Die ganzen Zahlen hat der liebe Gatt gemacht, alles andere ist Menschenwerk.
The dear God has made the whole numbers, all the rest is man's work.

Tolle numerum omnibus rebus et omnia pereunt.
Take from all things their number and all shall perish.

All is number

All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.

I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. 'No,' he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.'

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.

It is agreed that all sound which is the material of music is of three sorts. First is harmonica, which consists of vocal music; second is organica, which is formed from the breath; third is rhythmica, which receives its numbers from the beat of the fingers. For sound is produced either by the voice, coming through the throat; or by the breath, coming through the trumpet or tibia, for example; or by touch, as in the case of the cithara or anything else that gives a tuneful sound on being struck.

It seems to me, that the only objects of the abstract sciences or of demonstration are quantity and number, and that all attempts to extend this more perfect species of knowledge beyond these bounds are mere sophistry and illusion.

Number is divided into even and odd. Even number is divided into the following: evenly even, evenly uneven, and unevenly uneven. Odd number is divided into the following: prime and incomposite, composite, and a third intermediate class (mediocris) which in a certain way is prime and incomposite but in another way secondary and composite.

O comfortable allurement, O ravishing perswasion, to deal with a Science, whose subject is so Auncient, so pure, so excellent, so surmounting all creatures... By Numbers propertie ... we may... arise, clime, ascend, and mount up (with Speculative winges) in spirit, to behold in the Glas of creation, the Forme of Formes, the Exemplar Number of all things Numerable... Who can remaine, therefore, unpersuaded, to love, allow, and honor the excellent sciehce of Arithmatike?

Referring to the decimal system of numeration or its equivalent (with some base other than 10): To what heights would science now be raised if Archimedes had made that discovery!
Gauss regarded this oversight as the greatest calamity in the history of science.

That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.

The judicial mind is too commonly characterized by a regard for a fourth decimal as the equal of a whole number.

The method of producing these numbers is called a sieve by Eratosthenes, since we take the odd numbers mingled and indiscriminate and we separate out of them by this method of production, as if by some instrument or sieve, the prime and incomposite numbers by themselves, and the secondary and composite numbers by themselves, and we find separately those that are mixed.

The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.

There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.

Those who think 'Science is Measurement' should search Darwin's works for numbers and equations.

To a mathematician the eleventh means only a single unit: to the bushman who cannot count further than his ten fingers it is an incalculable myriad.

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.

Whenever a man can get hold of numbers, they are invaluable: if correct, they assist in informing his own mind, but they are still more useful in deluding the minds of others. Numbers are the masters of the weak, but the slaves of the strong.

[Boswell]: Sir Alexander Dick tells me, that he remembers having a thousand people in a year to dine at his house: that is, reckoning each person as one, each time that he dined there. [Johnson]: That, Sir, is about three a day. [Boswell]: How your statement lessens the idea. [Johnson]: That, Sir, is the good of counting. It brings every thing to a certainty, which before floated in the mind indefinitely.