Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.

Puzzles are made of the things that the mathematician, no less than the child, plays with, and dreams and wonders about, for they are made of things and circumstances of the world he [or she] live in.

Mathematics is man's own handiwork, subject only to the limitations imposed by the laws of thought.

When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.

There is a famous formula, perhaps the most compact and famous of all formulas - developed by Euler from a discovery of de Moivre: e^(i pi) + 1 = 0... It appeals equally to the mystic, the scientist, the philosopher, the mathematician.

The testament of science is so continually in a flux that the heresy of yesterday is the gospel of today and the fundamentalism of tomorrow.

. . . we have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.