Celebrating 19 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index P > Henri Poincaré Quotes

Thumbnail of Henri Poincaré (source)
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 (93 quotes)

>> Click for Henri Poincaré Quotes on | Definition | Fact | Mathematics | Mind | Science | Solution | Truth |


... 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 (232)  |  Idea (580)  |  Inspiration (61)  |  Non-Euclidian (2)  |  Thought (546)  |  Transformation (54)  |  Verify (17)

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 (17)  |  Series (51)

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 (680)  |  Guess (48)  |  Proof (245)

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 (504)  |  Convenience (34)  |  Doubt (160)  |  Equal (83)  |  Everything (181)  |  Saving (20)  |  Solution (216)  |  Thinking (231)

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 (342)  |  Observation (450)

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.
Science quotes on:  |  Assemble (10)  |  Claim (71)  |  Contemplation (52)  |  Content (69)  |  Created (6)  |  Curious (43)  |  Element (162)  |  Existence (299)  |  Faint (9)  |  Formation (59)  |  Glimmer (5)  |  Guess (48)  |  Impatience (12)  |  Impossibility (53)  |  Mind (760)  |  Origin Of The Universe (13)  |  Patience (39)  |  Perceived (4)  |  Reasonable (27)  |  Ripe (5)  |  Science (2067)  |  Solution (216)  |  Spectacle (14)  |  Star (336)  |  Trivial (41)  |  Universe (686)  |  Wait (58)  |  Wonder (169)

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 (120)  |  Simplicity (147)

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 (181)  |  Flash (34)  |  Gleam (12)  |  Lightning (33)  |  Night (118)  |  Thought (546)

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 (144)  |  Knowledge (1306)  |  Nature (1223)  |  Pleasure (133)  |  Scientist (522)  |  Study (476)  |  Useful (100)

Les faits ne parlent pas.
Facts do not speak.
— Henri Poincaré
Attributed. As quoted in Alan L. Mackay, The Harvest of a Quiet Eye.
Science quotes on:  |  Fact (733)  |  Speak (92)

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 (185)  |  Artificial (32)  |  Fact (733)  |  Rule (177)  |  Science (2067)  |  Teaching (108)  |  Truth (928)

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 (1205)  |  Nature (1223)

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 (14)  |  Definition (192)  |  Disguise (10)  |  Principle (292)

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 (1205)  |  Reasoning (100)

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.
Science quotes on:  |  Astronomy (204)  |  Beautiful (144)  |  Body (247)  |  Dazzling (11)  |  Enjoyment (29)  |  Grand (27)  |  Great (534)  |  Harmony (72)  |  Immensity (21)  |  Intelligence (168)  |  Man (373)  |  Mind (760)  |  Obscurity (27)  |  Raising (4)  |  Silent (28)  |  Useful (100)

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.
Science quotes on:  |  Ludwig Eduard Boltzmann (17)  |  J. Willard Gibbs (7)  |  Liquid (25)  |  James Clerk Maxwell (87)  |  Statistical Mechanics (6)

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 (384)  |  Physicist (161)  |  Problem (497)  |  Solution (216)

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
…...
Science quotes on:  |  Artist (69)  |  Experience (342)  |  Great (534)  |  Impression (72)  |  Mathematician (384)  |  Name (170)  |  Nature (1223)  |  Pleasure (133)  |  Same (156)  |  Scientist (522)  |  Work (635)  |  Worthy (34)

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).
Science quotes on:  |  Cause (285)  |  Chance (160)  |  Considerable (20)  |  Determine (76)  |  Effect (166)  |  Exactly (13)  |  Initial (17)  |  Know (556)  |  Law Of Nature (64)  |  Predict (21)  |  Situation (52)  |  Small (163)  |  Universe (686)

Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence…. The two propositions: “The earth turns round” and “it is more convenient to suppose the earth turns round” have the same meaning; there is nothing more in the one than in the other.
— Henri Poincaré
From La Science et l’Hypothèse (1908), 141, as translated by George Bruce Halsted in Science and Hypothesis (1905), 85-86. From the original French, “L’espace absolu, c’est-à-dire le repère auquel il faudrait rapporter la terre pour savoir si réellement elle tourne, n’a aucune existence objective. … Ces deux propositions: ‘la terre tourne’, et: ‘il est plus commode de supposer que la terre tourne’, ont un seul et même sens; il n’y a rien de plus dans l’une que dans l’autre.”
Science quotes on:  |  Absolute (98)  |  Convenience (34)  |  Earth (638)  |  Existence (299)  |  Know (556)  |  Move (94)  |  Necessary (154)  |  Objective (66)  |  Proposition (83)  |  Really (78)  |  Reference Frame (2)  |  Space (257)  |  Suppose (49)  |  Turn (118)

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.
Science quotes on:  |  Calculation (100)  |  Consequence (114)  |  Deduction (69)  |  Departure (9)  |  Fruit (71)  |  Hope (174)  |  Inspiration (61)  |  Obtain (45)  |  Result (389)  |  Unconscious (20)  |  Verification (27)  |  Work (635)

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.
Science quotes on:  |  Ambiguity (14)  |  Creation (242)  |  Dependence (37)  |  Employment (24)  |  Enunciation (5)  |  Evidence (183)  |  Fact (733)  |  Freedom (102)  |  Fulfillment (16)  |  Language (228)  |  Prediction (71)  |  Scientist (522)  |  Speaking (37)  |  Understanding (325)

Astronomy has not only taught us that there are laws, but that from these laws there is no escape, that with them there is no possible compromise.
— Henri Poincaré
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 86.
Science quotes on:  |  Astronomy (204)  |  Compromise (7)  |  Escape (47)  |  Law Of Nature (64)  |  Possible (158)  |  Teach (188)

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
…...
Science quotes on:  |  Actual (48)  |  Awareness (27)  |  Become (172)  |  Botanist (17)  |  Cease (39)  |  Class (84)  |  Complex (95)  |  Complexity (91)  |  Dissection (29)  |  Find (408)  |  Flower (77)  |  Herbarium (2)  |  Infinite (130)  |  Life (1131)  |  Lose (94)  |  Memory (106)  |  Recollection (11)  |  Sensation (29)  |  Time (595)

By natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. 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.
Science quotes on:  |  Advantage (77)  |  Geometry (232)  |  Truth (928)

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.
Science quotes on:  |  Chance (160)  |  Definition (192)  |  Ignorance (213)

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.
Science quotes on:  |  Action (185)  |  Atom (280)  |  Bubble (15)  |  Closeness (4)  |  Comet (50)  |  Course (84)  |  Deviation (11)  |  Distance (77)  |  Dust (49)  |  Gas (50)  |  Giant (38)  |  Grain (28)  |  Greatness (42)  |  Innumerable (23)  |  Jupiter (21)  |  Milky Way (24)  |  Motion (160)  |  Nearness (3)  |  Passage (20)  |  Slightness (2)  |  Star (336)  |  Sun (276)  |  Trajectory (4)  |  Velocity (16)

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
…...
Science quotes on:  |  Beyond (105)  |  Completely (32)  |  Conceive (39)  |  Discover (199)  |  Doubt (160)  |  Exist (148)  |  Feel (167)  |  Harmony (72)  |  Human (550)  |  Impossibility (53)  |  Independent (67)  |  Intelligence (168)  |  Mind (760)  |  Nature (1223)  |  Outside (48)  |  Reality (190)  |  See (369)  |  Think (347)

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
…...
Science quotes on:  |  Admit (45)  |  Assert (21)  |  Axiom (52)  |  Contradiction (54)  |  Define (49)  |  Definition (192)  |  Existence (299)  |  Imply (16)  |  Involve (48)  |  Justify (23)  |  Logical (55)  |  Object (175)  |  Point Of View (41)  |  Previously (11)  |  Prove (109)  |  Purely (28)  |  Term (122)  |  Truth (928)

