705 Quotes About Mathematics

Note that in the above construction we made a number of choices; here we must beware. Choosing a good categorification – like designing a good algebraic structure such as that of preorders or quantales – is part of the art of mathematics. There is no prescribed way to categorify, and the success of a chosen categorification is rather empirical: its richer structure should allow us more insights into the subject we want to model.

A physical law must possess mathematical beauty

Our true needs are deeper – yet in our modern society most of us reflexively and relentlessly pursue wealth, consumer goods and admiration. We have learned from Perelman's mathematics. Perhaps we should also pause to reflect on ourselves and learn from Perelman's attitude towards life.

Transire suum pectus mundoque potiri. - S'élever au-dessus de soi-même et conquérir le monde.

there was no shame in admitting you didn't have the answer, it was a necessary step toward the truth. It was as important to teach us about the unknown or the unknowable as it was to teach us what had already been safely proven.

If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

If you could get a “God’s eye view” of the universe from outside it, all you would “see” is just an immense equation with infinite variables relentlessly unfolding in a bewildering dance of competing mathematical functions. We ourselves are self-contained and eternal nodes of the cosmic equation. We have our own solution to our own equation: to become God.

Any theory on the principles of mathematics must always be inductive i.e. it must lie in the fact that the theory in question enables us to deduce ordinary mathematics.

Mathematics is the most mysterious subject of all. The properties of numbers deliver endless miracles. Who needs God when mathematics gives us so much more? Mathematics is the God factory: it does nothing but generate Gods … an infinity of them.