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- Arnold in His Own Words
A word about spelling: we use “Arnold”, as opposed to “Arnol'd”; the latter is closer to the Russian pronunciation, but Vladimir Arnold preferred the former (it is used in numerous translations of his books into English), and we use it throughout.
Q: You spend much time popularizing mathematics. What is your opinion about popularization? Please name merits and demerits of this hard genre.
A:One of the very first popularizers,M. Faraday, arrived at the conclusion that “Lectures which really teach will never be popular; lectures which are popular will never teach.” This Faraday effect is easy to explain: according toN. Bohr, clearness and truth are in a quantum complementarity relation.
Mathematicians differ dramatically by their time scale: some are very good tackling 15-minute problems, some are good with the problems that require an hour, a day, a week, the problems that take a month, a year, decades of thinking.
There are contraindications to becoming a research mathematician. The main one is lack of love of mathematics.
But mathematical talents can be very diverse: geometrical and intuitive, algebraic and computational, logical and deductive, natural scientific and inductive. And all kinds are useful. It seems to me that one’s difficulties with the multiplication table or a formal definition of half-plane should not obstruct one's way to mathematics. An extremely important condition for serious mathematical research is good health.
- Mikhail Sevryuk
According to Arnold, one needs mathematics to discover new laws of nature as opposed to “rigorously” justify obvious things. V. I. tried to teach his students this perception of mathematics and natural sciences as a unified tool for understanding the world.
On another occasion, Arnold was lecturing, and the proof of a theorem involved tedious computations: “Everyone must make these computations once—but only once. I made them in the past, so I won't repeat them now; they are left to the audience!”
这个很有趣，有机会要用一下，哈哈。
- Michael Berry
It suddenly occurs to me that in at least four respects Arnold was the mathematical counterpart of Richard Feynman. Like Feynman, Arnold made massive original contributions in his field, with enormous influence outside it; he was a master expositor, an inspiring teacher bringing new ideas to new and wide audiences; he was uncompromisingly direct and utterly honest; and he was a colorful character, bubbling with mischief, endlessly surprising.