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

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?

There is something in statistics that makes it very similar to astrology.

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.

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 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 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.