Algebra is the metaphysics of arithmetic.

The mathematics is not there till we put it there.

We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about ‘and’.

Proof is the idol before whom the pure mathematician tortures himself.

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.

I have hardly ever known a mathematician who was capable of reasoning.

In mathematics you don’t understand things. You just get used to them.

I went off to college planning to major in math or philosophy – of course, both those ideas are really the same idea.

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Mathematics is the queen of the sciences.

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