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Home > Dictionary of Science Quotations > Scientist Names Index P > Henri Poincaré Quotes

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Henri Poincaré
(29 Apr 1854 - 17 Jul 1912)

French mathematician, physicist and astronomer , who is often described as the last generalist in mathematics.


Science Quotes by Henri Poincaré (66 quotes)

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... I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Eudidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.
— Henri Poincaré
Quoted in Sir Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (1990), 541. Science and Method (1908) 51-52, 392.
Science quotes on:  |  Geometry (99)  |  Idea (440)  |  Inspiration (50)  |  Non-Euclidian (2)  |  Thought (374)  |  Transformation (47)  |  Verify (9)

Derrière la série de Fourier, d’autres séries analogues sont entrées dans la domaine de l’analyse; elles y sont entrées par la même porte; elles ont été imaginées en vue des applications.
After the Fourier series, other series have entered the domain of analysis; they entered by the same door; they have been imagined in view of applications.
— Henri Poincaré
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 74.
Science quotes on:  |  Baron Jean-Baptiste-Joseph Fourier (13)  |  Series (38)

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
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 218.
Science quotes on:  |  Discovery (591)  |  Guess (36)  |  Proof (192)

Douter de tout ou tout croire, ce sont deux solutions également commodes, qui l’une et l’autre nous dispensent de défléchir.
To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.
— Henri Poincaré
From 'Introduction', La Science et l’Hypothèse (1902), 2. Translation by George Bruce Halsted, 'Introduction', Science and Hypothesis (New York, 1905), 1. In 'Author’s Preface', Science and Hypothesis (London 1905), xxii, it is translated more closely as “To doubt everything and to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.”
Science quotes on:  |  Belief (400)  |  Convenience (25)  |  Doubt (121)  |  Equal (53)  |  Everything (120)  |  Saving (19)  |  Solution (168)  |  Thinking (222)

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 Poincaré
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 186.
Science quotes on:  |  Experience (268)  |  Observation (418)

Il est impossible de contempler le spectacle de l’univers étoilé sans se demander comment il s’est formé: nous devions peut-être attendre pour chercher une solution que nous ayons patiemment rassemblé les éléments …mais si nous étions si raisonnables, si nous étions curieux sans impatience, il est probable que nous n’avions jamais créé la Science et que nous nous serions toujours contentés de vivre notre petite vie. Notre esprit a donc reclamé impérieusement cette solution bien avant qu’elle fut mûre, et alors qu’il ne possédait que de vagues lueurs, lui permettant de la deviner plutôt que de l’attendre.
It is impossible to contemplate the spectacle of the starry universe without wondering how it was formed: perhaps we ought to wait, and not look for a solution until have patiently assembled the elements … but if we were so reasonable, if we were curious without impatience, it is probable we would never have created Science and we would always have been content with a trivial existence. Thus the mind has imperiously laid claim to this solution long before it was ripe, even while perceived in only faint glimmers—allowing us to guess a solution rather than wait for it.
— Henri Poincaré
From Leçons sur les Hypothèses Consmogoniques (1913) as cited in D. Ter Haar and A.G.W. Cameron, 'Historical Review of Theories of the Origin of the Solar System', collected in Robert Jastrow and A. G. W. Cameron (eds.), Origin of the Solar System: Proceedings of a Conference Held at the Goddard Institute for Space Studies, New York, January 23-24, 1962, (1963), 3. 'Cosmogonical Hypotheses' (1913), collected in Harlow Shapley, Source Book in Astronomy, 1900-1950 (1960), 347.
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Il faut bien s'arrêter quelque part, et pour que la science soit possible, il faut s'arrêter quand on a trouvé la simplicité.
Analyse data just so far as to obtain simplicity and no further.
— Henri Poincaré
La Science et L'Hypothèse (1902), 176. Sentence translated in A.D. Ritchie, Scientific Method: An Inquiry into the Character and Validy of Natural Law (1923), 201.
Science quotes on:  |  Data (100)  |  Simplicity (126)

