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.

The lack of real contact between mathematics and biology is either a tragedy, a scandal or a challenge, it is hard to decide which.

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.

The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated.

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

The advice we give others is the advice that we ourselves need.

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