That book is totally mindblowing, and obliterates artificial boundaries between physics and mathematics. It also (in the older Dover editions) had a cover where the phase portrait on the front looked like two angry eyes glaring at you that you hadn't learned enough math yet.
Well, modern theoretical physics seems to be nothing but mathematics (mostly advanced differential geometry and group theory). And this is a good thing, as it is the sign of how far along the subject has gone in its evolution. The theory of differential equations also reduces to differential geometry, which is what Arnold’s book seems to be striving to show, as does his other excellent text on mathematical principles of classical mechanics.
