That knowledge which adds greatness to character is knowledge so handled as to transform every phase of immediate experience.

Every intellectual revolution which has ever stirred humanity into greatness has been a passionate protest against inert ideas. Then, alas, with pathetic ignorance of human psychology, it has proceeded by some educational scheme to bind humanity afresh with inert ideas of its own fashioning.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute by rational interpretation.

Every philosophy is tinged with the coloring of some secret imaginative background, which never emerges explicitly into its train of reasoning.

Now in creative thought common sense is a bad master. Its sole criterion for judgement is that the new ideas shall look like the old ones. In other words it can only work by suppressing originality.

We must not expect simple answers to far-reaching questions. However far our gaze penetrates, there are always heights beyond which block our vision.