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

The paradox is now fully established that the utmost abstractions are the true weapons with which to control our thought of concrete fact.

The main importance of Francis Bacon's influence does not lie in any peculiar theory of inductive reasoning which he happened to express, but in the revolt against second-hand information of which he was a leader.

Great art is more than a transient refreshment. It is something which adds to the permanent richness of the soul's self-attainment. It justifies itself both by its immediate enjoyment, and also by its discipline of the inmost being. Its discipline is not distinct from enjoyment but by reason of it. It transforms the soul into the permanent realization of values extending beyond its former self.

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.

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise

Education is the acquisition of the art of the utilisation of knowledge.