Of the many forms of false culture, a premature converse with abstractions is perhaps the most likely to prove fatal to the growth of a masculine vigour of intellect.

There are as many forms of happiness as sorrow, though most prove fleeting.

Our intelligence cannot wall itself up alive, like a pupa in a chrysalis. It must at any cost keep on speaking terms with the universe that engendered it.

Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave nether room nor demand for a theory of probabilities.

It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.