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

The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

Seek simplicity but distrust it.

It takes an extraordinary intelligence to contemplate the obvious.

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

Human life is driven forward by its dim apprehension of notions too general for its existing language.

Other nations of different habits are not enemies: they are godsends. Men require of their neighbours something sufficiently akin to be understood, something sufficiently different to provoke attention, and something great enough to command admiration. We must not expect, however, all the virtues.