Quotes of All Topics . Occasions . Authors
One original thought is worth the sum total of human knowledge, because it advances the sum total of human knowledge by that one original thought.
I'm not John Lennon. I'm John Lennox. Now, 'imagine a world without' Stalin. The New Atheists are often silent about [the wrong done by atheists].
We mathematicians are used to the fact that our subject is widely misunderstood, perhaps more than any other subject (except perhaps linguistics).
All I remember about the examination is that there was a question on Sturm's theorem about equations, which I could not do then and cannot do now.
A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.
If there is something that I should know how to do but don't, it bugs me. I feel like I have to sit down and work out exactly what the problem is.
My occupation is an open question. I was once an assistant professor of mathematics. Since then, I have spent time living in the woods of Montana.
It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.
Rivers are roads that move and carry us whither we wish to go. [Fr., Les rivieres sont des chemins qui marchant et qui portent ou l'on veut aller.]
I would have far more fear of being mistaken, and of finding that the Christian religion was true, than of not being mistaken in believing it true.
The present is never the mark of our designs. We use both past and present as our means and instruments, but the future only as our object and aim.
E? loquence quipersuade par douceur, non par empire, en tyran, non en roi. Eloquence should persuade gently, not by force or like a tyrant or king.
Faith affirms many things, respecting which the senses are silent, but nothing that they deny. It is superior, but never opposed to their testimony
Every present state of a simple substance is the natural consequence of its preceding state, in such a way that its present is big with its future.
When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.
Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
The strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects, most deserving to be known.
Computers are here to stay. It is a major challenge for the future to use computers efficiently in combinatorics without losing its special appeal.
There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think.
The only goal of science is the honour of the human spirit, and a question in number theory is worth a question concerning the system of the world.
The big problem is that people don't believe a revolution is possible, and it is not possible precisely because they do not believe it is possible.
We think in generalities, but we live in detail. To make the past live, we must perceive it in detail in addition to thinking of it in generalities.
The mind naturally makes progress, and the will naturally clings to objects; so that for want of right objects, it will attach itself to wrong ones.
Le silence est la plus grande perse cution: jamais les saints ne se sont tus. Silence is the greatest of all persecutions: no saint was ever silent.
It is unworthy of excellent men to lose hours like slaves in the labor of calculation which could be relegated to anyone else if machines were used.
None are too wise to be mistaken, but few are so wisely just as to acknowledge and correct their mistakes, and especially the mistakes of prejudice.
To me the most interesting thing about man is that he is an animal who practices art and science and in every known society practices both together.
Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.
The Nazis victimized some people for what they did, some for what they refused to do, some for what they were, and some for the fact that they were.
Christianity, sharing the Christian faith, in common, gives you instant friendship, and that is the remarkable thing, because it transcends culture.
Indeed, nowadays no electrical engineer could get along without complex numbers, and neither could anyone working in aerodynamics or fluid dynamics.
The simplest type of breakdown exhibits itself as an oscillation in a goal-seeking process which appears only when that process is actively invoked.
It is still an unending source of surprise for me how a few scribbles on a blackboard or on a piece of paper can change the course of human affairs.
The foundations of the world are to be found, not in the cognitive experience of conscious thought, but in the aesthetic experience of everyday life.
We must not expect simple answers to far-reaching questions. However far our gaze penetrates, there are always heights beyond which block our vision.
We are not satisfied with real life; we want to live some imaginary life in the eyes of other people and to seem different from what we actually are.
The authority of reason is far more imperious than that of a master; for he who disobeys the one is unhappy, but he who disobeys the other is a fool.
We like security: we like the pope to be infallible in matters of faith, and grave doctors to be so in moral questions so that we can feel reassured.
When we would think of God, how many things we find which turn us away from Him, and tempt us to think otherwise. All this is evil, yet it is innate.
Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.
As Littlewood said to me once [of the ancient Greeks], they are not clever school boys or "scholarship candidates," but "Fellows of another college."
The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.
I have said more than once, that I hold space to be something purely relative, as time; an order of coexistences, as time is an order of successions.
There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.
Just as the eye was made to see colours, and the ear to hear sounds, so the human mind was made to understand, not whatever you please, but quantity.
Ships and sails proper for the heavenly air should be fashioned. Then there will also be people, who do not shrink from the dreary vastness of space.
A precisian professor had the habit of saying: "... quartic polynomial ax^4+bx^3+cx^2+dx+e , where e need not be the base of the natural logarithms."
I later spent... five to eight months in hospitals in New Jersey, always on an involuntary basis, and always attempting a legal argument for release.
The most fruitful areas for the growth of the sciences were those which had been neglected as a no-man's land between the various established fields.
The atheist is cheating whenever he makes a moral judgment, acting as though it has an objective reference, when his philosophy in fact precludes it.