Vladimir Arnold
Encyclopedia
Vladimir Igorevich Arnold (alternative spelling Arnol'd, , 12 June 1937 – 3 June 2010) was a Soviet and Russia
n mathematician
. While he is best known for the Kolmogorov–Arnold–Moser theorem
regarding the stability
of integrable Hamiltonian
systems, he made important contributions in several areas including dynamical systems theory
, catastrophe theory
, topology
, algebraic geometry
, classical mechanics
and singularity theory
, including posing the ADE classification
problem, since his first main result—the partial solution of Hilbert's thirteenth problem
in 1957 at the age of 19.
at Moscow State University
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 partially solving Hilbert's thirteenth problem
.
After graduating from Moscow State University
in 1959, he worked there until 1986 (a professor since 1965), and then at Steklov Mathematical Institute.
He became an academician of the USSR Academy of Sciences (Russian Academy of Science since 1991) in 1990. Arnold can be said to have initiated the theory of symplectic topology
as a distinct discipline. The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections were also a major motivation in the development of Floer homology
.
Arnold worked at the Steklov Mathematical Institute in Moscow
and at Paris Dauphine University up until his death. he was reported to have the highest citation index
among Russian scientists, and h-index
of 40.
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:
Arnold died of peritonitis
on 3 June 2010 in Paris
, nine days before his 73rd birthday. His students include Alexander Givental
, Victor Vassiliev and Askold Khovanskii.
In a telegram to Arnold's family, Russian President Dmitry Medvedev
stated:
s, and his many textbooks have proved influential in the development of new areas of mathematics. However, Arnold's books have been criticized for supporting the theory with statements meant to teach an intuitive understanding, without providing the tools necessary to prove these statements.
Arnold was an outspoken critic of the trend of 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, and then later other countries', mathematical education. Arnold's sharp critique of Bourbaki approach was in turn criticized by other mathematicians.
The minor planet
10031 Vladarnolda
was named after him in 1981 by Lyudmila Georgievna Karachkina
.
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
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....
. While he is best known for the Kolmogorov–Arnold–Moser theorem
Kolmogorov–Arnold–Moser theorem
The Kolmogorov–Arnold–Moser theorem is a result in dynamical systems about the persistence of quasi-periodic motions under small perturbations. The theorem partly resolves the small-divisor problem that arises in the perturbation theory of classical mechanics....
regarding the stability
Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions...
of integrable Hamiltonian
Hamiltonian mechanics
Hamiltonian mechanics is a reformulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton.It arose from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, but can be formulated without...
systems, he made important contributions in several areas including dynamical systems theory
Dynamical systems theory
Dynamical systems theory is an area of applied 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 continuous dynamical systems. When difference...
, catastrophe theory
Catastrophe theory
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry....
, topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
and singularity theory
Singularity theory
-The notion of singularity:In mathematics, singularity theory is the study of the failure of manifold structure. A loop of string can serve as an example of a one-dimensional manifold, if one neglects its width. What is meant by a singularity can be seen by dropping it on the floor...
, including posing the ADE classification
ADE classification
In mathematics, the ADE classification is the complete list of simply laced Dynkin diagrams or other mathematical objects satisfying analogous axioms; "simply laced" means that there are no multiple edges, which corresponds to all simple roots in the root system forming angles of \pi/2 = 90^\circ ...
problem, since his first main result—the partial solution of Hilbert's thirteenth problem
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 or not a solution exists for all 7th-degree equations using functions of two arguments...
in 1957 at the age of 19.
Biography
While a student of Andrey KolmogorovAndrey Kolmogorov
Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
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 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 partially solving Hilbert's thirteenth problem
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 or not a solution exists for all 7th-degree equations using functions of two arguments...
.
After graduating from 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...
in 1959, he worked there until 1986 (a professor since 1965), and then at Steklov Mathematical Institute.
