in November 1721 until the proclamation of the Russian Republic in September 1917. At its height in the late 19th century, it covered about , roughl ...

(now,

Odesa Oblast Odesa Oblast (), also referred to as Odeshchyna (Одещина), is an administrative divisions of Ukraine, oblast (province) of southwestern Ukraine, located along the northern coast of the Black Sea. Its administrative centre is the city of Ode ...

Ukraine Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...

), Gelfand was born into a

Jewish Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...

family in the small southern Ukrainian town of

Okny Okny (, ) is a Populated places in Ukraine#Rural settlements, rural settlement in Podilsk Raion in the west of Odesa Oblast, Ukraine. It hosts the administration of Okny settlement hromada, one of the hromadas of Ukraine. Population: Okny is loc ...

. According to his own account, Gelfand was expelled from high school under the

Soviets The Soviet people () were the citizens and nationals of the Soviet Union. This demonym was presented in the ideology of the country as the "new historical unity of peoples of different nationalities" (). Nationality policy in the Soviet Union ...

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

, where his advisor was the preeminent mathematician

Andrei Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...

. He received his PhD in 1935. Gelfand immigrated to the

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

in 1989.

Work

Gelfand is known for many developments including: * the book ''Calculus of Variations'' (1963), which he co-authored with

Sergei Fomin Sergei Vasilyevich Fomin (; 9 December 1917 – 17 August 1975) was a Soviet mathematician who was co-author with Andrey Kolmogorov of ''Introductory real analysis'', and co-author with Israel Gelfand of ''Calculus of Variations'' (1963),. b ...

; * Gelfand's formula, which expresses the spectral radius as a limit of matrix norms. * the

Gelfand representation In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) is either of two things: * a way of representing commutative Banach algebras as algebras of continuous functions; * the fact that for commutative C*-al ...

Banach algebra In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach sp ...

theory; * the

Gelfand–Mazur theorem In operator theory, the Gelfand–Mazur theorem is a theorem named after Israel Gelfand and Stanisław Mazur which states that a Banach algebra with unit over the complex numbers in which every nonzero element is invertible is isometrically isomorp ...

in Banach algebra theory; * the

Gelfand–Naimark theorem In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra ''A'' is isometrically *-isomorphic to a C*-subalgebra of bounded operators on a Hilbert space. This result was proven by Israel Gelfand and Mark Naimark in 1943 ...

; * the

Gelfand–Naimark–Segal construction In functional analysis, a discipline within mathematics, given a C^*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain linear functionals on A (called ''states''). ...

; * Gelfand–Shilov spaces; * the Gelfand–Pettis integral; * the

of the complex classical Lie groups; * contributions to the theory of

Verma module Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. Verma modules can be used in the classification of irreducible representations of a complex semisimple Lie algebra. Sp ...

s in the

semisimple Lie algebra In mathematics, a Lie algebra is semisimple if it is a direct sum of modules, direct sum of Simple Lie algebra, simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any non-zero proper Lie algebra#Subalgebras.2C ideals ...

s (with I. N. Bernstein and S. I. Gelfand); * contributions to

distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ...

theory and measures on infinite-dimensional spaces; * the first observation of the connection of

automorphic form In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G o ...

s with representations (with

); * conjectures about the

Atiyah–Singer index theorem In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space ...

; *

ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable (mathematics), variable. As with any other DE, its unknown(s) consists of one (or more) Function (mathematic ...

s (Gelfand–

Levitan Levitan is a surname. Notable people with the surname include: * Avri Levitan (born 1973), Israeli violist * Boris Levitan (1914–2004), Soviet-American mathematician * Dan Levitan, American businessman * Félix Lévitan (1911–2007), Tour de Fra ...

theory); * work on

calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...

and

soliton In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is , in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such local ...

theory (Gelfand–Dikii equations); * contributions to the '' philosophy of cusp forms''; * Gelfand– Fuchs

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed ...

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...

s; *

Gelfand–Kirillov dimension In algebra, the Gelfand–Kirillov dimension (or GK dimension) of a right module ''M'' over a ''k''-algebra ''A'' is: :\operatorname = \sup_ \limsup_ \log_n \dim_k M_0 V^n where the supremum is taken over all finite-dimensional subspaces V \sub ...

; *

integral geometry In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant (or equivariant) transformati ...

; * combinatorial definition of the

Pontryagin class In mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology groups with degrees a multiple of four. Definition Given a real vector bundl ...

; * Coxeter functors; *

general hypergeometric function In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function that was introduced by . The general hypergeometric function is a function that is (more or less) def ...

s; * Gelfand– Tsetlin patterns; * Gelfand–Lokutsievski method; * and many other results, particularly in the representation theory of

classical group In mathematics, the classical groups are defined as the special linear groups over the reals \mathbb, the complex numbers \mathbb and the quaternions \mathbb together with special automorphism groups of Bilinear form#Symmetric, skew-symmetric an ...

s. Gelfand ran a seminar at

from 19

until May 1989 (when it continued at

), which covered a wide range of topics and was an important school for many mathematicians.

