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

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

[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.

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

Why is it that Serge Lange's Linear Algebra, published by no less a Verlag than Springer, ostentatiously displays the sale of a few thousand copies over a period of fifteen years, while the same title by Seymour Lipschutz in the The Schaum's Outlines will be considered a failure unless it brings in a steady annual income from the sale of a few hundred thousand copies in twenty-six languages?

Very little mathematics has direct applications - though fortunately most of it has plenty of indirect ones.

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).