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.

It belongs to the self-respect of intellect to pursue every tangle of thought to its final unravelment.

There are no whole truths: all truths are half-truths. It is trying to treat them as whole truths that plays to the devil.

Not ignorance, but ignorance of ignorance, is the death of knowledge.

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

The way in which the persecution of Galileo has been remembered is a tribute to the quiet commencement of the most intimate change in outlook which the human race had yet encountered. Since a babe was born in a manger, it may be doubted whether so great a thing has happened with so little stir

But you can catch yourself entertaining habitually certain ideas and setting others aside; and that, I think, is where our personal destinies are largely decided.