He became an academician of the USSR Academy of Sciences (Russian Academy of Science since 1991) in 1990. Arnold can be said to have initiated the theory of symplectic topology
Symplectic topology
Symplectic geometry is a branch of differential geometry and differential topology which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form...
as a distinct discipline. The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections were also a major motivation in the development of Floer homology
Floer homology
Floer homology is a mathematical tool used in the study of symplectic geometry and low-dimensional topology. First introduced by Andreas Floer in his proof of the Arnold conjecture in symplectic geometry, Floer homology is a novel homology theory arising as an infinite dimensional analog of finite...
.
Arnold worked at the Steklov Mathematical Institute in Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
and at Paris Dauphine University up until his death. he was reported to have the highest citation index
Citation index
A citation index is a kind of bibliographic database, an index of citations between publications, allowing the user to easily establish which later documents cite which earlier documents. The first citation indices were legal citators such as Shepard's Citations...
among Russian scientists, and h-index
H-index
The h-index is an index that attempts to measure both the productivity and impact of the published work of a scientist or scholar. The index is based on the set of the scientist's most cited papers and the number of citations that they have received in other publications...
of 40.
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:
There is a general principle that a stupid man can ask such questions to which one hundred wise men would not be able to answer. In accordance with this principle I shall formulate some problems.
Arnold died of peritonitis
Peritonitis
Peritonitis is an inflammation of the peritoneum, the serous membrane that lines part of the abdominal cavity and viscera. Peritonitis may be localised or generalised, and may result from infection or from a non-infectious process.-Abdominal pain and tenderness:The main manifestations of...
on 3 June 2010 in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, nine days before his 73rd birthday. His students include Alexander Givental
Alexander Givental
Alexander Givental is a Russian American mathematician working in the area of symplectic topology, singularity theory and their relations to topological string theories. He got his Ph. D. under the supervision of V. I. Arnold. He, first, proved the mirror conjecture for toric Calabi-Yau manifolds,...
, Victor Vassiliev and Askold Khovanskii.
In a telegram to Arnold's family, Russian President Dmitry Medvedev
Dmitry Medvedev
Dmitry Anatolyevich Medvedev is the third President of the Russian Federation.Born to a family of academics, Medvedev graduated from the Law Department of Leningrad State University in 1987. He defended his dissertation in 1990 and worked as a docent at his alma mater, now renamed to Saint...
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. His writings present a fresh, often geometric approach to traditional mathematical topics like ordinary differential equationOrdinary differential equation
In 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, and his many textbooks have proved influential in the development of new areas of mathematics. However, Arnold's books have been criticized for supporting the theory with statements meant to teach an intuitive understanding, without providing the tools necessary to prove these statements.
Arnold was an outspoken critic of the trend of 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, and then later other countries', mathematical education. Arnold's sharp critique of Bourbaki approach was in turn criticized by other mathematicians.
Honours and awards
- Lenin PrizeLenin PrizeThe Lenin Prize was one of the most prestigious awards of the USSR, presented to individuals for accomplishments relating to science, literature, arts, architecture, and technology. It was created on June 23, 1925 and was awarded until 1934. During the period from 1935 to 1956, the Lenin Prize was...
(1965, with Andrey KolmogorovAndrey KolmogorovAndrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
) - Crafoord PrizeCrafoord PrizeThe Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord...
(1982, with Louis NirenbergLouis NirenbergLouis Nirenberg is a Canadian mathematician, and one of the outstanding analysts of the twentieth century. He has made fundamental contributions to linear and nonlinear partial differential equations and their application to complex analysis and geometry.He was born in Hamilton, Ontario and...
) - Foreign Honorary Member of the American Academy of Arts and SciencesAmerican Academy of Arts and SciencesThe 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...
(1987) - Harvey PrizeHarvey PrizeThe Harvey Prize is awarded by the Technion in Haifa, Israel. It is awarded in different disciplines of Science, Technology, Human Health, and Contributions to Peace in the Middle East. Two awards - each of $75,000 - are given away annually...
