Nowadays we can do computer experiments using Mathematica, and even solve a system of 42 equations. This offers another route to knowledge, rather than mere ideas.

In madness, I thought I was the most important person in the world.

In a dream it's typical not to be rational.

I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.

I had been offered fellowships to enter as a graduate student at either Harvard or Princeton. But the Princeton fellowship was somewhat more generous, since I had not actually won the Putnam competition... Thus Princeton became the choice for my graduate study location.

There are things that tend to moderate with age. Schizophrenia is somewhat like that.

Nowadays we can do computer experiments using Mathematica, and even solve a system of 42 equations. This offers another route to knowledge, rather than mere ideas.