Vladimir Arnold

Vladimir Arnold
Vladimir Arnold in 2008
Born	(1937-06-12)12 June 1937 Odessa, Soviet Union
Died	3 June 2010(2010-06-03) (aged 72) Paris, France
Nationality	Soviet Union Russian
Fields	Mathematics
Alma mater	Moscow State University
Doctoral advisor	Andrey Kolmogorov
Doctoral students	Alexander Givental Askold Khovanskii Boris Shapiro Alexander Varchenko
Known for	Arnold's cat map Arnold conjecture Arnold's rouble problem KAM theorem

Vladimir Igorevich Arnold (alternative spelling Arnol'd, Russian: Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010)^[1] was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable 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.

Biography

While a student of Andrey Kolmogorov 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 Academy of Sciences of the Soviet Union (Russian Academy of Science since 1991) in 1990.^[2] 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. As of 2006 he was reported to have the highest citation index among Russian scientists,^[3] 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:

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 acute pancreatitis^[4] on 3 June 2010 in Paris, nine days before his 73rd birthday.^[5] His students include Alexander Givental, Victor Vassiliev and Askold Khovanskii.

He was buried on June 15 in Moscow, at Novodevichy Monastery.^[6]

In a telegram to Arnold's family, Russian President Dmitry Medvedev stated:

“The death of Vladimir Arnold, one of the greatest mathematicians of our time, is an irretrievable loss for world science. It is difficult to overestimate the contribution made by academician Arnold to modern mathematics and the prestige of Russian science.

Teaching had a special place in Vladimir Arnold's life and he had great influence as an enlightened mentor who taught several generations of talented scientists.

The memory of Vladimir Arnold will forever remain in the hearts of his colleagues, friends and students, as well as everyone who knew and admired this brilliant man.”^[7]

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 equations, 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 is that his books are meant to teach the subject to "those who truly wish to understand it" (Chicone, 2007). ^[8]

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.^[9][10]

Honours and awards

• Lenin Prize (1965, with Andrey Kolmogorov)
• Crafoord Prize (1982, with Louis Nirenberg)
• Foreign Honorary Member of the American Academy of Arts and Sciences (1987)^[11]
• Harvey Prize (1994)
• Dannie Heineman Prize for Mathematical Physics (2001)
• Wolf Prize in Mathematics (2001)
• State Prize of the Russian Federation (2007)^[12]
• Shaw Prize in mathematical sciences (2008)

The minor planet 10031 Vladarnolda was named after him in 1981 by Lyudmila Georgievna Karachkina.

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 Verlag (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.
• Arnold, V. I.; V. S. Afraimovich (1999). Bifurcation Theory And Catastrophe Theory. Springer. ISBN 3-540-65379-1. 
• 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.
• Vladimir I. Arnold, ed. (2004). Arnold's Problems (2nd ed.). Springer-Verlag. ISBN 3-540-20748-1. 

See also

• Arnold's cat map
• Arnold conjecture
• Arnold's rouble problem
• KAM theorem
• Gömböc

References

External links

Wikimedia Commons has media related to Vladimir Arnold.

• 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
• Problems from 5 to 15, a text by Arnold for school students, available at the IMAGINARY platform
• Vladimir Arnold at the Mathematics Genealogy Project
• S. Kutateladze, Arnold Is Gone