Every epoch has its character determined by the way its population reacts to the material events which they encounter.

Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.

Imagination is not to be divorced from the facts. It is a way of illuminating the facts.

The worth of men consists in their liability to persuasion. They can persuade and can be persuaded by the disclosure of alternatives, the better and the worse. Civilization is the maintenance of social order, by its own inherent persuasiveness as embodying the nobler alternative. The recourse to force, however, unavoidable, is a disclosure of the failure of civilization, either in the general society or in a remnant of individuals. Thus in a live civilization there is always an element of unrest.

The importance of an individual thinker owes something to chance. For it depends upon the fate of his ideas in the minds of his successors.

If a dog jumps into your lap, it is because he is fond of you; but if a cat does the same thing, it is because your lap is warmer.

No Roman ever died in contemplation over a geometrical diagram.