Henri Poincaré Quotes

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

We do not have and cannot have any means of discovering whether or not we are carried along in a uniform motion of translation.

The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide.

La tâche de l'éducateur est de faire repasser l'esprit de l'enfant par où a passé celui de ses pères, en passant rapidement par certaines étapes mais en n'en supprimant aucune. À ce compte, l'histoire de la science doit être notre guide.

It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.

C'est même des hypothèses simples qu'il faut le plus se défier, parce que ce sont celles qui ont le plus de chances de passer inaperçues.

A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. ...we work not only to obtain the positive results which, according to the profane, constitute our one and only affection, as to experience this esthetic emotion and to convey it to others who are capable of experiencing it.

Le savant digne de ce nom, le géomètre surtout, éprouve en face de son œuvre la même impression que l'artiste ; sa jouissance est aussi grande et de même nature.

Every conclusion supposes premises; these premises themselves either are self-evident and need no demonstration, or can be established only by relying upon other propositions, and since we can not go back thus to infinity, every deductive science, and in particular geometry, must rest on a certain number of undemonstrable axioms.

Logic sometimes makes monsters.

When we say force is the cause of motion, we are talking metaphysics; and this definition, if we had to be content with it, would be absolutely fruitless, would lead to absolutely nothing.

Мысль никогда не должна подчиняться ни догме, ни направлению, ни страсти, ни интересу, ни предвзятой идее, ни чему бы то ни было, кроме фактов, потому что для нее подчинится — значило бы перестать существовать.

The essential characteristic of reasoning by recurrence [induction] is that it contains, condensed, so to speak, in a single formula, an infinity of syllogisms.

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think.

in a word, their geometry will be the spherical geometry.