God ever arithmetizes.

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God ever arithmetizes.

In H. Eves,
Mathematical Circles
Revisited, Boston:
Prindle, Weber and
Schmidt, 1971.

One should always generalize.

(Man muss immer generalisieren.)

In P. Davis and R.
Hersh, The
Mathematical
Experience, Boston:
Birkhauser, 1981.

It is true that Fourier had the opinion that the principal aim of mathematics was public utility and explanation of natural phenomena; but a philosopher like him should have known that the sole end of science is the honor of the human mind, and that under this title a question about numbers is worth as much as a question about the system of the world.

In N. Rose,
Mathematical Maxims
and Minims, Raleigh,
NC: Rome Press Inc.,
1988.

What vexes me most is, that my female friends, who could bear me very well a dozen years ago, have now forsaken me, although I am not so old in proportion to them as I formerly was: which I can prove by arithmetic, for then I was double their age, which now I am not.

Letter to Alexander
Pope, 7 Feb. 1736.

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.

Joseph Fourier

The calculus was the first achievement of modern mathematics, and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

John von Neumann

The experimental verification of a theory concerning any natural phenomenon generally rests on the result of an integration.

J. W. Mellor

The use of the axiomatic method, by showing clearly the source of each proposition and by showing which were the essential hypotheses and the superfluous hypotheses, has revealed unsuspected analogies and permitted extended generalizations; the origin of the modern developments of algebra, topology and group theory is to be found only in the employment of axiomatic methods.

Jeremy Gray, *The
Hilbert
Challenge* (2000)

Here is my picture of mathematics now. It is a ball of wool, a tangled hank where all mathematics react upon another in an almost unpredictable way. And then in this ball of wool, there are a certain number of threads coming out in all directions and not connecting with anything else. ... [T]he Bourbaki method is very simple: we cut the threads.

I would in the future make a machine, which would simultaneously print ... on paper any arbitrary arithmetical progression .... After setting the first figure, all one has to do is to turn a handle.

In *The Difference
Engine,* by Doron
Swade, Viking, 2000