Everyone is a philosopher. Not everyone is good at it.

There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.

Seek simplicity, and distrust it.

It is natural to think that an abstract science cannot be of much importance in affairs of human life, because it has omitted from its consideration everything of real interest.

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.

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

It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery - Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.