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Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of words.
I only know that when I study mathematics, I transport myself to another world, a world of exquisite beauty and truth. And in that world I am the person I like to be.
…numerical precision is the very soul of science, and its attainment affords the best, perhaps the only criterion of the truth of theories and the correctness of experiments.
It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
It appeared that way, Lawrence, but this raised the question of was mathematics really true or was it just a game played with symbols? In other words—are we discovering Truth, or just wanking?
Calculating does not equal mathematics. It's a subsection of it. In years gone by it was the limiting factor, but computers now allow you to make the whole of mathematics more intellectual.
It has become almost a cliche to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.
This is a global fight to get the right people in the right place and we're talking about people with PhDs in engineering, computer science, mathematics.
The object of pure physics is the unfolding of the laws of the intelligible world the object of pure mathematics that of unfolding the laws of human intelligence.