Influence outside mathematics

The Restricted representation#Gelfand–Tsetlin basis, Gelfand–Tsetlin (also spelled Zetlin) basis is a widely used tool in

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

and the result of Gelfand's work on the representation theory of the

unitary group Unitary may refer to: Mathematics * Unitary divisor * Unitary element * Unitary group * Unitary matrix * Unitary morphism * Unitary operator * Unitary transformation * Unitary representation * Unitarity (physics) * ''E''-unitary inverse semi ...

and

Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Eucli ...

s in general. Gelfand also published works on biology and medicine. For a long time he took an interest in

cell biology Cell biology (also cellular biology or cytology) is a branch of biology that studies the structure, function, and behavior of cells. All living organisms are made of cells. A cell is the basic unit of life that is responsible for the living an ...

and organized a research seminar on the subject. He worked extensively in mathematics education, particularly with correspondence education. In 1994, he was awarded a

MacArthur Fellowship The MacArthur Fellows Program, also known as the MacArthur Fellowship and colloquially called the "Genius Grant", is a prize awarded annually by the MacArthur Foundation, John D. and Catherine T. MacArthur Foundation to typically between 20 and ...

for this work.

Personal life

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 Leukemia ( also spelled leukaemia; pronounced ) is a group of blood cancers that usually begin in the bone marrow and produce high numbers of abnormal blood cells. These blood cells are not fully developed and are called ''blasts'' or '' ...

. 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. Memories about I. Gelfand are collected at a dedicated website handled by his family. Gelfand was an advocate of

animal rights Animal rights is the philosophy according to which many or all Animal consciousness, sentient animals have Moral patienthood, moral worth independent of their Utilitarianism, utility to humans, and that their most basic interests—such as ...

."Interview with Israel Gelfand and Tatiana V. Gelfand"
vita.org.ru. Retrieved 25 February 2023. He became a

vegetarian Vegetarianism is the practice of abstaining from the Eating, consumption of meat (red meat, poultry, seafood, insects as food, insects, and the flesh of any other animal). It may also include abstaining from eating all by-products of animal slau ...

in 1994 and

vegan Veganism is the practice of abstaining from the use of animal products and the consumption of animal source foods, and an associated philosophy that rejects the commodity status of animals. A person who practices veganism is known as a ve ...

in 2000.

Honors and awards

Gelfand held several honorary degrees and was awarded the

three times for his research. In 1977 he was elected a

Foreign Member of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

. He won the

in 1978,

Kyoto Prize The is Japan's highest private award for lifetime achievement in the arts and sciences. It is given not only to those that are top representatives of their own respective fields, but to "those who have contributed significantly to the scientific, ...

in 1989 and MacArthur Foundation Fellowship in 1994. He held the presidency of the

Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society w ...

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 American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

, the

Royal Irish Academy The Royal Irish Academy (RIA; ), based in Dublin, is an academic body that promotes study in the natural sciences, arts, literature, and social sciences. It is Ireland's premier List of Irish learned societies, learned society and one of its le ...

, the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

and the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

. In an October 2003 article in ''

The New York Times ''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of ...

'', 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", having exerted a tremendous influence on the field both through his own works and those of his students.

Death

Gelfand died at the

Robert Wood Johnson University Hospital The Robert Wood Johnson University Hospital (RWJUH) is a 965-bed hospital with campuses in New Brunswick, New Jersey, New Brunswick (Robert Wood Johnson University Hospital New Brunswick), and Somerville, New Jersey, Somerville, New Jersey (Rober ...

near his home in

Highland Park, New Jersey Highland Park is a Borough (New Jersey), borough in Middlesex County, New Jersey, Middlesex County, in the U.S. state of New Jersey, in the New York City metropolitan area. The borough is located on the northern banks of the Raritan River, in th ...

. He was less than five weeks past his 96th birthday. His death was first reported on the blog of his former collaborator Andrei Zelevinsky and confirmed a few hours later by an obituary in the Russian online newspaper ''Polit.ru''.

Publications

* * * * * * * * * * * * * * * * *
''Generalized Functions Volumes, 1-6''
American Math Society, (2015)

References

Citations

Sources

Chang, Kenneth. "Israel Gelfand, Math Giant, Dies at 96", ''The New York Times'' (October 7, 2009)
* Top mathematician, 96". ''The Philadelphia Inquirer'' (October 10, 2009)br>"Israel Gelfand" ''The Daily Telegraph'' (October 27, 2009)

External links

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

– Daily Telegraph obituary
Israel Gelfand
– Guardian obituary * *
Web page at RutgersList 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
{{DEFAULTSORT:Gelfand, Israel 1913 births 2009 deaths People from Podilsk Raion People from Ananyevsky Uyezd Russian Jews Soviet Jews Soviet emigrants to the United States American people of Russian-Jewish descent Operator theorists Soviet biologists Functional analysts American textbook writers Fluid dynamicists Russian mathematicians Mathematical analysts Soviet mathematicians 20th-century American biologists 20th-century American mathematicians 21st-century American mathematicians People from Highland Park, New Jersey Moscow State University alumni Full Members of the USSR Academy of Sciences Full Members of the Russian Academy of Sciences Members of the French Academy of Sciences Members of the Royal Irish Academy Kyoto laureates in Basic Sciences Foreign associates of the National Academy of Sciences Foreign members of the Royal Society MacArthur Fellows Recipients of the Stalin Prize Recipients of the Lenin Prize Recipients of the Order of Friendship of Peoples Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour State Prize of the Russian Federation laureates Wolf Prize in Mathematics laureates Members of the Royal Swedish Academy of Sciences Russian scientists