Henri Poincaré > Quotes

“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. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.”
― Henri Poincaré, Science and Method

“Is is by logic that we prove, but by intuition that we discover.”
― Henri Poincaré

“Le savant doit ordonner ; on fait la science avec des faits comme une maison avec des pierres ; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison.

The Scientist must set in order. 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 Poincare, Science and Hypothesis

“To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“Deviner avant de démontrer! Ai-je besoin de rappeler que c'est ainsi que se sont faites toutes les découvertes importantes.

Guessing before proving! Need I remind you that it is so that all important discoveries have been made?”
― Henri Poincaré, The Value of Science: Essential Writings of Henri Poincare

“Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer?”
― Henri Poincaré, Science and Method

“Mathematics is the art of giving the same name to different things.”
― Henri Poincaré

“Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so lone as the relations remain unchanged. Content to them is irrelevant; they are interested in form only.”
― Henri Poincaré

“En un mot, pour tirer la loi de l'expérience, if faut généraliser; c'est une nécessité qui s'impose à l'observateur le plus circonspect.

In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.”
― Henri Poincare, The Value of Science: Essential Writings of Henri Poincare

“The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.”
― Henri Poincare

“La pensée n'est qu'un écliar au milieu d'une longue nuit. Mais c'est cet éclair qui est tout.

Thought is only a flash in the middle of a long night. But this flash means everything.”
― Henri Poincaré, The Value of Science: Essential Writings of Henri Poincare

“Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.”
― Henri Poincaré, Science and Hypothesis

“Thinking must never submit itself, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, if not to facts themselves, because, for it, to submit would be to cease to be.”
― Jules Henri Poincare, OEUVRES, T. 2. FONCTIONS FUCHSIENNES

“Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.”
― Henri Poincaré, Science and Method

“A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.”
― Henri Poincaré

“How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.”
― Henri Poincaré, Science and Method

“Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.”
― Henri Poincaré

“It is through science that we prove, but through intuition that we discover.”
― Henri Poincaré

“The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.”
― Henri Poincaré, The Value of Science

“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

“It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.”
― Henri Poincaré, Science and Method

“Qu'une goutee de vin tombe dans un verre d'eau; quelle que soit la loi du movement interne du liquide, nous verrons bientôt se colorer d'une teinte rose uniforme et à partir de ce moment on aura beau agiter le vase, le vin et l'eau ne partaîtront plus pouvoir se séparer. Tout cela, Maxwell et Boltzmann l'ont expliqué, mais celui qui l'a vu plus nettement, dans un livre trop peu lu parce qu'il est difficile à lire, c'est Gibbs dans ses principes de la Mécanique Statistique.

Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from that moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics.”
― Henri Poincaré, The Value of Science: Essential Writings of Henri Poincare

“Logic sometimes creates monsters.”
― Henri Poincaré

“The aim of Mathematical Physics is not only to facilitate for the physicist the numerical calculation of certain constants or the integration of certain differential equations. It is besides, it is above all, to reveal to him the hidden harmony of things in making him see them in a new way.”
― Henri Poincaré, The Value of Science: Essential Writings of Henri Poincare

“I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.”
― Henri Poincaré, Science and Method

“Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable.”
― Henry Poincare

“It is impossible to study the works of the great mathematicians, or even those of the lesser, without noticing and distinguishing two opposite tendencies, or rather two entirely different kinds of minds. The one sort are above all preoccupied with logic; to read their works, one is tempted to believe they have advanced only step by step, after the manner of a Vauban who pushes on his trenches against the place besieged, leaving nothing to chance. The other sort are guided by intuition and at the first stroke make quick but sometimes precarious conquests, like bold cavalrymen of the advance guard.
[1913, p210]”
― Henri Poincaré

“Le cerveau du savant, qui n'est qu'un coin de l'Univers, ne pourra jamais contenir l'univers tout entier”
― Henri Poincaré

“If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.”
― Henri Poincaré, Science and Method

“La pensée ne doit jamais se soumettre, ni à un dogme, ni à un parti, ni à une passion, ni à un intérêt, ni à une idée préconçue, ni à quoi que ce soit, si ce n'est aux faits eux-mêmes, parce que, pour elle, se soumettre, ce serait cesser d'être.”
― Jules Henri Poincaré