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.

THE COMPUTER IS JUST AN INSTRUMENT for doing faster what we already know how to do slower. All pretensions to computer intelligence and paradise-tomorrow promises should be toned down before the public turns away in disgust. And if that should happen, our civilization might not survive.

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.

[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.

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

A technique is a trick that works.