One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it

Some people have got a mental horizon of radius zero and call it their point of view.

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

We do not master a scientific theory until we have shelled and completely prised free its mathematical kernel.

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

We ought not to believe those who today, adopting a philosophical air and with a tone of superiority, prophesy the decline of culter and are content with the unknowable in a self-satisfied way. For us there is no unknowable, and in my opinion there is also non whatsoever for the natural sciences. In place of this foolish unknowable, let our watchword on the contrary be: we must know - we shall know.

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.