Quotes of All Topics . Occasions . Authors
Kind words do not cost much. They never blister the tongue or lips. They make other people good-natured. They also produce their own image on men's souls, and a beautiful image it is.
Human life is thus only an endless illusion. Men deceive and flatter each other. No one speaks of us in our presence as he does when we are gone. Society is based on mutual hypocrisy.
The imagination enlarges little objects so as to fill our souls with a fantastic estimate; and, with rash insolence, it belittles the great to its own measure, as when talking of God.
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.
Indignant reply to the blatent sex discrimination expressed in a colleague's opposition when Hilbert proposed appointing Emmy Noether as the first woman professor at their university.
Archimedes, Newton, and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit.
If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician.
A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life.
The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.
I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general.
The mathematical education of the young physicist [Albert Einstein] was not very solid, which I am in a good position to evaluate since he obtained it from me in Zurich some time ago.
Man is a singular creature. He has a set of gifts which make him unique among the animals, so that unlike them, he is not a figure in the landscape, he is the shaper of the landscape.
One aim of physical sciences had been to give an exact picture the material world. One achievement of physics in the twentieth century has been to prove that that aim is unattainable.
A most unfailing experience... of the excitement of sublunary (that is, human) natures by the conjunctions and aspects of the planets has instructed and compelled my unwilling belief.
God created two acts of folly. First, He created the Universe in a Big Bang. Second, He was negligent enough to leave behind evidence for this act, in the form of microwave radiation.
The military gave me structure and process. That reflects on the way I believe we should handle legislative matters. If we do it that way in any field, the results are usually better.
Given two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime.
With sixty professors there are roughly eighteen hundred pairs of professors. Out of that many pairs it was not surprising that there were some whose members did not like one another.
The vitality of thought is in adventure. Ideas won't keep. Something must be done about them. When the idea is new, its custodians have fervor, live for it, and if need be, die for it.
The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions.
Mathematics... is a bit like discovering oil. ... But mathematics has one great advantage over oil, in that no one has yet ... found a way that you can keep using the same oil forever.
Bless yourself with holy water, have Masses said, and so on; by a simple and natural process this will make you believe, and will dull you - will quiet your proudly critical intellect.
Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
I wrote a great deal during the next ten [early] years,but very little of any importance; there are not more than four or five papers which I can still remember with some satisfaction.
We may say, that not only the soul (the mirror of an indestructible universe) is indestructible, but also the animal itself is, although its mechanism is frequently destroyed in parts.
I like to employ a form of repetition, in which the same elements recur but in different and unexpected ways. rather than being discarded as soon as they are understood or passed over.
There are some current 'theories' that, when divested of begged questions, reduce to the non-controversial statement, 'Here are some facts and there may be some relation between them.'
Most students who take math classes aren't going to be mathematicians. They're going to be engineers, statisticians - in many ways, that's the more important mission of math education.
Intuition makes much of it; I mean by this the faculty of seeing a connection between things that in appearance are completely different; it does not fail to lead us astray quite often.
Jesus was in a garden, not of delight as the first Adam, in which he destroyed himself and the whole human race, but in one of agony, in which he saved himself and the whole human race.
Reverend Fathers, my letters did not usually follow each other at such close intervals, nor were they so long.... This one would not be so long had I but the leisure to make it shorter.
L'homme n'est qu'un sujet plein d'erreur, naturelle et ineffa c° able sans la gra" ce. Man is nothing but a subject full of natural error that cannot be eradicated except through grace.
Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view.
Asked for a testimony to the effect that Emmy Noether was a great woman mathematician, he said: I can testify that she is a great mathematician, but that she is a woman, I cannot swear.
The analysts try in vain to conceal the fact that they do not deduce: they combine, they compose ... when they do arrive at the truth they stumble over it after groping their way along.
There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.
...a distinction must be made between true and false ideas, and that too much rein must not be given to a man's imagination under pretext of its being a clear and distinct intellection.
What I would pay much more attention to are the few points where the player can inadvertently make a career decision. Most players end up back-tracking, though some actually enjoy this.
Sex was invented as a biological instrument by (say) the green algae. But as an instrument in the ascent of man which is basic to his cultural evolution, it was invented by man himself.
Every religion contains, in varying degrees, elements of the soft and the hard. For the sake of world peace, dialogue within religions and among them must strengthen the softer aspects.
I dislike frontiers, political or intellectual, and I find that ignoring them is an essential catalyst for creative thought. Ideas should flow without hindrance in their natural course.
A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, I make it my first job to build one.
A theme that appears repeatedly in the writings of the social critics of the second half of the 20th century is the sense of purposelessness that afflicts many people in modern society.
Democracy...is a society in which the unbeliever feels undisturbed and at home. If there were only a half dozen unbelievers in America, their well-being would be a test of our democracy.
In this modern world, the celibacy of the medieval learned class has been replaced by a celibacy of the intellect which is divorced from the concrete contemplation of the complete facts.
Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth.
In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.
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.
The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.
The diversity of the phenomena of nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment.