Two passages on math from The Nothing That Is, by Robert Kaplan. First, on the yearning for generalization:

[W]e always expect it to come, being the children we are of the Great Paradigm shift, where autonomous species are bound to be subsumed under a just if distant genus.

And, on the role of intuition:

You may have guessed this wasn't the only time a procedure—such as the shrinking of h to 0—has been used in mathematics before it was formally justified: it has happened over and over again, from Archimedes on, because it springs from the ever-present tension between intuition and proof. These are the two poles of all mathematical thought. The first centers the free play of mind, which browses on the pastures of phenomena and from its ruminations invents objects so beautiful in themselves, relations that work so elegantly, both fitting in with our other inventions and clarifying their surroundings, that world and mind stand revealed as each the other's invention, conformably with the unique way that Things Are.