Every good mathematician should also be a good chess player and vice versa.
— Henri Poincaré
Science and Method (1914, 2003), 48.
Science quotes on:  |  Chess (23)  |  Mathematician (384)  |  Vice Versa (6)

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.
Science quotes on:  |  Beginning (122)  |  Cause (285)  |  Chance (160)  |  Concern (110)  |  Existence (299)  |  Foresight (5)  |  Game (61)  |  Infinity (72)  |  Law Of Nature (64)  |  Loss (73)  |  Mind (760)  |  Phenomenon (278)  |  Play (112)  |  Trifle (15)  |  Well-Informed (2)

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
…...
Science quotes on:  |  Belief (504)  |  Error (277)  |  Everybody (27)  |  Fact (733)  |  Firmly (6)  |  Imagine (76)  |  Law (515)  |  Mathematician (384)  |  Mathematics (1205)  |  Observation (450)  |  Observer (42)  |  Theory (696)

Exactness cannot be established in the arguments unless it is first introduced into the definitions.
— Henri Poincaré
In Science et Méthode, as translated by Francis Maitland, in Science and Method (1914), 123-124.
Science quotes on:  |  Argument (82)  |  Definition (192)  |  Establish (56)  |  Exact (68)  |  First (314)  |  Introduce (42)

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.
Science quotes on:  |  Certainty (131)  |  Experiment (602)  |  New (496)  |  Teaching (108)  |  Truth (928)

Freedom is for science what the air is for an animal.
— Henri Poincaré
In Dernieres Pensees.

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.
Science quotes on:  |  A Priori (22)  |  Among (3)  |  Ask (160)  |  Avoid (55)  |  Axiom (52)  |  Cartesian (3)  |  Choice (79)  |  Conclusion (160)  |  Contradiction (54)  |  Convention (14)  |  Definition (192)  |  Disguise (10)  |  Euclidean (3)  |  Experimental (20)  |  Fact (733)  |  False (99)  |  Free (92)  |  Geometrical (10)  |  Geometry (232)  |  Guide (65)  |  In Other Words (9)  |  Limit (126)  |  Measure (104)  |  Metric System (6)  |  Necessity (143)  |  Nonsense (41)  |  Old (147)  |  Polar (2)  |  Possible (158)  |  Question (404)  |  Remain (113)  |  Synthetic (16)  |  Think (347)  |  True (208)

Governments and parliaments must find that astronomy is one of the sciences which cost most dear: the least instrument costs hundreds of thousands of dollars, the least observatory costs millions; each eclipse carries with it supplementary appropriations. And all that for stars which are so far away, which are complete strangers to our electoral contests, and in all probability will never take any part in them. It must be that our politicians have retained a remnant of idealism, a vague instinct for what is grand; truly, I think they have been calumniated; they should be encouraged and shown that this instinct does not deceive them, that they are not dupes of that idealism.
— Henri Poincaré
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 84.
Science quotes on:  |  Appropriation (4)  |  Astronomy (204)  |  Complete (87)  |  Cost (44)  |  Deceive (16)  |  Dollar (22)  |  Dupe (3)  |  Eclipse (20)  |  Election (7)  |  Encourage (24)  |  Far (154)  |  Government (93)  |  Grand (27)  |  Idealism (4)  |  Instinct (66)  |  Instrument (95)  |  Millions (17)  |  Observatory (12)  |  Parliament (4)  |  Politician (26)  |  Remnant (6)  |  Retain (19)  |  Science (2067)  |  Show (93)  |  Star (336)  |  Stranger (15)  |  Supplementary (4)  |  Think (347)  |  Thousand (152)  |  Truly (33)  |  Vague (26)

