“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.”

“The Professor never really seemed to care whether we figured out the right answer to a problem. He preferred our wild, desperate guesses to silence, and he was even more delighted when those guesses led to new problems that took us beyond the original one. He had a special feeling for what he called the "correct miscalculation," for he believed that mistakes were often as revealing as the right answers.”

“Still, being alone doesn't mean you have to be miserable. In that sense it's different from losing something. You've still got yourself, even if you lose everything else. You've got to have faith in yourself and not get down just because you're on your own.”

“Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it’s not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley.”

“For a torture to be effective, the pain has to be spread out; it has to come at regular intervals, with no end in sight. The water falls , drop after drop after drop, like the second hand of a watch, carving up time. The shock of each individual drop is insignificant, but the sensation is impossible to ignore. At first, one might manage to think about other things, but after five hours, after ten hours, it becomes unendurable. The repeated stimulation excites the nerves to a point where they literally explode, and every sensation in the body is absorbed into that one spot on the forehead---indeed, you come to feel that you are nothing but a forehead, into which a fine needle is being forced millimeter by millimeter. You can’t sleep or even speak, hypnotized by a suffering that is greater than any mere pain. In general, the victim goes mad before a day has passed.”

“When we grow up, we find ways to hide our anxieties, our loneliness, our fear and sorrow. But children hide nothing, putting everything into their tears, which they spread liberally about for the whole world to see.”

“It was clear that he didn't remember me from one day to the next. The note clipped to his sleeve simply informed him that it was not our first meeting, but it could not bring back the memory of the time we had spent together.”