Vladimir Igorevich Arnold (alternative spelling Arnol'd, russian: link=no, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010)
was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem
The Kolmogorov–Arnold–Moser (KAM) theorem is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations. The theorem partly resolves the small-divisor problem that arises in the perturbation theory ...
regarding the stability
Stability may refer to:
Mathematics
*Stability theory, the study of the stability of solutions to differential equations and dynamical systems
** Asymptotic stability
** Linear stability
** Lyapunov stability
** Orbital stability
** Structural sta ...
of integrable system
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first ...
s, he made important contributions in several areas including dynamical systems theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called ' ...
, algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary a ...
, catastrophe theory, topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
, algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
, symplectic geometry
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed differential form, closed, nondegenerate form, nondegenerate different ...
, differential equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
, classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, hydrodynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
and singularity theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...
, including posing the ADE classification
In mathematics, the ADE classification (originally ''A-D-E'' classifications) is a situation where certain kinds of objects are in correspondence with simply laced Dynkin diagrams. The question of giving a common origin to these classifications, r ...
problem, since his first main result—the solution of Hilbert's thirteenth problem
Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether a solution exists for all 7th-degree equations using algebraic (variant: continuous) f ...
in 1957 at the age of 19. He co-founded two new branches of mathematics— KAM theory, and topological Galois theory In mathematics, topological Galois theory is a mathematical theory which originated from a Topology, topological proof of Abel–Ruffini theorem, Abel's impossibility theorem found by Vladimir Arnold, V. I. Arnold and concerns the applications of so ...
(this, with his student Askold Khovanskii
Askold Georgievich Khovanskii (russian: Аскольд Георгиевич Хованский; born 3 June 1947, Moscow) is a Russian and Canadian mathematician currently a professor of mathematics at the University of Toronto, Canada. His area ...
).
Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as the famous ''Mathematical Methods of Classical Mechanics
Mathematical Methods of Classical Mechanics is a classic graduate textbook by the mathematician Vladimir I. Arnold. It was originally written in Russian, but was translated into English by A. Weinstein and K. Vogtmann.
Contents
* Part I: Ne ...
'') and popular mathematics books, he influenced many mathematicians and physicists. Many of his books were translated into English. His views on education were particularly opposed to those of Bourbaki.
Biography
Vladimir Igorevich Arnold was born on 12 June 1937 in Odessa
Odesa (also spelled Odessa) is the third most populous city and municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern shore of the Black Sea. The city is also the administrativ ...
, Soviet Union
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...
(now Odesa
Odesa (also spelled Odessa) is the third most populous city and municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern shore of the Black Sea. The city is also the administrative ...
, 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 ...
). His father was Igor Vladimirovich Arnold (1900–1948), a mathematician. His mother was Nina Alexandrovna Arnold (1909–1986, ''née
A birth name is the name of a person given upon birth. The term may be applied to the surname, the given name, or the entire name. Where births are required to be officially registered, the entire name entered onto a birth certificate or birth re ...
'' Isakovich), a Jewish art historian. While a school student, Arnold once asked his father on the reason why the multiplication of two negative numbers yielded a positive number, and his father provided an answer involving the field properties of real numbers and the preservation of the distributive property. Arnold was deeply disappointed with this answer, and developed an aversion to the axiomatic method
In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually conta ...
that lasted through his life. When Arnold was thirteen, his uncle Nikolai B. Zhitkov,[''Swimming Against the Tide'', p. 3] who was an engineer, told him about calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
and how it could be used to understand some physical phenomena, this contributed to spark his interest for mathematics, and he started to study by himself the mathematical books his father had left to him, which included some works of Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
and Charles Hermite
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
Hermi ...
.
While a student of Andrey 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 ...
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 still a teenager, Arnold showed in 1957 that any continuous function of several variables can be constructed with a finite number of two-variable functions, thereby solving Hilbert's thirteenth problem
Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether a solution exists for all 7th-degree equations using algebraic (variant: continuous) f ...
