True courage is not the brutal force of vulgar heroes, but the firm resolve of virtue and reason.

The antithesis between a technical and a liberal education is fallacious. There can be no adequate technical education which is not liberal, and no liberal education which is not technical.

The factor in human life provocative of a noble discontent is the gradual emergence of a sense of criticism, founded upon appreciation of beauty, and of intellectual distinction, and of duty.

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.

Learning preserves the errors of the past, as well as its wisdom. For this reason, dictionaries are public dangers, although they are necessities.

The way in which the persecution of Galileo has been remembered is a tribute to the quiet commencement of the most intimate change in outlook which the human race had yet encountered. Since a babe was born in a manger, it may be doubted whether so great a thing has happened with so little stir

The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.