He "was one of the most eminent contemporary mathematicians from all points of view," according to a statement from the Russian Academy of Sciences. "His work contained many things indispensable to the other sciences," including physics, chemistry and biology.
He also has an asteroid named after him, Vladarnolda.
Vladimir Igorevich Arnold was born June 12, 1937, in Odessa in what is now Ukraine to a family of several generations of scientists. He became interested in problem solving at a very young age. "Many Russian families have the tradition of giving hundreds of [mathematical] problems to their children, and mine were no exception," he later said in an interview.
Arnold enrolled at Moscow State University, where he was mentored by famed mathematician Andrey Kolmogorov. For his thesis, he completed a proof of a problem that was number 13 on a famous list of 23 unsolved mathematical challenges compiled by David Hilbert in 1900.
Kolmogorov had been working on a problem related to the motion of particles and other objects. In a solar system with one star and one planet, for example, it is easy to predict future positions of each. But in systems like ours, with many planets whose gravitational interactions are difficult to calculate, it is exceptionally difficult, and researchers had spent decades trying to calculate it and even to prove that such a system is stable.
In 1954, Kolmogorov provided a theoretical breakthrough that suggested it would be possible to predict the stability of such a system. In 1962, German American mathematician Jurgen Moser provided the proof for the theorem for one set of circumstances and the next year, Arnold, by then a faculty member at Moscow State, provided a second. The theorem is now known as the Kolmogorov-Arnold-Moser or KAM theorem.
Among other things, the theorem shows that exceptionally small gaps or errors in information can cause predictions to diverge widely from reality — which is why, for example, long-term weather forecasts are not reliable.
Through much of the 1970s and '80s, Arnold was not permitted to travel abroad because he had signed letters criticizing the persecution of dissidents, even though he was not one himself. That restriction was relaxed in the late 1980s, and he was ultimately allowed to join the Soviet Academy of Sciences in 1990, after he had already been elected to the academies in Britain, France and the United States.
In 1986, Arnold joined the Steklov Mathematical Institute in Moscow and, in 1993, he began spending fall and winter at the Steklov and spring and summer at Dauphine University in Paris.
Arnold is survived by his wife of 33 years, Eleonora; a brother, Dmitry, of Moscow; a sister, Katya Arnold, of New York; two sons, Igor of Jersey City, N.J., and Dmitry of Moscow; four grandchildren; and two great-grandchildren.