. This is the Kolmogorov–Arnold representation theorem
In real analysis and approximation theory, the Kolmogorov-Arnold representation theorem (or superposition theorem) states that every multivariate continuous function can be represented as a superposition of the two-argument addition and continuou ...
.
After graduating from Moscow State University in 1959, he worked there until 1986 (a professor since 1965), and then at Steklov Mathematical Institute
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part o ...
.
He became an academician of the Academy of Sciences of the Soviet Union
The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...
(Russian Academy of Science
The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...
since 1991) in 1990.Great Russian Encyclopedia
The ''Great Russian Encyclopedia'' (GRE; russian: Большая российская энциклопедия, БРЭ, transliterated as ''Bolshaya rossiyskaya entsiklopediya'' or academically as ''Bolšaja rossijskaja enciklopedija'') is a u ...
(2005), Moscow: Bol'shaya Rossiyskaya Enciklopediya Publisher, vol. 2. Arnold can be said to have initiated the theory of symplectic topology
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Ha ...
as a distinct discipline. The Arnold conjecture
The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry.
Statement
Let (M, \omega) be a compact symplectic manifold. For any smooth f ...
on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections were also a major motivation in the development of Floer homology
In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer in ...
.
In 1999 he suffered a serious bike accident in Paris, resulting in traumatic brain injury
A traumatic brain injury (TBI), also known as an intracranial injury, is an injury to the brain caused by an external force. TBI can be classified based on severity (ranging from mild traumatic brain injury TBI/concussionto severe traumatic b ...
, and though he regained consciousness after a few weeks, he had amnesia and for some time could not even recognize his own wife at the hospital, but he went on to make a good recovery.
Arnold worked at the Steklov Mathematical Institute
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part o ...
in Moscow and at Paris Dauphine University
Paris Dauphine University - PSL (french: Université Paris-Dauphine, also known as Paris Dauphine - PSL or Dauphine - PSL) is a public research university based in Paris, France. It is one of the 13 universities formed by the division of the ancie ...
up until his death. he was reported to have the highest citation index
A citation index is a kind of bibliographic index, an index of citations between publications, allowing the user to easily establish which later documents cite which earlier documents. A form of citation index is first found in 12th-century Hebr ...
among Russian scientists, and h-index
The ''h''-index is an author-level metric that measures both the productivity and citation impact of the publications, initially used for an individual scientist or scholar. The ''h''-index correlates with obvious success indicators such as winn ...
of 40. His students include Alexander Givental
Alexander Givental (russian: Александр Борисович Гивенталь) is a Russian-American mathematician working in symplectic topology and singularity theory, as well as their relation to topological string theories. He graduat ...
, Victor Goryunov
Victor Vladimirovich Goryunov is a Russian mathematician born in 1956. He is a leading figure in Singularity theory, whose contributions to the subject are fundamental. He has published several books and a variety of papers in singularity theory, ...
, Sabir Gusein-Zade, Emil Horozov, Boris Khesin, Askold Khovanskii
Askold Georgievich Khovanskii (russian: Аскольд Георгиевич Хованский; born 3 June 1947, Moscow) is a Russian and Canadian mathematician currently a professor of mathematics at the University of Toronto, Canada. His area ...
, Nikolay Nekhoroshev, Boris Shapiro, Alexander Varchenko, Victor Vassiliev
Victor Anatolyevich Vassiliev or Vasilyev ( ru , Виктор Анатольевич Васильев; born April 10, 1956), is a Soviet and Russian mathematician. He is best known for his discovery of the Vassiliev invariants in knot theory (als ...
and Vladimir Zakalyukin.
To his students and colleagues Arnold was known also for his sense of humour. For example, once at his seminar in Moscow, at the beginning of the school year, when he usually was formulating new problems, he said:
Death
Arnold died of acute pancreatitis
Acute pancreatitis (AP) is a sudden inflammation of the pancreas. Causes in order of frequency include: 1) a gallstone impacted in the common bile duct beyond the point where the pancreatic duct joins it; 2) heavy alcohol use; 3) systemic disea ...
on 3 June 2010 in Paris, nine days before his 73rd birthday. He was buried on 15 June in Moscow, at the Novodevichy Monastery.
