God created infinity, and man, unable to understand infinity, had to invent finite sets.

Theorems are not to mathematics what successful courses are to a meal.

Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of cows, moving slowly in the direction they are being driven towards. If we make one point, we have a good chance that the audience will take the right direction; if we make several points, then the cows will scatter all over the field. The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture.

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

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.

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

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