Vladimir Arnold

Vladimir Igorevich Arnold (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 Hamiltonian systems, he made important contributions in a number of 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 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 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.[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 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. 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.[3]

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 (see [1] and other essays in [2]).

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 worked at the Steklov Mathematical Institute in Moscow and at Paris Dauphine University up until his death. As of 2006[update] he was reported to have the highest citation index among Russian scientists,[4] and h-index of 40.[5]

Arnold died of peritonitis on 3 June 2010 in Paris, just 9 days before his 73rd birthday.[6] His students include Alexander Givental, Victor Vassiliev and Askold Khovanskii.

Honours and awards

Arnold has been the recipient of many awards, such as the Lenin Prize (1965, with Andrey Kolmogorov), the Crafoord Prize (1982, with Louis Nirenberg), the Harvey prize (1994), Dannie Heineman Prize for Mathematical Physics (2001), the Wolf Prize in Mathematics (2001) and the State Prize of the Russian Federation (2007).[7] He was awarded the Shaw Prize in mathematical sciences in 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, 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 3540653791.
* 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
Nuvola apps edu mathematics blue-p.svg Mathematics portal

* Arnold's cat map
* Arnold conjecture
* Arnold's rouble problem

References

1. ^ Mort d'un grand mathématicien russe, AFP (Le Figaro)
2. ^ Great Russian Encyclopedia (2005), Moscow: Bol'shaya Rossiyskaya Enciklopediya Publisher, vol. 2.
3. ^ Carmen Chicone (2007), Book review of "Ordinary Differential Equations", by Vladimir I. Arnold. Springer-Verlag, Berlin, 2006. SIAM Review 49(2):335–336. (Chicone mentions the criticism but does not agree with it.)
4. ^ http://www.scientific.ru/whoiswho/gt1000_6.html
5. ^ http://www.brics.dk/cgi-mis/hnumber?name=V.+I.+Arnold&words=
6. ^ "Number's up as top mathematician Vladimir Arnold dies". Herald Sun. 4 June 2010. http://www.heraldsun.com.au/news/breaking-news/numbers-up-as-top-mathematician-vladimir-arnold-dies/story-e6frf7jx-1225875367896. Retrieved 2010-06-06.
7. ^ Названы лауреаты Государственной премии РФ Kommersant 20 May 2008.

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
* Vladimir Arnold at the Mathematics Genealogy Project

* S. Kutateladze, Arnold Is Gone

Mathematics Encyclopedia