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.

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.

I have had my results for a long time: but I do not yet know how I am to arrive at them.

To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.

God does arithmetic.

To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.

Life stands before me like an eternal spring with new and brilliant clothes.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

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.

Mathematicians stand on each other's shoulders.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.

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.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.

The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.

When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.

It is not knowledge but the act of learning not possession but the act of getting there which grants the greatest enjoyment.

Mathematics is concerned only with the enumeration and comparison of relations.

Mathematics is the queen of science.

This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem - and in particular to perform integration - you have to be smart about which integration technique should be used: integration by partial fractions, integration by parts, and so on.

The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.

God does arithmetic.

Algebra is the metaphysics of arithmetic.

The numbers may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete equipment of the mathematician.

He who refuses to do arithmetic is doomed to talk nonsense.

We have the most crude accounting tools. It's tragic because our accounts and our national arithmetic doesn't tell us the things that we need to know.

Crystals grew inside rock like arithmetic flowers. They lengthened and spread, added plane to plane in an awed and perfect obedience to an absolute geometry that even stones - maybe only the stones - understood.

The desire to economize time and mental effort in arithmetical computations, and to eliminate human liability to error is probably as old as the science of arithmetic itself.

What would life be without arithmetic, but a scene of horrors?

I was always looking ahead. I used to do all kinds of things for entertainment. When I was young, we had no radio, no TV. We were 30 miles from the public library, out in the sticks in Western Kansas, and so I'd do arithmetic exercises.

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.

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.

I refer, of course, to the debts our nation has amassed for itself over decades of indulgence. It is the new Red Menace, this time consisting of ink. We can debate its origins endlessly and search for villains on ideological grounds, but the reality is pure arithmetic.

In the arithmetic of love, one plus one equals everything, and two minus one equals nothing.

Music is the arithmetic of sounds as optics is the geometry of light.

Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.

Schools are really bad now. Schools are not only bad in reading, writing and arithmetic, they're worse in cultural aspects, like in music and art. They don't teach you anything.

The hardest arithmetic to master is that which enables us to count our blessings.

Arithmetic is where the answer is right and everything is nice and you can look out of the window and see the blue sky - or the answer is wrong and you have to start over and try again and see how it comes out this time.

I said, 'Okay, it's the year 2000, I'm getting a computer and a Palm Pilot.' I know how to check my e-mail, and I've listed some phone numbers on it. Half the time the battery has gone out so I can't use it.

It's a tough thing to know that when you're making your album, you're going to end up collaborating with, say, Wal-Mart, on your artwork. That just sucks. And the pressure behind getting the numbers real fast is, to me, dizzying.

I'm writing a book. I've got the page numbers done.

I mean it's the most objective industry in the world. If your numbers stink, you're out. If your numbers are good, you get more money. It's the most Darwinian, it's beautiful, it's brutal, it works.

You know too well the forces which compose their army to dread their superior numbers.

He's a world-famous name to people who care about his music, but there are many people who have never heard of George Gershwin and those numbers increase.

But that is the only thing that slows me down is the system. No one, two or three was big enough to slow me down, only the system. It was the system that slowed me down to make my numbers fall. Not because I am older.

I think my numbers speak for themselves.