Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.
Cassius Jackson KeyserIt 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.
Cassius Jackson KeyserThe 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.
Cassius Jackson KeyserMathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.
Cassius Jackson KeyserThe present is no more exempt from the sneer of the future than the past has been.
Cassius Jackson KeyserIf 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.
Cassius Jackson Keyser