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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.
explaining why a formula is beautiful is like trying to explain why the stars are beautiful.”
“A problem has a rhythm of its own, just like a piece of music,” the Professor said. “Once you get the rhythm, you get the sense of the problem as a whole, and you can see where the traps might be waiting.”
Among the many things that made the Professor an excellent teacher was the fact that he wasn’t afraid to say “we don’t know.” For the Professor, there was no shame in admitting you didn’t have the answer, it was a necessary step toward the truth. It was as important to teach us about the unknown or the unknowable as it was to teach us what had already been safely proven.
“The mathematical order is beautiful precisely because it has no effect on the real world. Life isn’t going to be easier, nor is anyone going to make a fortune, just because they know something about prime numbers.
“Eternal truths are ultimately invisible, and you won’t find them in material things or natural phenomena, or even in human emotions. Mathematics, however, can illuminate them, can give them expression—in fact, nothing can prevent it from doing so.”