...it is certain that the real function of art is to increase our self-consciousness; to make us more aware of what we are, and therefore of what the universe in which we live really is. And since mathematics, in its own way, also performs this function, it is not only aesthetically charming but profoundly significant. It is an art, and a great art.

If you can give your son or daughter only one gift, let it be enthusiasm.

I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. . . But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming-- and a little mad.

The most extensive computation known has been conducted over the last billion years on a planet-wide scale: it is the evolution of life. The power of this computation is illustrated by the complexity and beauty of its crowning achievement, the human brain.

There is an astonishing imagination, even in the science of mathematics... We repeat, there was far more imagination in the head of Archimedes than in that of Homer.

You can not apply mathematics as long as words still becloud reality.

God does not care about our mathematical difficulties. He integrates empirically.

Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.

Mathematics transfigures the fortuitous concourse of atoms into the tracery of the finger of God.

My specific goal is to revolutionize the future of the species. Mathematics is just another way of predicting the future.