If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.

The next-most difficult thing in the world is to get perspective. The most difficult is to keep it.

Absolute certainty is a privilege of uneducated minds and fanatics. - It is, for scientific folk, an unattainable ideal.

It is commonly, but erroneously, believed that it is easy to ask questions. A fool, it is said, can ask questions that a wise man cannot answer. The fact is that a wise man can answer many questions that a fool cannot ask.

The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.

Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.

Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.