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Vladimir Igorevich Arnold (Russian: Влади́мир И́горевич Арно́льд, born June 12, 1937 in Odessa, Ukrainian SSR) is a Russian mathematician. While he is best known for the Kolmogorov-Arnold-Moser theorem regarding the stability of integrable Hamiltonian systems, he has made important contributions in a number of areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory in a career spanning over 45 years after his first main result—the solution of Hilbert's thirteenth problem in 1957.

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 has been working at Steklov Mathematical Institute since then. He became an academician of the USSR Academy of Sciences (Russian Academy of Science since 1991) in 1990.^[1] 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 are criticized for supporting the theory with statements meant to teach an intuitive understanding, without providing the tools necessary to prove these statements.^[2]

Arnold is an outspoken critic of the trend of high levels of abstraction in mathematics during the middle of last century. He has very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had negative impact on French, and then later other countries', mathematical education (see [1] and other essays in [2]).

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) and the Wolf Prize in Mathematics (2001).

Arnold presently works at the Steklov Mathematical Institute in Moscow and at the University of Paris IX. As of 2006 he was reported to have the highest citation index among Russian scientists, [3] and h-index of 40[4].

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

• 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, Yesterday and Long Ago, Springer (2007), ISBN 978-3-540-28734-6.

• Arnold's cat map
• Arnold conjecture
• Kolmogorov–Arnold–Moser theorem

1. ^ Great Russian Encyclopedia (2005), Moscow: Bol'shaya Rossiyskaya Enciklopediya Publisher, vol. 2
2. ^ 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.)

• 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