L'analyse mathématique, n'est elle donc qu'un vain jeu d'esprit? Elle ne peut pas donner au physicien qu'un langage commode; n'est-ce pa là un médiocre service, dont on aurait pu se passer à la rigueur; et même n'est il pas à craindre que ce langage artificiel ne soit pas un voile interposé entre la réalité at l'oeil du physicien? Loin de là, sans ce langage, la pluspart des anaologies intimes des choses nous seraient demeurées à jamais inconnues; et nous aurions toujours ignoré l'harmonie interne du monde, qui est, nous le verrons, la seule véritable réalité objective.
So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality.
— Henri Poincaré
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 6.
Science quotes on:  |  Language (155)  |  Mathematics (587)  |  Physicist (130)  |  Reality (140)

La pensée n’est qu’un éclair au milieu d’une longue nuit. Mais c’est cet éclair qui est tout.
Thought is only a gleam in the midst of a long night. But it is this gleam which is everything.
— Henri Poincaré
Concluding remark to La Valeur de la Science (1904), 276, translated by George Bruce Halsted, in The Value of Science (1907), 142. “Éclair” might also be translated as “flash” or “lightning,” which would better signify only an instantaneous existence in his context of geologic time.
Science quotes on:  |  Everything (120)  |  Flash (25)  |  Gleam (9)  |  Lightning (28)  |  Night (73)  |  Thought (374)

Le savant n’étudie pas la nature parce que cela est utile; il l’étudie parce qu’il y prend plaisir et il y prend plaisir parce qu’elle est belle. Si la nature n’était pas belle, elle ne vaudrait pas la peine d’être connue, la vie ne vaudrait pas la peine d’être vécue.
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
In Science et Méthode (1920), 48, as translated by Francis Maitland, in Science and Method (1908, 1952), 15.
Science quotes on:  |  Beautiful (81)  |  Knowledge (1128)  |  Nature (1029)  |  Pleasure (98)  |  Scientist (447)  |  Study (331)  |  Useful (66)

Les faits ne parlent pas.
Facts do not speak.
— Henri Poincaré
Attributed.
Science quotes on:  |  Fact (609)  |  Speaking (38)

Les faits ne parlent pas. (Facts do not speak)
— Henri Poincaré
quoted in The Harvest of a Quiet Eye by Alan L. Mackay

Les faits scientifiques, et à fortiori, les lois sont l’œuvre artificielle du savant ; la science ne peut donc rien nous apprendre de la vérité, elle ne peut nous servir que de règle d’action.
The facts of science and, à fortiori, its laws are the artificial work of the scientist; science therefore can teach us nothing of the truth; it can only serve us as rule of action.
— Henri Poincaré
In La Valeur de la Science (1904), 214, translated by George Bruce Halsted, in The Value of Science (1907), 112.
Science quotes on:  |  Action (151)  |  Artificial (26)  |  Fact (609)  |  Rule (135)  |  Science (1699)  |  Teaching (99)  |  Truth (750)

Les mathématique sont un triple. Elles doivent fournir un instrument pour l'étude de la nature. Mais ce n'est pas tout: elles ont un but philosophique et, j'ose le dire, un but esthétique.
Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.
— Henri Poincaré
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 161.
Science quotes on:  |  Mathematics (587)  |  Nature (1029)

Les principes sont des conventions et des définitions déguisés.
Principles are conventions and definitions in disguise.
— Henri Poincaré
From La Science et l’Hypothèse (1902), 165. Translation by George Bruce Halsted, Science and Hypothesis (New York, 1905), 100. In Science and Hypothesis (London 1905), 138.
Science quotes on:  |  Convention (13)  |  Definition (152)  |  Disguise (8)  |  Principle (228)

Longtemps les objets dont s'occupent les mathématiciens étaient our la pluspart mal définis; on croyait les connaître, parce qu'on se les représentatit avec le sens ou l'imagination; mais on n'en avait qu'une image grossière et non une idée précise sure laquelle le raisonment pût avoir prise.
For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.
— Henri Poincaré
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 97.
Science quotes on:  |  Mathematics (587)  |  Reasoning (79)

