Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".

The examination system, and the fact that instruction is treated mainly as a training for a livelihood, leads the young to regard knowledge from a purely utilitarian point of view as the road to money, not as the gateway to wisdom.

What Galileo and Newton were to the seventeenth century, Darwin was to the nineteenth.

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

In his youth, Wordsworth sympathized with the French Revolution, went to France, wrote good poetry and had a natural daughter. At this period, he was a bad man. Then he became good, abandoned his daughter, adopted correct principles and wrote bad poetry.

In America everybody is of the opinion that he has no social superiors, since all men are equal, but he does not admit that he has no social inferiors, for, from the time of Jefferson onward, the doctrine that all men are equal applies only upwards, not downwards.

Mathematics rightly viewed possesses not only truth but supreme beauty.