Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.

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

It is not too much to say that next after the passion to learn there is no quality so indispensable to the successful prosecutionof science as imagination. Find me a people whose early medicine is not mixed up with magic and incantations, and I will find you a people devoid of all scientific ability.

And what, then, is belief? It is the demi-cadence which closes a musical phrase in the symphony of our intellectual life.

Some think to avoid the influence of metaphysical errors, by paying no attention to metaphysics; but experience shows that these men beyond all others are held in an iron vice of metaphysical theory, because by theories that they have never called in question.

True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men. To employ these rare minds on such work is like running a steam engine by burning diamonds.

We do not really think, we are barely conscious, until something goes wrong.