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.

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.

The present is no more exempt from the sneer of the future than the past has been.

If people would stop objectifying abstractions (which they probably never will), or if they would stop objectifying the abstractions they make consciously (which they might learn to do), at least half the pseudo-questions befuddling the world today - as they have befuddled it since time immemorial - would vanish. And that would be a very, very great gain.

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.

The pursuit of excellence is the proper vocation of man.