“Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail somebody 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.”
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.