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

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.

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).

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

There is something in statistics that makes it very similar to astrology.

The progress of mathematics can be viewed as progress from the infinite to the finite.

Mathematicians also make terrible salesmen. Physicists can discover the same thing as a mathematician and say 'We've discovered a great new law of nature. Give us a billion dollars.' And if it doesn't change the world, then they say, 'There's an even deeper thing. Give us another billion dollars.'