Combinatorics

"Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions, and enumerative geometry."

"The result of a counting process is independent of the way in which it is done. This is really an assumption about what counting is. It would be senseless to try to prove it, because it is so basic; either you see it or you don't—but in the latter case, a proof won't help you a bit."