Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are cavalry charges in a battle - they are limited in number, they require fresh horses, and must only be made at decisive moments.

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

I regret that it has been necessary for me in this lecture to administer a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are.

Learning is often spoken of as if we are watching the open pages of all the books which we have ever read, and then, when occasion arises, we select the right page to read aloud to the universe.

The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

The consequences of a plethora of half-digested theoretical knowledge are deplorable.

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.