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.

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.

There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. It is only myth that attempts to say how the universe came to be, either four thousand or twenty billion years ago.

When in doubt wear red.

As I think through the issue of funding the rebuilding of Iraq, I think about the analogy of a bankruptcy proceeding. There is no doubt that Iraq as a country is bankrupt.

After having dispatched a meal, I went ashore, and found no habitation save a single house, and that without an occupant; we had no doubt that the people had fled in terror at our approach, as the house was completely furnished.

If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things.

We criticize, copy, patronize, idolize and insult but we never doubt that the U.S. has a unique position in the history of human hopes.

If you've got talent, stick with it... because talent wins out, without a doubt.

That a great battle must soon be fought no one could doubt; but, in the apparent and perhaps real absence of plan on the part of Lee, it was impossible to foretell the precise scene of the encounter.

I would not be gotten into a schoolhouse until I was eight years old. Nor did I accomplish much after I started. I doubt if I had gone to school six months in all when my father died. I was fourteen at the time.

No doubt Western civilization has in the past been full of wars and revolutions, and the national elements in our culture, even when they were ignored, always provided an unconscious driving force of passion and aggressive self-assertion.

You have to not listen to the nay sayers because there will be many and often they'll be much more qualified than you and cause you to sort of doubt yourself.

It has since been agreed that speeches given in English will be translated into French and vice versa, and even into German and Italian when necessary. No doubt translations into Esperanto will also soon be in demand.

Who has suffered? The families of the dead, no doubt. But a greater loss was inflicted on Pakistan because, as I said, we lost the pillars of our society.

I find that the best way to do things is to constantly move forward and to never doubt anything and keep moving forward, if you make a mistake say you made a mistake.

I know that we're being inexorably taken over by the Americans. Without a doubt. I don't mean invaded or anything like that, just taken over. By degrees.

My esoteric doctrine, is that if you entertain any doubt, it is safest to take the unpopular side in the first instance. Transit from the unpopular, is easy... but from the popular to the unpopular is so steep and rugged that it is impossible to maintain it.

What matters to us, the judgment of men? What have we to doubt, since we are pure before life?

Doubt is part of all religion. All the religious thinkers were doubters.

Should doubt knock at your doorway, just say to those skeptical, disturbing, rebellious thoughts, I propose to stay with my faith, with the faith of my people.

When in doubt, take more time.

The road to perseverance lies by doubt.

It's a technical, fairly difficult job that has no particular political connotations, so I doubt there are any big campaign contributors dying to be on the Fed. And remember, it doesn't pay very well, certainly by Republican standards.

We work n the dark - we do what we can - we give what we have. Our doubt is our passion and our passion is our task. The rest is the madness of art.

Roger King is, without a doubt, the greatest salesman in the history of anything. And I don't ever limit him just to television. He could sell you anything.

In arriving at a decision in a question of doubt, the apostles in the Acts were guided solely by their sense of the Spirit behind the action, not by any speculations as to consequences which might ensue. And so they found the truth.

To get an Oscar would be an incredible moment in my career, there is no doubt about that. But the 'Lord of the Rings' films are not made for Oscars, they are made for the audience.

I no doubt deserved my enemies, but I don't believe I deserved my friends.

If you look at the whole thing, I think the most gratifying thing is my kids, without a doubt.