[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.

Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one microcentury as von Neumann used to say) everybody's attention will turn elsewhere.

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.'

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?

Our faith in Mathematics is not likely to wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else.

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

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.