(1994) - Dannie Heineman Prize for Mathematical PhysicsDannie Heineman Prize for Mathematical PhysicsDannie 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...
(2001) - Wolf Prize in MathematicsWolf Prize in MathematicsThe Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
(2001) - State Prize of the Russian FederationState Prize of the Russian FederationState Prize of the Russian Federation is a state honorary prize established in 1992 as the substitute for the USSR State Prize. In 2004 the rules for selection of laureates and the status of the award was significantly changed making them closer to such awards as Nobel Prize or the Soviet Lenin...
(2007). - Shaw PrizeShaw PrizeThe Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong, it honours living "individuals, regardless of race, nationality and religious belief, who have achieved significant breakthrough in academic and scientific research or...
in mathematical sciences (2008)
The minor planet
Minor planet
An asteroid group or minor-planet group is a population of minor planets that have a share broadly similar orbits. Members are generally unrelated to each other, unlike in an asteroid family, which often results from the break-up of a single asteroid...
10031 Vladarnolda
10031 Vladarnolda
10031 Vladarnolda is a main belt asteroid with an orbital period of 1521.8960898 days . The asteroid was discovered on September 7, 1981....
was named after him in 1981 by Lyudmila Georgievna Karachkina
Lyudmila Georgievna Karachkina
Lyudmila Georgievna Karachkina is a Soviet and Ukrainian astronomer.Working at the Crimean Astrophysical Observatory since 1978, she has discovered a number of asteroids, including the Amor asteroid 5324 Lyapunov and the Trojan asteroid 3063 Makhaon. She has received a Ph.D. in astronomy from I. I...
.
Selected bibliography
- V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag (1989), ISBN 0-387-96890-3.
- V. I. Arnold, Geometrical Methods In The Theory Of Ordinary Differential Equations, Springer-Verlag (1988), ISBN 0-387-96649-8.
- V. I. Arnold, Ordinary Differential Equations, The MIT Press (1978), ISBN 0-262-51018-9.
- V. I. Arnold, A. Avez, Ergodic Problems of Classical Mechanics, Addison-Wesley (1989), ISBN 0-201-09406-1.
- V.I. Arnold, Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals, Eric J.F. Primrose translator, Birkhäuser VerlagBirkhäuser VerlagBirkhäuser Verlag is the leading European publisher for architecture, landscaping and design. Since 2010 it is part of the ActarBirkhäuser Group.-Scientific publishing:Founded in 1879 by Emil Birkhäuser the publishers program focused on regional literature...
(1990) ISBN 3-7643-2383-3 . - V. I. Arnold, Teoriya Katastrof (Catastrophe Theory, in Russian), 4th ed. Moscow, Editorial-URSS (2004), ISBN 5-354-00674-0.
- V. I. Arnold, "Tsepniye Drobi" (Continued Fractions, in Russian), Moscow (2001).
- V. I. Arnold, Yesterday and Long Ago, Springer (2007), ISBN 978-3-540-28734-6.
- Arnolʹd, V. I.: On the teaching of mathematics. (Russian) Uspekhi Mat. Nauk 53 (1998), no. 1(319), 229—234; translation in Russian Math. Surveys 53 (1998), no. 1, 229—236.
See also
- Arnold's cat mapArnold's cat mapIn mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name....
- Arnold conjecture
- Arnold's rouble problem
- KAM theorem
- GömböcGömböcA gömböc is a convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium. Its existence was conjectured by Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by Hungarian scientists Gábor Domokos and Péter...
External links
- V. I. Arnold's web page
- Personal web page
- V. I. Arnold lecturing on Continued Fractions
- A short curriculum vitae
- On Teaching Mathematics, text of a talk espousing Arnold's opinions on mathematical instruction
- S. Kutateladze, Arnold Is Gone