L’Astronomie est utile, parce qu’elle nous élève au-dessus de nous-mêmes; elle est utile, parce qu’elle est grande; elle est utile, parce qu’elle est belle… C’est elle qui nous montre combien l’homme est petit par le corps et combien il est grand par l’esprit, puisque cette immensité éclatante où son corps n’est qu’un point obscur, son intelligence peut l’embrasser tout entière et en goûter la silencieuse harmonie.
Astronomy is useful because it raises us above ourselves; it is useful because it is grand[; it is useful because it is beautiful]… It shows us how small is man’s body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.
— Henri Poincaré
In La Valeur de la Science (1904), 276, translated by George Bruce Halsted, in The Value of Science (1907), 84. Webmaster added the meaning of “elle est utile, parce qu’elle est belle,” in brackets, which was absent in Halsted’s translation.
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On fait la science avec des faits, comme on fait 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.
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
From La Science et l’Hypothèse (1908), 168. In George Bruce Halsted (trans.) Science and Hypothesis (1905), 101. Also seen translated as “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.”
Science quotes on:  |  Fact (609)  |  Science (1699)

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 th at 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
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 3.
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Quand les physiciens nous demandent la solution d'un problème, ce n'est pas une corvée qu'ils nous impsent, c'est nous au contraire qui leur doivent des remercîments.
When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.
— Henri Poincaré
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 111.
Science quotes on:  |  Mathematician (177)  |  Physicist (130)  |  Problem (362)  |  Solution (168)

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.
— Henri Poincaré
…...
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A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment.
— Henri Poincaré
In 'Chance', Science et Méthode (1908). Quoted in Richard Kautz, Chaos: The Science of Predictable Random Motion (2011), 167 as translated in Science and Method by F. Maitland (1918).
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All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work which follows the inspiration, and in which the results of the inspiration are verified and the consequences deduced.‎
— Henri Poincaré
Science and Method (1914, 2003), 62.
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All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not.
— Henri Poincaré
The Value of Science (1905), in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method(1946), trans. by George Bruce Halsted, 332.
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Before a complex of sensations becomes a recollection placeable in time, it has ceased to be actual. We must lose our awareness of its infinite complexity, or it is still actual ... It is only after a memory has lost all life that it can be classed in time, just as only dissected flowers find their way into the herbarium of a botanist.
— Henri Poincaré
…...
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Chance ... must be something more than the name we give to our ignorance.
— Henri Poincaré
In Science and Method (1908) translated by Francis Maitland (1914, 2007), 66.
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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 (1908), trans. Francis Maitland (1914), 254-5.
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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
…...
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Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have ‘proved’ that it involves no contradiction either in its terms or with the truths previously admitted.
— Henri Poincaré
…...
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Every good mathematician should also be a good chess player and vice versa.
— Henri Poincaré
Science and Method (1914, 2003), 48.
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Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages. If a being with such a mind existed, we could play no game of chance with him; we should always lose.
— Henri Poincaré
Science and Method (1908), trans. Francis Maitland (1914), 65.
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Everybody firmly believes in it [Nomal Law of Errors] because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.
— Henri Poincaré
…...
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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 (1902), trans. W. J. G. and preface by J. Larmor (1905), 140.
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Geometrical axioms are neither synthetic a priori conclusions nor experimental facts. They are conventions: our choice, amongst all possible conventions, is guided by experimental facts; but it remains free, and is only limited by the necessity of avoiding all contradiction. ... In other words, axioms of geometry are only definitions in disguise.
That being so what ought one to think of this question: Is the Euclidean Geometry true?
The question is nonsense. One might as well ask whether the metric system is true and the old measures false; whether Cartesian co-ordinates are true and polar co-ordinates false.
— Henri Poincaré
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 110.
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Geometry is not true, it is advantageous.
— Henri Poincaré
Science and Hypothesis (1902), in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method(1946), trans. by George Bruce Halsted, 91.
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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 (1914, 2003), 117-118.
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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 (1908), trans. Francis Maitland (1914), 53-4.
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If all the parts of the universe are interchained in a certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of causes infinitely numerous.
— Henri Poincaré
…...
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If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.
— Henri Poincaré
Henri Poincaré and George Bruce Halsted (trans.), The Value of Science (1907), 12.
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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 (1914, 2003), 25.
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It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.
— Henri Poincaré
Science and Hypothesis (1902), trans. W. J. G. and preface by J. Larmor (1905), 181.
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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.
— Henri Poincaré
…...
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It is by logic that we prove, but by intuition that we discover.
— Henri Poincaré
In Science and Method (1908) translated by Francis Maitland (1914, 2007), 129.
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It is not nature which imposes time and space upon us, it is we who impose them upon nature because we find them convenient.
— Henri Poincaré
…...
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It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.
— Henri Poincaré
Science and Hypothesis (1902), trans. W.J.G. (1905), 143.
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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.
— Henri Poincaré
…...
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It is through it [intuition] that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to fill up the gulf that separates the symbol from reality.
— Henri Poincaré
…...
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It is through science that we prove, but through intuition that we discover.
— Henri Poincaré
…...
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It may be appropriate to quote a statement of Poincare, 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
Quoted in Mark Kac, Statistical Independence in Probability, Analysis and Number Theory (1959), 52.
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Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.
— Henri Poincaré
…...
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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
…...
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Mathematics is the art of giving the same name to different things.
— Henri Poincaré
Henri Poincaré and George Bruce Halsted (trans.) The Foundations of Science: Science and Hypothesis (1921), 375.
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One does not ask whether a scientific theory is true, but only whether it is convenient.
— Henri Poincaré
La Science et l'Hypothèse (1902) as quoted in Encyclopedia of World Biography, 2nd ed. Gale Research (1998)