In a telegram to Arnold's family, Russian President
The president of the Russian Federation ( rus, Президент Российской Федерации, Prezident Rossiyskoy Federatsii) is the head of state of the Russian Federation. The president leads the executive branch of the federal ...
Dmitry Medvedev
Dmitry Anatolyevich Medvedev ( rus, links=no, Дмитрий Анатольевич Медведев, p=ˈdmʲitrʲɪj ɐnɐˈtolʲjɪvʲɪtɕ mʲɪdˈvʲedʲɪf; born 14 September 1965) is a Russian politician who has been serving as the dep ...
stated:
Popular mathematical writings
Arnold is well known for his lucid writing style, combining mathematical rigour with physical intuition, and an easy conversational style of teaching and education. His writings present a fresh, often geometric approach to traditional mathematical topics like 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, and his many textbooks have proved influential in the development of new areas of mathematics. The standard criticism about Arnold's pedagogy is that his books "are beautiful treatments of their subjects that are appreciated by experts, but too many details are omitted for students to learn the mathematics required to prove the statements that he so effortlessly justifies." His defense was that his books are meant to teach the subject to "those who truly wish to understand it" (Chicone, 2007).
Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education, and then later on that of other countries as well.[An Interview with Vladimir Arnol'd](_blank)
by S. H. Lui, ''AMS Notices
''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...
'', 1991. Arnold was very interested in the history of mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...
. In an interview, he said he had learned much of what he knew about mathematics through the study of Felix Klein
Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group ...
's book ''Development of Mathematics in the 19th Century'' —a book he often recommended to his students. He studied the classics, most notably the works of Huygens, Newton
Newton most commonly refers to:
* Isaac Newton (1642–1726/1727), English scientist
* Newton (unit), SI unit of force named after Isaac Newton
Newton may also refer to:
Arts and entertainment
* ''Newton'' (film), a 2017 Indian film
* Newton ( ...
and Poincaré, and many times he reported to have found in their works ideas that had not been explored yet.
Work
Arnold worked on dynamical systems theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called ' ...
, catastrophe theory, topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
, algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
, symplectic geometry
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed differential form, closed, nondegenerate form, nondegenerate different ...
, differential equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
, classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, hydrodynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
and singularity theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...
. Michèle Audin described him as "a geometer in the widest possible sense of the word" and said that "he was very fast to make connections between different fields".
Hilbert's thirteenth problem
The problem is the following question: can every continuous function of three variables be expressed as a composition
Composition or Compositions may refer to:
Arts and literature
*Composition (dance), practice and teaching of choreography
*Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
of finitely many continuous functions of two variables? The affirmative answer to this general question was given in 1957 by Vladimir Arnold, then only nineteen years old and a student of Andrey 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 ...
. Kolmogorov had shown in the previous year that any function of several variables can be constructed with a finite number of three-variable functions. Arnold then expanded on this work to show that only two-variable functions were in fact required, thus answering the Hilbert's question when posed for the class of continuous functions.
Dynamical systems
Moser and Arnold expanded the ideas of 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 ...
(who was inspired by questions of Poincaré) and gave rise to what is now known as Kolmogorov–Arnold–Moser theorem
The Kolmogorov–Arnold–Moser (KAM) theorem is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations. The theorem partly resolves the small-divisor problem that arises in the perturbation theory ...
(or "KAM theory"), which concerns the persistence of some quasi-periodic motions (nearly integrable Hamiltonian systems) when they are perturbed. KAM theory shows that, despite the perturbations, such systems can be stable over an infinite period of time, and specifies what the conditions for this are.
In 1964, Arnold introduced the Arnold web, the first example of a stochastic web.
Singularity theory
In 1965, Arnold attended René Thom
René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958.
