Henri Poincaré Quotes

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.

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.

It follows from this that sight and touch could not have given us the notion of space without the aid of the 'muscular sense.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

Formal logic is nothing but the study of the properties common to all classifications; it teaches us that two soldiers who are members of the same regiment belong by this very fact to the same brigade, and consequently to the same division; and the whole theory of the syllogism is reduced to this.

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.

Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.

We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them.
...We ...choose these rules, not because they are true, but because they are the most convenient, and we may recapitulate them as follows: "The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions, are only the fruit of an unconscious opportunism."

What we call geometry is nothing but the study of formal properties of a certain continuous group; so that we may say, space is a group. The notion of this continuous group exists in our mind prior to all experience; but the assertion is no less true of the notion of many other continuous groups; for example, that which corresponds to the geometry of Lobatchevski.

The readings we shall be able to make on our instruments at any instant will depend only on the readings we could have made on these same instruments at the initial instant.

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

John Stuart Mill understood the word existence in a material and empirical sense; he meant that in defining a circle we assert that there are round things in nature.
In this form his opinion is inadmissible. Mathematics is independent of the existence of material objects. In mathematics the word exist can only have one meaning; it signifies exemption from contradiction. Thus rectified, Mill's thought becomes accurate. In defining an object, we assert that the definition involves no contradiction.

Je ne sais si je n’ai déjà dit quelque part que la Mathématique est l’art de donner le même nom à des choses différentes.

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