“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.”

“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.”

“A problem isn't finished just because you've found the right answer.”

“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.”

“Because he had been- and in many ways still was- such a brilliant man, he no doubt understood the nature of his memory problem. It wasn't pride that prevented him from asking for help but a deep aversion to causing more trouble than necessary for those of us who lived in the normal world.”

“He preferred smart questions to smart answers.”

“Eternal truths are ultimately invisible, and you won't find them in material things or natural phenomena, or even in human emotions.”