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.

Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding.

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.'

Mathematicians - for what they do - are really poorly rewarded. And it's a very competitive field, almost as bad as being a concert pianist.

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

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