He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became w ...
's seminar on catastrophe theory. He later said of it: "I am deeply indebted to Thom, whose singularity seminar at the Institut des Hautes Etudes Scientifiques
An institute is an organisational body created for a certain purpose. They are often research organisations (research institutes) created to do research on specific topics, or can also be a professional body.
In some countries, institutes can ...
, which I frequented throughout the year 1965, profoundly changed my mathematical universe." After this event, singularity theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...
became one of the major interests of Arnold and his students. Among his most famous results in this area is his classification of simple singularities, contained in his paper "Normal forms of functions near degenerate critical points, the Weyl groups of Ak,Dk,Ek and Lagrangian singularities".
Fluid dynamics
In 1966, Arnold published "", in which he presented a common geometric interpretation for both the Euler's equations for rotating rigid bodies and the Euler's equations of fluid dynamics, this effectively linked topics previously thought to be unrelated, and enabled mathematical solutions to many questions related to fluid flows and their turbulence.
Real algebraic geometry
In the year 1971, Arnold published "On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
s, and the arithmetic of integral quadratic forms", which gave new life to real algebraic geometry In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial ...
. In it, he made major advances in the direction of a solution to Gudkov's conjecture In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem, which states that an M-curve of even degree 2d obeys the congruence
: p - n \equiv d^2\, (\! ...
, by finding a connection between it and four-dimensional topology. The conjecture was to be later fully solved by V. A. Rokhlin building on Arnold's work.
Symplectic geometry
The Arnold conjecture
The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry.
Statement
Let (M, \omega) be a compact symplectic manifold. For any smooth f ...
, linking the number of fixed points of Hamiltonian symplectomorphisms and the topology of the subjacent manifolds, was the motivating source of many of the pioneer studies in symplectic topology.
Topology
According to Victor Vassiliev, Arnold "worked comparatively little on topology for topology's sake." And he was rather motivated by problems on other areas of mathematics where topology could be of use. His contributions include the invention of a topological form of the Abel–Ruffini theorem
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, ''general'' means th ...
and the initial development of some of the consequent ideas, a work which resulted in the creation of the field of topological Galois theory In mathematics, topological Galois theory is a mathematical theory which originated from a Topology, topological proof of Abel–Ruffini theorem, Abel's impossibility theorem found by Vladimir Arnold, V. I. Arnold and concerns the applications of so ...
in the 1960s.
Theory of plane curves
According to Marcel Berger
Marcel Berger (14 April 1927 – 15 October 2016) was a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques (IHÉS), France. Formerly residing in Le Castera in Las ...
, Arnold revolutionized plane curves theory. Among his contributions are the Arnold invariants of plane curves.
Other
Arnold conjectured the existence of the gömböc
The Gömböc ( ) is the first known physical example of a class of convex three-dimensional homogeneous bodies, called mono-monostatic, which, when resting on a flat surface have just one stable and one unstable point of equilibrium. The ...
.
Honours and awards
* Lenin Prize (1965, with Andrey 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 ...
), "for work on celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
."
* Crafoord Prize
The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foun ...
(1982, with Louis Nirenberg
Louis Nirenberg (February 28, 1925 – January 26, 2020) was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
Nearly all of his work was in the field of partial differential equat ...
), "for contributions to the theory of non-linear differential equations
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many othe ...
."
* Elected member of the United States National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
in 1983).
* Foreign Honorary Member of 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 ...
(1987)
* 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 ...
(ForMemRS) of London in 1988.[
* Elected member of the ]American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...
in 1990.
* Lobachevsky Prize of the Russian Academy of Sciences (1992)
* Harvey Prize
Harvey Prize is an annual Israeli award for breakthroughs in science and technology, as well as contributions to peace in the Middle East granted by the Technion in Haifa.
History
The prize is named for industrialist and inventor Leo Harvey. T ...
(1994), "for basic contribution to the stability theory of dynamical system
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...
s, his pioneering work on singularity theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...
and seminal contributions to analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
and geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
."
