The importance of an individual thinker owes something to chance. For it depends upon the fate of his ideas in the minds of his successors.

The difference between ancients and moderns is that the ancients asked what have we experienced, and moderns asked what can we experience.

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.

In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas.

Our reasonings grasp at straws for premises and float on gossamers for deductions.

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.