Henri Poincaré Quotes

133 Sourced Quotes

The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living.

Henri Poincaré
Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

Henri Poincaré
The man of science must work with method. Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.

Henri Poincaré
Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.

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

Henri Poincaré
Chance is only the measure of our ignorance.

Henri Poincaré
The true man of science has no such expression in his vocabulary as useful science... if there can be no science for science's sake there can be no science.

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

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

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

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
To observe is not enough. We must use our observations, and to do that we must generalize.

Henri Poincaré
Later generations will regard Mengenlehre as a disease from which one has recovered.

Henri Poincaré
We should always aim toward the economy of thought. It is not enough to give models for imitation. It must be possible to pass beyond these models and, in place of repeating their reasoning at length each time, to sum this in a few words.

Henri Poincaré
This intuition of mathematical order, which enables us to perceive harmonies and hidden relations, cannot be present in everyone.

Henri Poincaré
That being so what ought one to think of this question: Is the Euclidean Geometry true? The question is nonsense. One might as well ask whether the metric system is true and the old measures false; whether Cartesian co-ordinates are true and polar co-ordinates false.

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

Henri Poincaré