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

Philosophy is the self-correction by consciousness of its own initial excess of subjectivity.

The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.

Education with inert ideas is not only useless; it is above all things harmful.

Through and through the world is infested with quantity: To talk sense is to talk quantities. It is no use saying the nation is large. . . . How large? It is no use saying the radium is scarce. . . . How scarce? You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.

What is morality in any given time or place? It is what the majority then and there happen to like and immorality is what they dislike.

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.