* Dannie Heineman Prize for Mathematical Physics
Dannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by the American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman. As of 2010 ...
(2001), "for his fundamental contributions to our understanding of dynamics and of singularities of maps with profound consequences for mechanics
Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...
, astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...
, statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
, hydrodynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
and optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
."
* Wolf Prize in Mathematics (2001), "for his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory."
* State Prize of the Russian Federation
The State Prize of the Russian Federation, officially translated in Russia as Russian Federation National Award, is a state honorary prize established in 1992 following the breakup of the Soviet Union. In 2004 the rules for selection of laureates ...
(2007),[Названы лауреаты Государственной премии РФ]
Kommersant
''Kommersant'' (russian: Коммерсантъ, , ''The Businessman'' or Commerce Man, often shortened to Ъ) is a nationally distributed daily newspaper published in Russia mostly devoted to politics and business. The TNS Media and NRS Russia ...
20 May 2008. "for outstanding success in mathematics."
* Shaw Prize in mathematical sciences (2008, with Ludwig Faddeev
Ludvig Dmitrievich Faddeev (also ''Ludwig Dmitriyevich''; russian: Лю́двиг Дми́триевич Фадде́ев; 23 March 1934 – 26 February 2017) was a Soviet and Russian mathematical physicist. He is known for the discovery of the ...
), "for their contributions to mathematical physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
."
The minor planet
According to the International Astronomical Union (IAU), a minor planet is an astronomical object in direct orbit around the Sun that is exclusively classified as neither a planet nor a comet. Before 2006, the IAU officially used the term ''minor ...
10031 Vladarnolda was named after him in 1981 by Lyudmila Georgievna Karachkina
Lyudmila Georgievna Karachkina (russian: Людмила Георгиевна Карачкина, born 3 September 1948, Rostov-on-Don) is an astronomer and discoverer of minor planets.
In 1978 she began as a staff astronomer of the Institute for ...
.
The '' Arnold Mathematical Journal'', published for the first time in 2015, is named after him.
The Arnold Fellowships, of the London Institute
University of the Arts London is a collegiate university in London, England, specialising in arts, design, fashion and the performing arts. It is a federation of six arts colleges: Camberwell College of Arts, Central Saint Martins, Chelsea Coll ...
are named after him.
He was a plenary speaker at both the 1974 and 1983 International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
in Vancouver and Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...
, respectively.
Fields Medal omission
Even though Arnold was nominated for the 1974 Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
, which was then viewed as the highest honour a mathematician could receive, interference from the Soviet government led to it being withdrawn. Arnold's public opposition to the persecution of dissident
A dissident is a person who actively challenges an established political or religious system, doctrine, belief, policy, or institution. In a religious context, the word has been used since the 18th century, and in the political sense since the 20th ...
s had led him into direct conflict with influential Soviet officials, and he suffered persecution himself, including not being allowed to leave the Soviet Union during most of the 1970s and 1980s.
Selected bibliography
* 1966:
* 1978: ''Ordinary Differential Equations'', The MIT Press .
* 1985:
* 1988:
* 1988:
* 1989:
* 1989
* 1989: (with A. Avez) ''Ergodic Problems of Classical Mechanics'', Addison-Wesley .
* 1990: ''Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals'', Eric J.F. Primrose translator, Birkhäuser Verlag
Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields:
* Springer continues to publish science (particu ...
(1990) .
* 1991:
* 1995:''Topological Invariants of Plane Curves and Caustics'', American Mathematical Society (1994)
* 1998: "On the teaching of mathematics" (Russian) Uspekhi Mat. Nauk 53 (1998), no. 1(319), 229–234; translation in '' Russian Math. Surveys'' 53(1): 229–236.
* 1999: (with Valentin Afraimovich) ''Bifurcation Theory And Catastrophe Theory'' Springer
* 2001: "Tsepniye Drobi" (Continued Fractions, in Russian), Moscow (2001).
