Pierre Cartier describing Alexander Grothendieck’s approach to mathematics:
Grothendieck’s favorite method is not unlike Joshua’s method for conquering Jericho. The thing was to patiently encircle the solid walls without actually doing anything: at a certain point, the walls fall flat without a fight. This was also the method used by the Romans when they conquered the natural desert fortress Masada, the last stronghold of the Jewish revolt, after spending months patiently building a ramp. Grothendieck was convinced that if one has a sufficiently unifying vision of mathematics, if one can sufficiently penetrate the essence of mathematics and the strategies of its concepts, then particular problems are nothing but a test; they do not need to be solved for their own sake.
Related post: The great reformulation of algebraic geometry
Grothendiek’s other nice analogy along these lines is about opening a nut with a “rising sea” that softens it. (In contrast with cracking it with a hammer or something, I think.)
However, not everyone can be Grothendieck :)
@Steve: And that’s a Good Thing.