Henri Poincaré - The foundations of science

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Isolated amidst a nature where everything was a mystery to him, terrified at each unexpected manifestation of incomprehensible forces, he [primitive man] was incapable of seeing in the conduct of the universe anything but caprice.

Henri Poincaré
Man, then, can not be happy through science, but to-day he can be much less be happy without it.

Henri Poincaré
Science is a rule of action which is successful...

Henri Poincaré
It is not sufficient for a theory to affirm no false relations; it must not hide true relations.

Henri Poincaré
Chance is only the measure of our ignorance.

Henri Poincaré
There are facts common to several sciences, which seem the common source of streams diverging in all directions and which are comparable to that knoll of Saint Gothard whence spring waters which fertilize four different valleys.

Henri Poincaré
The facts of greatest outcome are those we think simple; may be they really are so, because they are influenced only by a small number of well-defined circumstances, may be they take on an appearance of simplicity because the various circumstances upon which they depend obey the laws of chance and so come to mutually compensate.

Henri Poincaré
Space is only a word that we have believed a thing.

Henri Poincaré
The historian, the physicist, even, must make a choice among facts; the head of the scientist, which is only a corner of the universe, could never contain the universe entire; so that among the innumerable facts nature offers, some will be passed by, others retained.

Henri Poincaré
Nothing but facts are of importance. John Lackland passed by here. Here is something that is admirable. Here is a reality for which I would give all the theories in the world." That is the language of the historian. The physicist would say rather: "John Lackland passed by here; that makes no difference to me, for he never will pass this way again."

Henri Poincaré
Today we no longer beg of nature; we command her, because we have discovered certain of her secrets and shall discover others each day. We command her in the name of laws she cannot challenge, because they are hers; these laws we do not madly ask her to change, we are the first to submit to them. Nature can only be governed by obeying her.

Henri Poincaré
A final word about the theory of errors. Here it is that the causes are complex and multitude. To how many snares is not the observer exposed, even with the best instruments.

Henri Poincaré
The science of physics does not only give us [mathematicians] an opportunity to solve problems, but helps us to discover the means of solving them, and it does this in two ways: it leads us to anticipate the solution and suggests suitable lines of argument.

Henri Poincaré
It is far better to foresee even without certainty than not to foresee at all.

Henri Poincaré
The stars are majestic laboratories, gigantic crucibles, such as no chemist could dream.

Henri Poincaré
How does it happen that there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds; if its evidence is based on principles common to all men, and that none could deny without being mad, how does it come about that so many persons are here refractory?

Henri Poincaré
Need we add that mathematicians themselves are not infallible?

Henri Poincaré
To obtain a result of real value, it is not enough to grind out calculations or to have a machine to put things in order; it is not order alone, it is unexpected order, which is worth while. The machine may gnaw on the crude fact; the soul of the fact will always escape it.

Henri Poincaré
Why do the rains, the tempests themselves seem to us to come by chance, so that many persons find it quite natural to pray for rain or shine, when they would think it ridiculous to pray for an eclipse?

Henri Poincaré
The most interesting facts are those which may serve many times; these are the facts which have a chance of coming up again. We have been so fortunate as to be born in a world where there are such.

Henri Poincaré
Not to suffer is a negative ideal more surely attained by the annihilation of the world. If we wish more and more to free man from material cares, it is that he may be able to employ the liberty obtained in the study and contemplation of truth.

Henri Poincaré
If we ought not to fear moral truth, still less should we dread scientific truth. In the first place it can not conflict with ethics. Ethics and science have their own domains, which touch but do not interpenetrate.

Henri Poincaré
It is not minds that have changed, it is ideas; the intuitional minds have remained the same; but their readers have required of them greater concessions.

Henri Poincaré
It is the intuition of pure number, that of pure logical forms, which illumines and directs those we have called analysts. This it is which enables them not alone to demonstrate, but also to invent.

Henri Poincaré
If we look at any particular law, we may be certain in advance that it can only be approximate. It is, in fact, deduced from experimental verifications, and these verifications were and could be only approximate. We should always expect that more precise measurements will oblige us to add new terms to our formulas.

Henri Poincaré
Ethics and science have their own domain which touch but do not interpenetrate. The one shows us to what goal we should aspire, the other, given the goal, teaches us how to attain it. So they can never conflict since they can never meet. There can no more be immoral science than there can be scientific morals.

Henri Poincaré
We know not to what are due the accidental errors, and precisely because we do not know, we are aware they obey the law of Gauss. Such is the paradox.

Henri Poincaré
If there were no solid bodies in nature, there would be no geometry.

Henri Poincaré
The search for truth should be the goal of our activities; it is the sole end worthy of them.

Henri Poincaré
The stars send us not only that visible and gross light which strikes our bodily eyes, but from them also comes to us a light far more subtle, which illuminates our minds.

Henri Poincaré