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.

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.

And their conviction is that if it is done with that kind of purity it will go somewhere. I believe that with all my heart, but I'm not responsible for its going somewhere.

The compensation of a very early success is a conviction that life is a romantic matter. In the best sense one stays young.

Ronald Reagan's well documented final battles with Alzheimer's disease were fought with the same conviction and courage that his many public battles were fought.

Many hard comments have been made on my efforts in India from the side of the Congress party, yet I feel content in the deep conviction that the offer I traveled 22,000 miles to discuss with Indian leaders was a real contribution to a solution of our differences.

For a successful revolution it is not enough that there is discontent. What is required is a profound and thorough conviction of the justice, necessity and importance of political and social rights.

I was induced to establish several orders of merit, from conviction that emulation, well directed, becomes a useful servant; and, that the latent genius of some youth is more easily brought into action this way, than by the more sordid gratification of self-interest.

Music is a hobby, because I'm not making any money out of it, but I put just as much conviction into that as I do into my acting.

The deepest thing in any one is the conviction of the bad luck that follows boasting.

One of the dreariest spots on life's road is the point of conviction that nothing will ever again happen to you.

Insurance - an ingenious modern game of chance in which the player is permitted to enjoy the comfortable conviction that he is beating the man who keeps the table.

The whole conviction of my life now rests upon the belief that loneliness, far from being a rare and curious phenomenon, peculiar to myself and to a few other solitary men, is the central and inevitable fact of human existence.

Hope is not the conviction that something will turn out well but the certainty that something makes sense, regardless of how it turns out.

It was very important that it be done in such a way that it be executed with complete conviction. If I had done it both ways, if I was trying to cover myself in case it didn't work, then it would have been to no purpose.

Courage and conviction are powerful weapons against an enemy who depends only on fists or guns. Animals know when you are afraid; a coward knows when you are not.

I retired from public Business from a thorough Conviction that it was not in my Power to do any Good, and very much disgusted with Measures, which appeared to me inconsistent with common Policy and Justice.

And indeed this theme has been at the centre of all my research since 1943, both because of its intrinsic fascination and my conviction that a knowledge of sequences could contribute much to our understanding of living matter.

My personal conviction is that science is concerned wholly with truth, not with ethics.

There was an implicit conviction that the UN would be stronger than the sum of its constituent member-states.

A large part of the present anxiety to improve the education of girls and women is also due to the conviction that the political disabilities of women will not be maintained.

I have arrived at the conviction that the neglect by economists to discuss seriously what is really the crucial problem of our time is due to a certain timidity about soiling their hands by going from purely scientific questions into value questions.

Liberals subscribe to the new flexible, pluralistic definition of the family; their defense of families carries no conviction.

I tried to instill a different motivation, to give them the security and the conviction that they were doing something good, something necessary, something useful - if you want to use a grandiose expression, that they were doing something for peace.

The ultimate goal of the educational system is to shift to the individual the burden of pursing his own education. This will not be a widely shared pursuit until we get over our odd conviction that education is what goes on in school buildings and nowhere else.

The trouble with this country is that there are too many politicians who believe, with a conviction based on experience, that you can fool all of the people all of the time.

In examining the evidence of the Christian religion, it is essential to the discovery of truth that we bring to the investigation a mind freed, as far as possible, from existing prejudice, and open to conviction.

When you take a stand out of deep conviction, people know. They may not even agree, but they ask, 'Do I want someone who is willing to take a hard stand and someone I can trust to do that when the chips are down?' They want that.

I have the conviction that excessive literary production is a social offence.

Honest conviction is my courage; the Constitution is my guide.