Henri Poincaré Quotes

The greatest chance is the birth of a great man. It is only by chance that two reproductive cells, of different sexes, met, each containing precisely those mysterious elements whose mutual reaction was to produce genius. We will agree that these elements must be rare and that their meeting is even rarer. That it would have taken little to deviate the spermatozoon that carried them from its course; it would have been enough to deviate it by a tenth of a millimeter and Napoleon would not have been born and the destiny of a continent would have been changed. No other example can better explain the true nature of chance.

L’état actuel et l’avenir de la physique mathematique (1904)

only reach him after having traversed reflecting media of complicated form. The two indications which serve us in judging distances would cease to be connected by a constant relation. A being who should achieve in such a world the education of his senses would no doubt attribute four dimensions to complete visual space.

Logic sometimes creates monsters.

Si toutes les parties de l’univers sont solidaires dans une certaine mesure, un phénomène quelconque ne sera pas l’effet d’une cause unique, mais la résultante de causes infiniment nombreuses ; il est, dit-on souvent, la conséquence de l’état de l’univers un instant auparavant.

Les mathématiciens n'étudient pas des objets, mais des relations entre les objets ; il leur est donc indifférent de remplacer ces objets par d'autres, pourvu que les relations ne changent pas. La matière ne leur importe pas, la forme seule les intéresse.

The mathematician is born, not made.

Il n'y a pas de logique et d'épistémologie indépendantes de la psychologie.

Why then does this judgement [mathematical induction] force itself upon us with an irresistible evidence? It is because 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.

Each muscle gives rise to a special sensation capable of augmenting or of diminishing, so that the totality of our muscular sensations will depend upon as many variables as we have muscles. From this point of view, motor space would have as many dimensions as we have muscles.

Only Science and Art make civilization worth-while. One may be startled by the formula: Science for the sake of Science; and yet, it is worth as much as Life for Life's sake, if life is but misery; and even as Happiness for Happiness' sake, unless one believes that all pleasures are the same in quality, unless one is ready to admit that the goal of civilization is to furnish alcohol to all who love to drink.
All actions have goals. We must suffer, we must work, we must pay for our seats at the show. But, we pay that we may see, or that, at least, others may see some day.

La logique parfois engendre des monstres. Depuis un demi-siècle on a vu surgir une foule de fonctions bizarres qui semblent s’efforcer de ressembler aussi peu que possible aux honnêtes fonctions qui servent à quelque chose. Plus de continuité, ou bien de la continuité, mais pas de dérivées, etc. Bien plus, au point de vue logique, ce sont ces fonctions étranges qui sont les plus générales, celles qu’on rencontre sans les avoir cherchées n’apparaissent plus que comme un cas particulier. Il ne leur reste qu’un tout petit coin.

Tout le monde y croit cependant, me disait un jour M. Lippmann, car les expérimentateurs s'imaginent que c'est un théorème de mathématiques, et les mathématiciens que c'est un fait expérimental.

It is because simplicity and vastness are both beautiful that we seek by preference simple facts and vast facts; that we take delight, now in following the giant courses of the stars, now in scrutinizing the microscope that prodigious smallness which is also a vastness, and now in seeking in geological ages the traces of a past that attracts us because of its remoteness.

Douter de tout ou tout croire, ce sont deux solutions également commodes, qui l'une et l'autre nous dispensent de réfléchir.