Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.

Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs