Stan Ulam was lazy, ... He talked too much ... He was self-centered ... . He had an overpowering personality.

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.

We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"

Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, "How did he do it? He must be a genius!"

God created infinity, and man, unable to understand infinity, had to invent finite sets.

[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.

Mathematicians - for what they do - are really poorly rewarded. And it's a very competitive field, almost as bad as being a concert pianist.