Quotes of All Topics . Occasions . Authors
The painter's portrait and the physicist's explanation are both rooted in reality, but they have been changed by the painter or the physicist into something more subtly imagined than the photographic appearance of things.
One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can't, almost surely you are not going to.
Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.
I have suffered a great deal from writers who have quoted this or that sentence of mine either out of its context or in juxtaposition to some incongruous matter which quite distorted my meaning, or destroyed it altogether.
It is commonly, but erroneously, believed that it is easy to ask questions. A fool, it is said, can ask questions that a wise man cannot answer. The fact is that a wise man can answer many questions that a fool cannot ask.
[Alternate translation:] The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity.
In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.
Repudiating the sensible world, which he neither sees himself nor believes from those who have, the Peripatetic joins combat by childish quibbling in a world on paper, and denies the Sun shines because he himself is blind.
In fact, we tend to think things have been getting much worse. In fact, over the last 50 years, almost everything in the world on a global scale has got better. And the way that Hans [ Rosling] did this - it was very good.
Some philosophers fail to distinguish propositions from judgements; ... But in the real world it is more important that a proposition be interesting than that it be true. The importance of truth is that it adds to interest.
Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used.
How comes it that a cripple does not offend us, but a fool does? Because a cripple recognizes that we walk straight, whereas a fool declares that it is we who are silly; if it were not so, we should feel pity and not anger.
Discourses on humility are a source of pride in the vain and of humility in the humble. So those on scepticism cause believers to affirm. Few men speak humbly of humility, chastely of chastity, few doubtingly of scepticism.
Without the knowledge of our wretchedness, the knowledge of God creates pride. With it, the knowledge of God creates despair. The knowledge of Christ offers a third way, because in him we find both God and our wretchedness.
In my judgment an organic machine new to nature never arises, since it always contains an infinity of organs so that it can express, in its own way, the whole universe; indeed, it always contains all past and present times.
Who has not hoped To outrage an enemy's dignity? Who has not been swept By the wish to hurt? And who has not thought that the impersonal world Deserves no better than to be destroyed By one fabulous sign of his displeasure?
Capablanca did not apply himself to opening theory (in which he never therefore achieved much), but delved deeply into the study of end-games and other simple positions which respond to technique rather than to imagination.
In its solitariness the spirit asks, What, in the way of value, is the attainment of life? And it can find no such value till it has merged its individual claim with that of the objective universe. Religion is world-loyalty.
The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide.
My life may be encapsulated by one of Graham Greene's "entertainments" titles: 'Loser Takes All'. Since I was thrown out of highschool for political reasons, I was free to study on my own and develop my own ways of thinking.
The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.
We find, therefore, under this orderly arrangement, a wonderful symmetry in the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that is not possible to obtain in any other way.
And what I learned in Church's course. He trained us intensively in his new system, which he was just developing. Two papers were presented. I think the second paper wasn't published until well after the course was finished.
Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
The secrets of nature are concealed; her agency is perpetual, but we do not always discover its effects; time reveals them from age to age; and although she is always the same in herself, she is not always equally well known.
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.
The values by which we are to survive are not rules for just and unjust conduct, but are those deeper illuminations in whose light justice and injustice, good and evil, means and ends are seen in fearful sharpness of outline.
It seems to be expected of every pilgrim up the slopes of the mathematical Parnassus, that he will at some point or other of his journey sit down and invent a definite integral or two towards the increase of the common stock.
The higher mental activities are pretty tough and resilient, but it is a devastating experience if the drive does stop. Some people lose it in their forties and can only stop. In England they are a source of Vice-Chancellors.
I look upon statistics as the handmaid of medicine, but on that very account I hold that it befits medicine to treat her handmaid with proper respect, and not to prostitute her services for controversial or personal purposes.
Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.
In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas.
We are all afraid for our confidence, for the future, for the world. That is the nature of the human imagination. Yet every man, every civilization, has gone forward because of its engagement with what it has set itself to do.
Parents can learn that parental authority doesn't depend on knowing everything. The more you pretend, the more risk that it'll be traumatic and damaging to the kids and their relationship with you when they find out the truth.
Natural selection certainly operates. It explains how bacteria will gain antibiotic resistance; it will explain how insects get insecticide resistance, but it doesn't explain how you get bacteria or insects in the first place.
What the learned world tends to offer is one second-hand scrap of information illustrating ideas derived from another second-hand scrap of information. The second-handedness of the learned world is the secret of its mediocrity.
The heart has its order, the mind has its own, which uses principles and demonstrations. The heart has a different one. We do not prove that we ought to be loved by setting out in order the causes of love; that would be absurd.
The gist is that good and evil are foreordained. What is foreordained comes necessarily to be after a prior act of divine volition...Rather, everything small and large is written and comes to be in a known and expected measure.
In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.
There is great exhilaration in breaking one of these things. ... Ramanujan gives no hints, no proof of his formulas, so everything you do you feel is your own.[About verifying Ramanujan's equations in a newly found manuscript.]
Thus God himself was too kind to remain idle and began to play the game of signatures signing his likeness unto the world: therefore I chance to think that all nature and the graceful sky are symbolized in the art of Geometria.
There are two reasons why I propose to make myself thoroughly and unashamedly happy by talking about myself. The first is that on several occasions, both in England and America, I have been told that I am a legendary character.
The principles of pleasure are not firm and stable. They are different in all mankind, and variable in every particular with such a diversity that there is no man more different from another than from himself at different times.
When we see an effect happen always in the same manner, we infer that it takes place by a natural necessity; as, for instance, that the sun will rise to morrow; but nature often deceives us, and will not submit to its own rules.
Scientific knowledge scarcely exists amongst the higher classes of society. The discussion in the Houses of Lords or of Commons, which arise on the occurrence of any subjects connected with science, sufficiently prove this fact.
A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it (whatever its value may be).
It seems to me there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally suprise me. I do not think of mathemaatics as invented but rather discovered.
A painter like Picasso, who runs through many periods and phases, ends up by saying all those things which are on the tip of the tongue of the age to say, and finally sterilizes the originality of his contemporaries and juniors.
Today the major reason for our interest in Flatland is that for the first time we can achieve some of the dreams of our ancestors a century ago and obtain direct visual experience of phenomena in a dimension higher than our own.
Thus, in its relation to Christianity, intelligent design should be viewed as a ground-clearing operation that gets rid of the intellectual rubbish that for generations has kept Christianity from receiving serious consideration.