705 Quotes About Mathematics

The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.

Knowledge cuts and differentiates, while Wisdom soothes and integrates.

I should attempt to treat human vice and folly geometrically... the passions of hatred, anger, envy, and so on, considered in themselves, follow from the necessity and efficacy of nature... I shall, therefore, treat the nature and strength of the emotion in exactly the same manner, as though I were concerned with lines, planes, and solids.

Mathematics is the study of the mind-world interactions defined by models of intelligibility and knowledge.

No part of mathematics is ever, in the long run, "useless." Most of number theory has very few "practical" applications. That does not reduce its importance, and if anything it enhances its fascination. No one can predict when what seems to be a most obscure theorem may suddenly be called upon to play some vital and hitherto unsuspected role.

On Mars, the joke went, a man’s hole was his castle where values of castle approached dorm room.

We often hear that mathematics consists mainly of 'proving theorems.' Is a writer's job mainly that of 'writing sentences?

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

Music was not so very different from mathematics. It was all just patterns and sequences. The only difference was that they hung in the air instead of on a piece of paper. Dancing was a grand equation. One side was sound, the other movement. The dancer's job was to make them equal.