The fact of the religious vision, and its history of persistent expansion, is our one ground for optimism. Apart from it, human life is a flash of occasional enjoyments lighting up a mass of pain and misery, a bagatelle of transient experience.

The worship of God is not a rule of safety - it is an adventure of the spirit, a flight after the unattainable.

Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.

Civilization advances by extending the number of important operations which we can perform without thinking of them.

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.

No Roman ever died in contemplation over a geometrical diagram.

With the sense of sight, the idea communicates the emotion, whereas, with sound, the emotion communicates the idea, which is more direct and therefore more powerful.