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

It is a common public relations gimmick to give the entire credit for the solution of famous problems to the one mathematician who is responsible for the last step.

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

How did he do it? He must be a genius!

Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).

The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated.

If we have no idea why a statement is true, we can still prove it by induction.