“The truly correct proof is one that strikes a harmonious balance between strength and flexibility. There are plenty of proofs that are technically correct but are messy and inelegant or counterintuitive. But it's not something you can put into words — explaining why a formula is beautiful is like trying to explain why the stars are beautiful.”

“It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.”

“One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul.”

“Why?""Because...because he's so tall," Mindy explained, like height was proof of good character. "And did I mention European?""Yes. It's so much better to be stalked by a tall European that an American of average height.”

“Actually Gabriel’s an archangel,” I corrected. “But otherwise, yes.”“Well, that explains why he’s so hard to impress,” said Xavier flippantly”

“I couldn’t explain my need to myself, and that’s why it was such a beautiful need”