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.

[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.

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.

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

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.