Every existence above a certain rank has its singular points; the higher the rank the more of them. At these points, influences whose physical magnitude is too small to be taken account of by a finite being may produce results of the greatest importance.

The mathematical difficulties of the theory of rotation arise chiefly from the want of geometrical illustrations and sensible images, by which we might fix the results of analysis in our minds.

Thoroughly conscious ignorance is the prelude to every real advance in science.

Francis Galton, whose mission it seems to be to ride other men's hobbies to death, has invented the felicitous expression 'structureless germs'.

One of the chief peculiarities of this treatise is the doctrine that the true electric current, on which the electromagnetic phenomena depend, is not the same thing as the current of conduction, but that the time-variation of the electric displacement must [also] be taken into account.

The mind of man has perplexed itself with many hard questions. Is space infinite, and in what sense? Is the material world infinite in extent, and are all places within that extent equally full of matter? Do atoms exist or is matter infinitely divisible?

In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data.