Israel Gelfand
Encyclopedia
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand was a Soviet mathematician
who made major contributions to many branches of mathematics, including group theory
, representation theory
and functional analysis
. The recipient of numerous awards and honors, including the Order of Lenin
and the Wolf Prize, he was a Fellow of the Royal Society and a lifelong academic, serving decades 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 is known for having educated and inspired generations of students through his legendary seminar at Moscow State University. His legacy continues in the mathematicians who were his students, such as Endre Szemerédi
, Alexandre Kirillov
, Joseph Bernstein
as well as his own son, Sergei Gelfand.
, Gelfand was born into a Jewish family in the small 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.
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
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 for this work.
. 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, all in the U.S., also includes four grandchildren and three great-grandchildren.
The memories about I.Gelfand are collected at the special site handled by his family.
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", having exerted a tremendous influence on the field both through his own works and those of his students.
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 and confirmed a few hours later by an obituary in the Russian online newspaper Polit.ru.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made major contributions to many branches of mathematics, including group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
, representation theory
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 studiesmodules over these abstract algebraic structures...
and functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
. The recipient of numerous awards and honors, including the Order of Lenin
Order of Lenin
The Order of Lenin , named after the leader of the Russian October Revolution, was the highest decoration bestowed by the Soviet Union...
and the Wolf Prize, he was a Fellow of the Royal Society and a lifelong academic, serving decades as a professor at Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
and, after immigrating to the United States shortly before his 76th birthday, at the Busch Campus
Busch Campus (Rutgers University)
Busch Campus is one of the five campuses at Rutgers University's main New Brunswick/Piscataway area campus, and is located entirely within Piscataway Township, New Jersey. Academic facilities and departments centered on this campus are primarily those related to the natural sciences: physics,...
of New Jersey
New Jersey
New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...
's Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
.
He is known for having educated and inspired generations of students through his legendary seminar at Moscow State University. His legacy continues in the mathematicians who were his students, such as Endre Szemerédi
Endre Szemerédi
Endre Szemerédi is a Hungarian mathematician, working in the field of combinatorics and theoretical computer science. He is the State of New Jersey Professor of computer science at Rutgers University since 1986...
, Alexandre Kirillov
Alexandre Kirillov
Alexandre Aleksandrovich Kirillov is a Soviet and Russian mathematician, renowned for his works in the fields of representation theory, topological groups and Lie groups. In particular he introduced the orbit method into representation theory....
, Joseph Bernstein
Joseph Bernstein
Joseph Bernstein is an Israeli mathematician working at Tel Aviv University. He works in algebraic geometry, representation theory, and number theory....
as well as his own son, Sergei Gelfand.
Early years
A native of Kherson gubernia of the Russian EmpireRussian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
, Gelfand was born into a Jewish family in the small town of Okny (subsequently, Krasni Okny
Odessa Oblast
Odesa Oblast, also written as Odessa Oblast , is the southernmost and largest oblast of south-western Ukraine. The administrative center of the oblast is the city of Odessa.-History:...
). 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.
Work
Gelfand is known for many developments including:- the book Calculus of Variations (1963), which he co-authored with Sergei FominSergei FominSergei Vasilyevich Fomin was a Soviet mathematician whowas co-author with Kolmogorov of Introductory real analysis,and co-author with I.M. Gelfand of Calculus of Variations ,both books that are widely read in Russian and in English....
- the Gelfand representationGelfand representationIn mathematics, the Gelfand representation in functional analysis has two related meanings:* a way of representing commutative Banach algebras as algebras of continuous functions;...
in Banach algebraBanach algebraIn mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space...
theory; - the Gelfand–Mazur theorem in Banach algebraBanach algebraIn mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space...
theory; - the Gelfand–Naimark theoremGelfand–Naimark theoremIn mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-algebra of bounded operators on a Hilbert space...
; - the Gelfand–Naimark–Segal construction;
- Gelfand–Shilov spaceGelfand–Shilov spaceIn the mathematical field of functional analysis, a Gelfand–Shilov space S is a space of test functions for the theory of generalized functions, introduced by ....
s - the Gelfand–Pettis integralPettis integralIn mathematics, the Pettis integral or Gelfand–Pettis integral, named after I. M. Gelfand and B.J. Pettis, extends the definition of the Lebesgue integral to functions on a measure space which take values in a Banach space, by the use of duality. The integral was introduced by Gelfand for the...
