"Development of mathematics resembles a fast revolution of a wheel: sprinkles of water are flying in all directions. Fashion—it is the stream that leaves the main trajectory in the tangential direction. These streams of epigone works attract the most attention, and they constitute the main mass, but they inevitably disappear after a while because they parted with the wheel. To remain on the wheel, one must apply the effort in the direction perpendicular to the main stream."

that's the most creative metaphor I've ever read

I'm reading him now (Dynamics, statistics and projective geometry of Galois fields) and find the ideas likable. He talks about dynamic systems whose state spaces are finite fields, for instance the geometric progression of the primitive element (the powers of a multiplicative group generator). "The resulting theory is some number-theoretic finite version of the ergodic theory of toric automorphisms where the chaoticity and the mixing properties of the progressions A^k have been studied for volume-preserving automorphisms A of the continuous torus T^n" He used the nice fact that finite state space discrete dynamics are described by unions of affluent rivers in an attraction basin leading to limiting cycles. He would have loved messing with python Jupiter notebooks having been guided by paper-and-pencil explorations himself.

If you enjoyed the article, do dig out the memoir that he wrote while recovering from a cycling accident. http://www.springer.com/gb/book/9783540287346

For the story on the fish, you'll need to get the book.

That was wonderful, thank you. In my (very basic) mathematical travels, VI Arnold, like Conway and Thurston, is a name that keeps popping up everywhere.