It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty.

It is a common observation that those who dwell continually upon their expectations are apt to become oblivious to the requirements of their actual situation.

Kepler's discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler-such penetrating minds as Descartes and Pascal-were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.

We, one and all of us, have an instinct to pray; and this fact constitutes an invitation from God to pray.

In all the works on pedagogy that ever I read — and they have been many, big, and heavy — I don't remember that any one has advocated a system of teaching by practical jokes, mostly cruel. That, however, describes the method of our great teacher, Experience.

No general description of the mode of advance of human knowledge can be just which leaves out of account the social aspect of knowledge. That is of its very essence. What a thing society is! The workingman, with his trade union, knows that. Men and women moving in polite society understand it, still better. But Bohemians, like me, whose work is done in solitude, are apt to forget that not only is a man as a whole little better than a brute in solitude, but also that everything that bears any important meaning to him must receive its interpretation from social considerations.

It is a common observation that a science first begins to be exact when it is quantitatively treated. What are called the exact sciences are no others than the mathematical ones.