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.

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

Why was everyone dying? They had all been so alive just yesterday.

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.

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.