Henri Poincaré Quotes

133 Sourced Quotes

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

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

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

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
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
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
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 physicist cannot demand of the analyst a revelation of new truth; the analyst can at best aid the physicist in the presentation of truth.

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
Modern mathematics can be kept alive only by a large number of mathematicians cultivating different parts of the same system of values: a community which can be kept coherent only by the passionate vigilance of universities, journals and meetings, fostering these values and imposing the same respect for them on all mathematicians.

Henri Poincaré
As science progress, it becomes more and more difficult to fit in the new facts when they will not fit in spontaneously. The older theories depend upon the coincidences of so many numerical results which can not be attributed to chance. We should not separate what has been joined together.

Henri Poincaré
Scientific truth, which is demonstrated, can in no way be likened to moral truth, which is felt.

Henri Poincaré
The facts of geometry are naught else than the facts of algebra and analytical geometry expressed in another language.

Henri Poincaré
An isolated fact can be observed by all eyes; by those of the ordinary person as well as of the wise. But it is the true physicist alone who may see the bond which unites several facts among which the relationship is important though obscure.

Henri Poincaré
To give a complete mechanical explanation of electrical phenomena, reducing the laws of physics to the fundamental principles of dynamics is a problem that has attracted many investigators.... If the problem admitted of only one solution, the possession of this solution, which would be the truth, could not be bought too dearly.

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
A well-chosen word usually suffices to do away with the exceptions from which the rules stated in the old way suffer; this is why we have created negative quantities, imaginaries, points at infinity, and what not. And exceptions, we must not forget, are pernicious because they hide the laws.

Henri Poincaré
What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

Henri Poincaré
Every age has ridiculed the one before it, and accused it of having generalized too quickly and too naively. Descartes pitied the lonians; Descartes, in his turn, makes us smile. No doubt our children will someday laugh at us.

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
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
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 theory of groups is an extensive subject upon which there is much to be said. There are many kinds of groups, and whatever classification may be adopted we will always find new groups which will not fit it.

Henri Poincaré
Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

Henri Poincaré