Sir W. Ramsay has striven to show that radium is in process of transformation, that it contains a store of energy enormous but not inexhaustible. The transformation of radium then would produce a million times more heat than all known transformations; radium would wear itself out in 1,250 years; this is quite short, and you see that we are at least certain to have this point settled some hundreds of years from now. While waiting, our doubts remain.
— Henri Poincaré
In La Valeur de la Science (1904), 199, as translated by George Bruce Halsted, in The Value of Science (1907), 105.
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Sociology is the science with the greatest number of methods and the least results.
— Henri Poincaré
…...
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The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain.
— Henri Poincaré
The Value of Science (1905), in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method(1946), trans. by George Bruce Halsted, 208.
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
— Henri Poincaré
Science and Hypothesis, translated by William John Greenstreet, (1905, 1952), xxiv.
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The genesis of mathematical creation is a problem which should intensely interest the psychologist.
— Henri Poincaré
In 'Mathematical Creation', The Value of Science, collected in Henri Poincaré and George bruce Halsted (trans.), The Foundations of Science (1913), 383.
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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.
— Henri Poincaré
…...
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Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts since they are infinite in number. We must make a selection ... guided by utility ... Have we not some better occupation than counting the number of lady-birds in existence on this planet?
— Henri Poincaré
In Science and Method (1914, 2003), 15
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What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
— Henri Poincaré
Science and Method (1914, 2003), 117.
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What, in fact, is mathematical discovery? It does not consist in making new combinations with mathematical entities that are already known. That can be done by anyone, and the combinations that could be so formed would be infinite in number, and the greater part of them would be absolutely devoid of interest. Discovery consists precisely in not constructing useless combinations, but in constructing those that are useful, which are an infinitely small minority. Discovery is discernment, selection.
— Henri Poincaré
In Science et Méthode (1920), 48, as translated by Francis Maitland, in Science and Method (1908, 1952), 50-51.
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When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.
— Henri Poincaré
Science and Method (1914 edition, reprint 2003), 126.
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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 (1908), trans. Francis Maitland (1914), 68.
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[Poincaré was] the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of philosophic vision that Poincare had, and none in his superior in the gift of clear exposition.
— Henri Poincaré
In Eric Temple Bell, Men of Mathematics as quoted in Henri Poincare, Science and Hypothesis (1952 reprint), back cover notes.

… it may happen that small differences in the initial conditions produce very great ones in the final phenomena.
— Henri Poincaré
Science and Method (1908) translated by Francis Maitland (2003), 68.
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Quotes by others about Henri Poincaré (1)

Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.
Quoted in Thomson Gale, Online, 'Jules Henri Poincaré', World of Mathematics (2006).
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See also:
  • 29 Apr - short biography, births, deaths and events on date of Poincaré's birth.
  • The Value of Science: Essential Writings of Henri Poincaré, by Henri Poincaré. - book suggestion.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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