* 2004: ''Teoriya Katastrof'' (Catastrophe Theory, in Russian), 4th ed. Moscow, Editorial-URSS (2004), .
* 2004:
* 2004:
* 2007: ''Yesterday and Long Ago'', Springer (2007), .
* 2013: [Review by Fernando Q. Gouvêa of ''Real Algebraic Geometry'' by Arnold https://www.maa.org/press/maa-reviews/real-algebraic-geometry]
* 2014:
* 2015: ''Experimental Mathematics''. American Mathematical Society (translated from Russian, 2015).
* 2015: ''Lectures and Problems: A Gift to Young Mathematicians'', American Math Society, (translated from Russian, 2015)
Collected works
* 2010: A. B. Givental; B. A. Khesin; J. E. Marsden; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; V. M. Zakalyukin (editors). ''Collected Works, Volume I: Representations of Functions, Celestial Mechanics, and KAM Theory (1957–1965)''. Springer
Springer or springers may refer to:
Publishers
* Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag.
** Springer Nature, a multinationa ...
* 2013: A. B. Givental; B. A. Khesin; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; (editors). ''Collected Works, Volume II: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry (1965–1972)''. Springer.
* 2016: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). ''Collected Works, Volume III: Singularity Theory 1972–1979. Springer.
* 2018: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). ''Collected Works, Volume IV: Singularities in Symplectic and Contact Geometry 1980–1985''. Springer.
* 2022 (To be published, September 2022): Alexander B. Givental, Boris A. Khesin, Mikhail B. Sevryuk, Victor A. Vassiliev, Oleg Ya. Viro (Eds.). ''Collected Works, Volume VI: Dynamics, Combinatorics, and Invariants of Knots, Curves, and Wave Fronts 1992–1995''. Springer.
See also
* List of things named after Vladimir Arnold
*Independent University of Moscow
The Independent University of Moscow (IUM) (russian: Независимый Московский Университет (НМУ)) is an educational organisation with rather informal status located in Moscow, Russia. It was founded in 1991 by a gro ...
*Geometric mechanics Geometric mechanics is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid bodies to fluid mechanics to control theory.
Geometric mechanics applies principally to systems f ...
References
Further reading
* Khesin, Boris; Tabachnikov, Serge (Coordinating Editors).
Tribute to Vladimir Arnold
, ''Notices of the American Mathematical Society
''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...
'', March 2012, Volume 59, Number 3, pp. 378–399.
* Khesin, Boris; Tabachnikov, Serge (Coordinating Editors).
Memories of Vladimir Arnold
, ''Notices of the American Mathematical Society'', April 2012, Volume 59, Number 4, pp. 482–502.
*
*
*
External links
V. I. Arnold's web page
Personal web page
V. I. Arnold lecturing on Continued Fractions
A short curriculum vitae
text of a talk espousing Arnold's opinions on mathematical instruction
* ttp://imaginary.org/sites/default/files/taskbook_arnold_en_0.pdf Problems from 5 to 15 a text by Arnold for school students, available at th
IMAGINARY platform
*
В.Б.Демидовичем (2009), МЕХМАТЯНЕ ВСПОМИНАЮТ 2: В.И.Арнольд, pp. 25–58
Author profile
in the database zbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ...
{{DEFAULTSORT:Arnold, Vladimir
1937 births
2010 deaths
Scientists from Odesa
20th-century Russian mathematicians
21st-century Russian mathematicians
Fellows of the American Academy of Arts and Sciences
Foreign Members of the Royal Society
Lenin Prize winners
Mathematical analysts
Full Members of the USSR Academy of Sciences
Full Members of the Russian Academy of Sciences
Members of the French Academy of Sciences
Foreign associates of the National Academy of Sciences
Moscow State University alumni
Soviet mathematicians
State Prize of the Russian Federation laureates
Topologists
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University of Paris faculty
Wolf Prize in Mathematics laureates
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Moscow State University faculty
Steklov Institute of Mathematics faculty
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Odesa Jews