... and it is probably that there is some secret here which remains to be discovered.

Notwithstanding all that has been discovered since Newton's time, his saying that we are little children picking up pretty pebbles on the beach while the whole ocean lies before us unexplored remains substantially as true as ever, and will do so though we shovel up the pebbles by steam shovels and carry them off in carloads.

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

Law is par excellence the thing that wants a reason. Now the only possible way of accounting for the laws of nature, and for uniformity in general, is to suppose them results of evolution.

It is... easy to be certain. One has only to be sufficiently vague.

It is impossible not to envy the man who can dismiss reason, although we know how it must turn out at last.

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.