One of the world’s greatest and most influential mathematicians, Vladimir Arnold, passed away today in Paris, France. He made major contributions, inter alia, to the fields of dynamical systems (the famous KAM (Kolmogorov-Arnold-Moser) theory) and topology (he is one of the founding fathers of symplectic topology). I hope that the prominent mathematicians like Terence Tao or Timothy Gowers will say more on their blogs about Arnold’s scientific legacy as they did for Israel Gelfand (update: Terence Tao has a recent post on the Euler–Arnold equation).

In addition to leaving a great legacy of mathematical theories, results and open problems, he authored a number of graduate and undergraduate textbooks (the best known perhaps being Mathematical Methods of Classical Mechanics) which were a major influence.

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3 Responses to Vladimir Arnold (1937-2010). R.I.P.

Vladimir Arnold’s parents were Igor Vladimorovich Arnold and Nina Alexandrova Isakovich. Several generations of Arnold’s family had been scientists. His interest in mathematics began when he was as young as five years old. He explained that this was a consequence of the Russian mathematical tradition [4]:-

Very young children start thinking about [old merchant] problems even before they have any knowledge of numbers. Children five to six years old like them very much and are able to solve them, but they may be too difficult for university graduates, who are spoiled by formal mathematical training. … Many Russian families have the tradition of giving hundreds of [mathematical] problems to their children, and mine were no exception.

When he was twelve years old he was given challenging problems by his schoolteacher. He quoted one such problem in [4]:-

Two old women started at sunrise and each walked as a constant velocity. One went from A to B and the other from B to A. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m. At what time was sunrise on this day?

Arnold said:-

I spent a whole day thinking on this oldies, and the solution … came as a revelation. The feeling of discovery I had then was exactly the same as in all the subsequent much more serious problems …

He entered Moscow State University in 1954 as an undergraduate student in the Faculty of Mechanics and Mathematics. He was awarded his first degree in 1959 with a dissertation On mappings of a circle to itself written with Kolmogorov as advisor. Speaking of his undergraduate years he said [4]:-

The constellation of great mathematicians in the same department when I was studying at the Faculty of Mechanics and Mathematics was really exceptional, and I have never seen anything like it at any other place. Kolmogorov, Gelfand, Petrovsky, Pontryagin, P Novikov, Markov, Gelfond, Lusternik, Khinchin and P S Aleksandrov were teaching students like Manin, Sinai, Sergi Novikov, V M Alexeev, Anosov, A A Kirillov, and me. All these mathematicians were so different! It was almost impossible to understand Kolmogorov’s lectures, but they were full of ideas and were really rewarding! … Pontryagin was already very weak when I was a student at the Faculty of Mechanics and Mathematics, but he was perhaps the best of the lecturers.

[...] Posted on June 4, 2010 by pengpengche123 Vladimir Arnold (1937-2010). R.I.P. [...]

Best online biography I could quickly find begins:

http://www-history.mcs.st-and.ac.uk/Biographies/Arnold.html

Vladimir Arnold’s parents were Igor Vladimorovich Arnold and Nina Alexandrova Isakovich. Several generations of Arnold’s family had been scientists. His interest in mathematics began when he was as young as five years old. He explained that this was a consequence of the Russian mathematical tradition [4]:-

Very young children start thinking about [old merchant] problems even before they have any knowledge of numbers. Children five to six years old like them very much and are able to solve them, but they may be too difficult for university graduates, who are spoiled by formal mathematical training. … Many Russian families have the tradition of giving hundreds of [mathematical] problems to their children, and mine were no exception.

When he was twelve years old he was given challenging problems by his schoolteacher. He quoted one such problem in [4]:-

Two old women started at sunrise and each walked as a constant velocity. One went from A to B and the other from B to A. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m. At what time was sunrise on this day?

Arnold said:-

I spent a whole day thinking on this oldies, and the solution … came as a revelation. The feeling of discovery I had then was exactly the same as in all the subsequent much more serious problems …

He entered Moscow State University in 1954 as an undergraduate student in the Faculty of Mechanics and Mathematics. He was awarded his first degree in 1959 with a dissertation On mappings of a circle to itself written with Kolmogorov as advisor. Speaking of his undergraduate years he said [4]:-

The constellation of great mathematicians in the same department when I was studying at the Faculty of Mechanics and Mathematics was really exceptional, and I have never seen anything like it at any other place. Kolmogorov, Gelfand, Petrovsky, Pontryagin, P Novikov, Markov, Gelfond, Lusternik, Khinchin and P S Aleksandrov were teaching students like Manin, Sinai, Sergi Novikov, V M Alexeev, Anosov, A A Kirillov, and me. All these mathematicians were so different! It was almost impossible to understand Kolmogorov’s lectures, but they were full of ideas and were really rewarding! … Pontryagin was already very weak when I was a student at the Faculty of Mechanics and Mathematics, but he was perhaps the best of the lecturers.

Thanks for the link, Jonathan.