; - the representation theoryRepresentation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
of the complex classical Lie groupLie groupIn mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s; - contributions to the theory of Verma moduleVerma moduleVerma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.The definition of a Verma module looks complicated, but Verma modules are very natural objects, with useful properties...
s in the representation theoryRepresentation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
of semisimple Lie algebras (with I.N. Bernstein and S.I. Gelfand); - contributions to distributionDistribution (mathematics)In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...
theory and measures on infinite-dimensional spaces; - the first observation of the connection of automorphic formAutomorphic formIn mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps of several complex variables, of the theory of modular forms...
s with representations (with Sergei FominSergei FominSergei Vasilyevich Fomin was a Soviet mathematician whowas co-author with Kolmogorov of Introductory real analysis,and co-author with I.M. Gelfand of Calculus of Variations ,both books that are widely read in Russian and in English....
); - conjectures about the Atiyah–Singer index theoremAtiyah–Singer index theoremIn differential geometry, the Atiyah–Singer index theorem, proved by , states that for an elliptic differential operator on a compact manifold, the analytical index is equal to the topological index...
; - Ordinary differential equationOrdinary differential equationIn mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
s (Gelfand–LevitanBoris LevitanBoris Levitan was a mathematician known in particular for his work on almost periodic functions, and Sturm–Liouville operators, especially, on inverse scattering.-Life:...
theory); - work on calculus of variationsCalculus of variationsCalculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
and solitonSolitonIn mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. 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–Fuks cohomology of foliationFoliationIn mathematics, a foliation is a geometric device used to study manifolds, consisting of an integrable subbundle of the tangent bundle. A foliation looks locally like a decomposition of the manifold as a union of parallel submanifolds of smaller dimension....
s; - Gelfand–Kirillov dimension;
- integral geometryIntegral geometryIn 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 transformations from the space of functions on one geometrical space to the...
; - combinatorial definition of the Pontryagin classPontryagin classIn mathematics, the Pontryagin classes are certain characteristic classes. The Pontryagin class lies in cohomology groups with degree a multiple of four...
; - Coxeter functors;
- general hypergeometric functionGeneral hypergeometric functionIn mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function that was introduced by...
s; - 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 physicsTheoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
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
Cell biology is a scientific discipline that studies cells – their physiological properties, their structure, the organelles they contain, interactions with their environment, their life cycle, division and death. This is done both on a microscopic and molecular level...
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 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 leukemiaLeukemia
Leukemia or leukaemia is a type of cancer of the blood or bone marrow characterized by an abnormal increase of immature white blood cells called "blasts". Leukemia is a broad term covering a spectrum of diseases...
. 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, all in the U.S., also includes four grandchildren and three great-grandchildren.
The memories about I.Gelfand are collected at the special site handled by his family.
Honors and awards
Gelfand held several honorary degrees and was awarded the Order of LeninOrder of Lenin
The Order of Lenin , named after the leader of the Russian October Revolution, was the highest decoration bestowed by the Soviet Union...
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
Kyoto Prize
The has been awarded annually since 1985 by the Inamori Foundation, founded by Kazuo Inamori. The prize is a Japanese award similar in intent to the Nobel Prize, as it recognizes outstanding works in the fields of philosophy, arts, science and technology...
in 1989 and MacArthur Foundation Fellowship in 1994. He held the presidency of the Moscow Mathematical Society
Moscow Mathematical Society
The Moscow Mathematical Society is a society of Moscow mathematicians aimed at the development of mathematics in Russia.The first meeting of the society was . Nikolai Brashman was the first president of MMO. Victor Vassiliev is the current president of MMO....
between 1968 and 1970, and was elected a foreign member of the U.S. National Academy of Science
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
, the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
, the Royal Irish Academy
Royal Irish Academy
The Royal Irish Academy , based in Dublin, is an all-Ireland, independent, academic body that promotes study and excellence in the sciences, humanities and social sciences. It is one of Ireland's premier learned societies and cultural institutions and currently has around 420 Members, elected in...
, the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
and the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
.
In an October 2003 article in The New York Times
The New York Times
The New York Times is an American daily newspaper founded and continuously published in New York City since 1851. The New York Times has won 106 Pulitzer Prizes, the most of any news organization...
, 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
Israel Gelfand died at the Robert Wood Johnson University HospitalRobert Wood Johnson University Hospital
Robert Wood Johnson University Hospital is the clinical campus of the Robert Wood Johnson Medical School in New Brunswick, New Jersey. It provides a full range of health care services as Central New Jersey's only Level 1 Trauma and academic medical center. The hospital is a member of the Robert...
near his home in Highland Park, New Jersey
Highland Park, New Jersey
Highland Park is a borough in Middlesex County, New Jersey, United States. As of the 2010 United States Census, the borough population was 13,982....
. 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.
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 Gelfand - Daily Telegraph obituary
- Israel Gelfand - Guardian obituary
- Web page at Rutgers
- List of publications.
- Steele Prize citation.