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.

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

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.

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

[The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.

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