Vladimir Arnold, 72
Vladimir Arnold, noted Russian mathematician, dies at 72
Vladimir Arnold, 72, a Russian mathematician who pioneered work on the arcane field known as catastrophe theory and whose research led to a better understanding of the motion of planets in the solar system, died of peritonitis in Paris on June 3.
He "was one of the most eminent contemporary mathematicians from all points of view," the Russian Academy of Sciences said in a statement. "His work contained many things indispensable to the other sciences," including physics, chemistry and biology.
Dr. Arnold received numerous awards, including the Crafoord Prize in 1982, the Shaw Prize in 2008 and the Wolf Prize, which some consider the math equivalent of a Nobel, in 2001. He should have received the equally prestigious Fields Medal in 1974, but the Soviet government refused to let him accept it.
He 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 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.
Dr. Arnold enrolled at Moscow State University, where he was mentored by noted 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. 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 problem for one set of circumstances; the next year, Dr. Arnold, by then a faculty member at Moscow State, provided a second. The theory is known as the Kolmogorov-Arnold-Moser, or KAM, theory.
Among other things, the theory 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, Dr. 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 been elected to the academies in Britain, France and the United States.
In 1986, Dr. Arnold joined the Steklov Mathematical Institute in Moscow. In 1993, he began spending fall and winter at the Steklov and spring and summer at Dauphine University in Paris.
He is survived by his wife of 33 years, Eleonora Arnold; a brother; a sister; two sons, Igor Arnold of Jersey City and Dmitry Arnold of Moscow; four grandchildren; and two great-grandchildren.
-- Los Angeles Times