Quotes of All Topics . Occasions . Authors
Nowadays we can do computer experiments using Mathematica, and even solve a system of 42 equations. This offers another route to knowledge, rather than mere ideas.
If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.
Starting in the seventeenth century, the general theory of extreme values - maxima and minima - has become one of the systematic integrating principles of science.
Roughly speaking, this hypothesis asks whether drug use causes some of the diseases officially associated with AIDS, such as immunodeficiency and Kaposi's sarcoma.
Now more people are doing work that requires individual decision-making and problem-solving, and we need an educational system that will help develop those skills.
I am almost inclined to coin a word and call the appearance fluorescence, from fluor-spar, as the analogous term opalescence is derived from the name of a mineral.
It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.
I have been lucky to find very good collaborators who have taught me a lot, have introduced me to several new fields of mathematics, or have shown me new insights.
To pry into the secrets of this world, we must make experiments. But experiment is a clumsy instrument, afflicted with a fatal determinacy which destroys causality.
What can be seen on earth points to neither the total absence nor the obvious presence of divinity, but to the presence of a hidden God. Everything bears this mark.
We are only troubled by the fears which we, and not nature, give ourselves, for they add to the state in which we are the passions of the state in which we are not.
Nothing is good but mediocrity. The majority has settled that, and finds fault with him who escapes it at whichever end... To leave the mean is to abandon humanity.
La vraie e loquence se moque de l'e loquence, la vraie morale se moque de la morale. True eloquence has notime foreloquence, true morality has no time for morality.
Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there.
It is a common public relations gimmick to give the entire credit for the solution of famous problems to the one mathematician who is responsible for the last step.
Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
It is very much easier to divide your outlook on the world into two halves, to say that you know this belongs to the daily half and this belongs to the Sunday half.
[Lord Brougham's writings on the bee's cell contain] as striking examples of bad reasoning as are often to be met with in writings related to mathematical subjects.
The nervous system and the automatic machine are fundamentally alike in that they are devices, which make decisions on the basis of decisions they made in the past.
If the human being is condemned and restricted to perform the same functions over and over again, he will not even be a good ant, not to mention a good human being.
The more we get out of the world the less we leave, and in the long run we shall have to pay our debts at a time that may be very inconvenient for our own survival.
If a kid really is retarded and can only come up to a certain level, he will still have more success if what he learns is connected with something important to him.
Ada came from Lwów. She was a very good looking girl who was studying mathematics at the University of Geneva. For a few years I had an off-and-on romance with her.
With the sense of sight, the idea communicates the emotion, whereas, with sound, the emotion communicates the idea, which is more direct and therefore more powerful.
I know it's a rare privilege, but if one can really tackle something in adult life that means that much to you, then it's more rewarding than anything I can imagine.
The art of discovering the causes of phenomena, or true hypotheses, is like the art of deciphering, in which an ingenious conjecture often greatly shortens the road.
Emptiness is everywhere and it can be calculated, which gives us a great opportunity. I know how to control the universe. So tell me, why should I run for a million?
A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
It is not the business of science to inherit the earth, but to inherit the moral imagination; because without that, man and beliefs and science will perish together.
Some people are always critical of vague statements. I tend rather to be critical of precise statements; they are the only ones which can correctly be labeled wrong.
The pagans do not know God, and love only the earth. The Jews know the true God, and love only the earth. The Christians know the true God, and do not love the earth.
Of the many forms of false culture, a premature converse with abstractions is perhaps the most likely to prove fatal to the growth of a masculine vigour of intellect.
This means keeping many trails open at once, inevitably requiring a fairly 'parallel' plot. This plot should be discovered rather than announced, so show, don't tell.
If pushed, though, I'd say that the next stage will be reached when it it's no longer true that about 75% of the best games were written in 1980's on the way to that.
Fifty years from now if an understanding of man's origins, his evolution, his history, his progress is not in the common place of the school books we shall not exist.
There is one quality more important than know-how.... This is know-how by which we determine not only how to accomplish our purposes, but what our purposes are to be.
The mind has its illusions as the sense of sight; and in the same manner that the sense of feeling corrects the latter, reflection and calculation correct the former.
We feel much happier and more secure when we think we know precisely what to do, no matter what happens, then when we have lost our way and do not know where to turn.
"One and one make two" assumes that the changes in the shift of circumstance are unimportant. But it is impossible for us to analyze this notion of unimportant change.
Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts. Math and physics are very pleasant things to do.
The object of pure Physic[s] is the unfolding of the laws of the intelligible world; the object of pure Mathematic[s] that of unfolding the laws of human intelligence.
Some people are always critical of vague statements. I tend rather to be critical of precise statements; they are the only ones which can correctly be labeled 'wrong'.
If things are nice there is probably a good reason why they are nice: and if you do not know at least one reason for this good fortune, then you still have work to do.
There is nothing wrong with violence in itself. In any particular case, whether violence is good or bad depends on how it is used and the purpose for which it is used.
I tried reading Hilbert. Only his papers published in mathematical periodicals were available at the time. Anybody who has tried those knows they are very hard reading.
Lord, help me to do great things as though they were little, since I do them with your power; And little things as though they were great, since I do them in your name!
Imagination cannot make fools wise, but it makes them happy, as against reason, which only makes its friends wretched: one covers them with glory, the other with shame.
Curiosity is only vanity. Most frequently we wish not to know, but to talk. We would not take a sea voyage for the sole pleasure of seeing without hope of ever telling.
I had not thought of this regular decrease of gravity, namely that it is as the inverse square of the distance; this is a new and highly remarkable property of gravity.
There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician.