Henri Poincaré Quotes

134 Sourced Quotes

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 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
It may be appropriate to quote a statement of Poincaré, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

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

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

Henri Poincaré
Principles are conventions and definitions in disguise.

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
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
Time and Space … It is not nature which imposes them upon us, it is we who impose them upon nature because we find them convenient.

Henri Poincaré
But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by induction? We see successively that a theorem is true of the number 1, of the number 2, of the number 3 and so on; the law is evident, we say, and it has the same warranty as every physical law based on observations, whose number is very great but limited. But there is an essential difference. Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us. Mathematical induction, that is, demonstration by recurrence, on the contrary, imposes itself necessarily, because it is only the affirmation of a property of the mind itself.

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

Henri Poincaré
We can not... escape the conclusion that the rule of reasoning by recurrence is irreducible to the principle of contradiction.... Neither can this rule come to us from experience... This rule, inaccessible to analytic demonstration and to experience, is the veritable type of the synthetic a priori judgment. On the other hand, we can not think of seeing in it a convention, as in some of the postulates of geometry.... it is only the affirmation of the power of the mind which knows itself capable of conceiving the indefinite repetition of the same act when once this act is possible. The mind has a direct intuition of this power, and experience can only give occasion for using it and thereby becoming conscious of it.

Henri Poincaré
Chance is only the measure of our ignorance.

Henri Poincaré
Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence? No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility.

Henri Poincaré
Now what is science?... it is before all a classification, a manner of bringing together facts which appearances separate, though they are bound together by some natural and hidden kinship. Science, in other words, is a system of relations.... it is in relations alone that objectivity must be sought.... it is relations alone which can be regarded as objective.
External objects... are really objects and not fleeting and fugitive appearances, because they are not only groups of sensations, but groups cemented by a constant bond. It is this bond, and this bond alone, which is the object in itself, and this bond is a relation.

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
Mathematics is the art of giving the same name to different things.

Henri Poincaré
As we can not give a general definition of energy, the principle of the conservation of energy signifies simply that there is something which remains constant.

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

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