Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гельфанд; – 5 October 2009) was a prominent

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

-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, structure, space, models, and change. History On ...

. 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 algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

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 (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

. The recipient of many awards, including the

Order of Lenin The Order of Lenin (russian: Орден Ленина, Orden Lenina, ), named after the leader of the Russian October Revolution, was established by the Central Executive Committee on April 6, 1930. The order was the highest civilian decoration b ...

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 judges 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 M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

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

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

. 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 Kirillov (russian: Алекса́ндр Алекса́ндрович Кири́ллов, born 1936) is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups a ...

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 University of California, Berkeley, a member ...

Joseph Bernstein Joseph Bernstein (sometimes spelled I. N. Bernshtein; he, יוס(י)ף נאומוביץ ברנשטיין; russian: Иосиф Наумович Бернштейн; born 18 April 1945) is a Soviet-born Israeli mathematician working at Tel Aviv Univ ...

David Kazhdan David Kazhdan ( he, דוד קשדן), born Dmitry Aleksandrovich Kazhdan (russian: Дми́трий Александро́вич Кажда́н), is a Soviet and Israeli mathematician known for work in representation theory. Kazhdan is a 1990 Ma ...

, as well as his own son, Sergei Gelfand.

Early years

A native of

Kherson Governorate The Kherson Governorate (1802–1922; russian: Херсонская губерния, translit.: ''Khersonskaya guberniya''; uk, Херсонська губернія, translit=Khersonska huberniia), was an administrative territorial unit (als ...

Russian Empire The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War. ...

(now,

Odessa Oblast Odesa Oblast ( uk, Оде́ська о́бласть, translit=Odeska oblast), also referred to as Odeshchyna ( uk, Оде́щина) is an administrative divisions of Ukraine, oblast (province) of southwestern Ukraine, located along the northern ...

Ukraine Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian inv ...

), Gelfand was born into a

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

family in the small southern

Ukrainian Ukrainian may refer to: * Something of, from, or related to Ukraine * Something relating to Ukrainians, an East Slavic people from Eastern Europe * Something relating to demographics of Ukraine in terms of demography and population of Ukraine * So ...

town of

Okny Okny ( uk, Окни, russian: Окны) is an urban-type settlement in the west of Odesa Oblast, Ukraine. It served as the administrative center of Okny Raion. Population: Okny is located on the banks of the Yahorlik River, a left tributary of ...

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

Soviets Soviet people ( rus, сове́тский наро́д, r=sovyétsky naród), or citizens of the USSR ( rus, гра́ждане СССР, grázhdanye SSSR), was an umbrella demonym for the population of the Soviet Union. Nationality policy in th ...

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 Sovi ...

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

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

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 (russian: Серге́й Васи́льевич Фоми́н; 9 December 1917 – 17 August 1975) was a Soviet mathematician who was co-author with Andrey Kolmogorov of ''Introductory real analysis'', and co-author wi ...

; * 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*-alge ...

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 spa ...

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 an ...

; * 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 '' ...

; * 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. Spe ...

s in the

semisimple Lie algebra In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any non-zero proper ideals). Throughout the article, unless otherwise stated, a Lie algebra i ...

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 vari ...

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 of ...

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 whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast w ...

s (Gelfand– Levitan 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 functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

and

soliton In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium ...

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 viewe ...

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

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) transformation ...

; * 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 bundle ...

; * Coxeter functors; * general hypergeometric functions; * 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 , the complex numbers and the quaternions together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or ske ...

s. Gelfand ran a seminar at

from 1945(?) 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 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 natural phenomena. This is in contrast to experimental physics, which uses experim ...

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. 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 and ...

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 commonly but unofficially known as the "Genius Grant", is a prize awarded annually by the MacArthur Foundation, John D. and Catherine T. MacArthur Foundation typically to ...

for this work.

Family

Gelfand was married to

Zorya Shapiro Zorya Yakovlevna Shapiro (russian: Зоря Яковлевна Шапиро; 7 December 1914 – 4 July 2013) was a Soviet mathematician, educator and translator. She is known for her contributions to representation theory and functional analys ...

, and their two sons, Sergei and Vladimir both live in the United States. The third son, Aleksandr, died of

leukemia Leukemia ( also spelled leukaemia and pronounced ) is a group of blood cancers that usually begin in the bone marrow and result in 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.

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 judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematics ...

. 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 wa ...

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 (abbreviation: AAA&S) 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 ...

, the

Royal Irish Academy The Royal Irish Academy (RIA; ga, Acadamh Ríoga na hÉireann), based in Dublin, is an academic body that promotes study in the sciences, humanities and social sciences. It is Ireland's premier List of Irish learned societies, learned socie ...

, 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 societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

. In an October 2003 article in ''

The New York Times ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...

'', 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 an American 965-bed hospital with campuses in New Brunswick (Robert Wood Johnson University Hospital New Brunswick), and Somerville, New Jersey ( Robert Wood Johnson University Hospital Somer ...

near his home in

Highland Park, New Jersey Highland Park is a borough in Middlesex County, New Jersey, United States in the New York City metropolitan area. The borough is located on the northern banks of the Raritan River, in the Raritan Valley region. As of the 2020 United States Cens ...

. 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 Odesa Oblast People from Ananyevsky Uyezd Ukrainian Jews Soviet Jews Soviet emigrants to the United States American people of Ukrainian-Jewish descent Operator theorists Soviet biologists Functional analysts Textbook writers Fluid dynamicists Ukrainian mathematicians Mathematical analysts Soviet mathematicians 20th-century 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 Stalin Prize winners Lenin Prize winners 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