Henri Poincaré Quotes

133 Sourced Quotes

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
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
In repeating an argument that I have learned, I could readily have discovered it myself: or rather, even if this is an illusion, if I were not clever enough to have created it myself, I rediscover it myself, to the extent that I repeat it.

Henri Poincaré
Facts are sterile until there are minds capable of choosing between them and discerning those which conceal something and recognizing that which is concealed; minds which under the bare fact see the soul of the fact.

Henri Poincaré
Sometimes truth frightens us. And in fact we know that it is sometimes deceptive, that it is a phantom never showing itself for a moment except to ceaselessly flee, that it must be pursued further and ever further without ever being attained.

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
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
Scientific theories are like empires, they are not certain of the morrow.

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

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
The importance of a fact is known by its fruits, that is to say, by the amount of thought which it enables us to economize.

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

Henri Poincaré
Zero is the number of objects that satisfy a condition that is never satisfied. But as never means no case, I do not see that any progress has been made.

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

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

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

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
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
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
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