Henri Poincaré Quotes

133 Sourced Quotes

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
The brain is as weak as the senses, and it would be lost in the complexities of the world were there not harmony in that complexity. After the manner of the short-sighted, we would see only detail after detail, losing sight of each detail before the examination of another, unable to bind them together.

Henri Poincaré
In mathematics rigor is not everything, but without it there would be nothing; a demonstration which is not rigorous is void.

Henri Poincaré
Physical theories must not introduce as many arbitrary constants as there are phenomena to be accounted for; they must establish connections among the various experimental facts and, above all, must lead to predictions.

Henri Poincaré
Scientific laws are not artificial creations; we have no reason to regard them as accidental, though it be impossible to prove they are not.

Henri Poincaré
The mere fact is oftentimes without interest; it has been noted many times, but has rendered no service to science; it becomes of value only on that day when some happily advised thinker perceives a relationship which he indicates and symbolizes by a word.

Henri Poincaré
If a new result has value it is when, by binding together long-known elements, until now scattered and appearing unrelated to each other, it suddenly brings order where there reigned apparent disorder.

Henri Poincaré
Mathematician ought not to be for the physicist a simple provider of formulae.

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
Thanks to the formula, a single algebraic demonstration spares us the pains of going over the same ground time after time for each new calculation.

Henri Poincaré
We can not know all facts and it is necessary to choose those which are worthy of being known.

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
Inventing consists precisely in not constructing combinations that are useless, but in constructing those which are useful and these are a small minority. Inventing mean discerning, means choosing.

Henri Poincaré
A science produced with a view single to its applications is impossible; truths are fruitful only if they are concatenated; if we cleave to those only of which we expect an immediate result, the connecting links will be lacking, and there will be no longer a chain.

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

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
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
The scientist is accustomed to conquer truth only by degrees; for him all certainty should be bought by long hesitations, by perpetually feeling his way. He suspects what comes too easily, and accepts it only after submitting it to numerous and diverse proofs.

Henri Poincaré
In a word, the sentiment of mathematical elegance is naught else than the satisfaction due to some, I know not just what, adaptation between the solution just found and the needs of our mind, and it is because of this adaptation itself that the solution becomes an instrument to us.

Henri Poincaré
Logic and intuition have each their necessary role. Each is, indispensable. Logic, which alone can give certainty, is the instrument of demonstration; intuition is the instrument of invention.

Henri Poincaré
The ultimate aim of celestial mechanics is to solve the great question whether Newton 'a law alone will explain all astronomical phenomena.

Henri Poincaré
It matters little whether the ether really exists; that is the affair of metaphysicians. The essential thing for us is that everything happens as if it existed......some day, no doubt, the ether will be thrown aside as useless.

Henri Poincaré
One geometry cannot be more true than another; it can only be more convenient.

Henri Poincaré
If science is feared, it is above all because it cannot give us happiness.

Henri Poincaré
The true method of forecasting the future of mathematics lies in the study of its history and its present state.

Henri Poincaré
The scientific fact is only the crude fact translated into a convenient language.

Henri Poincaré
The firm determination to submit to experiment is not enough; there are still dangerous hypotheses; first, and above all, those which are tacit and unconscious. Since we make them without knowing it, we are powerless to abandon them.

Henri Poincaré
The very name calculus of probabilities is a paradox. Probability opposed to certainty is what we do not know, and how can we calculate what we do not know?

Henri Poincaré
It is often said that experiments must be made without preconceived idea. That is impossible. Not only would it make all experiment barren, but that would be attempted which could not be done.

Henri Poincaré
For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rules.

Henri Poincaré