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.
Science quotes on:  |  Attention (121)  |  Education (347)  |  Incapable (17)  |  Majority (42)  |  Mathematics (1205)  |  Mind (760)  |  Problem (497)  |  Skeleton (20)  |  Solution (216)  |  Understanding (325)

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.
Science quotes on:  |  Arithmetic (121)  |  Beginning (122)  |  Certainty (131)  |  Characteristic (96)  |  Cliff (11)  |  Conciseness (2)  |  Connection (111)  |  Difference (246)  |  Disgust (6)  |  Geometry (232)  |  Idea (580)  |  Identity (11)  |  Immediacy (2)  |  Non-Euclidian (2)  |  Previous (12)  |  Quadratic (3)  |  Question (404)  |  Research (590)  |  Result (389)  |  Seaside (2)  |  Study (476)  |  Success (250)  |  Suddenness (4)  |  Thinking (231)  |  Transformation (54)  |  Walk (67)  |  Wanting (2)

I think, and I am not the only one who does, that it is important never to introduce any conception which may not be completely defined by a finite number of words. Whatever may be the remedy adopted, we can promise ourselves the joy of the physician called in to follow a beautiful pathological case [beau cas pathologique].
— Henri Poincaré
From address read at the general session of the Fourth International Congress of Mathematicians in Rome (10 Apr 1908). As translated in 'The Future of Mathematics: by Henri Poincaré', General Appendix, Annual Report of the Boars of Regents of The Smithsonian Institution: For the Year Ending June 1909 (1910), 140.
Science quotes on:  |  Adopt (19)  |  Beautiful (144)  |  Case (99)  |  Completely (32)  |  Conception (92)  |  Define (49)  |  Finite (32)  |  Follow (124)  |  Important (205)  |  Introduce (42)  |  Joy (88)  |  Number (282)  |  Pathological (8)  |  Physician (243)  |  Promise (38)  |  Remedy (54)  |  Word (302)

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
…...
Science quotes on:  |  Cause (285)  |  Certain (126)  |  Effect (166)  |  Infinitely (13)  |  Measure (104)  |  Numerous (29)  |  Part (222)  |  Phenomenon (278)  |  Single (120)  |  Universe (686)

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.
Science quotes on:  |  Ethics (36)  |  Fear (142)  |  Happiness (94)  |  Truth (928)

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.
Science quotes on:  |  Condition (163)  |  Course (84)  |  Foresee (13)  |  Future (287)  |  History (369)  |  Mathematics (1205)  |  Present (176)  |  Proper (38)  |  Study (476)

If we work, it is less to obtain those positive results the common people think are our only interest, than to feel that aesthetic emotion and communicate it to those able to experience it.
— Henri Poincaré
From the original French, “Si nous travaillons, c’est moins pour obtenir ces résultats auxquels le vulgaire nous croit uniquement attachés, que pour ressentir cette émotion esthétique et la communiquer à ceux qui sont capables de l’éprouver,” quoted in Henri Poincaré,'Notice sur Halphen', Journal de l’École Polytechnique (1890), 60, 143, cited in Oeuvres de G.H. Halphen (1916), Vol. 1, xxiv. As translated in Armand Borel, 'On the Place of Mathematics in Culture', in Armand Borel: Œvres: Collected Papers (1983), Vol. 4, 421.
Science quotes on:  |  Aesthetic (35)  |  Common People (2)  |  Communicate (17)  |  Emotion (78)  |  Experience (342)  |  Feel (167)  |  Interest (237)  |  Positive (44)  |  Result (389)  |  Think (347)  |  Work (635)

In addition to this it [mathematics] provides its disciples with pleasures similar to painting and music. They admire the delicate harmony of the numbers and the forms; they marvel when a new discovery opens up to them an unexpected vista; and does the joy that they feel not have an aesthetic character even if the senses are not involved at all? … For this reason I do not hesitate to say that mathematics deserves to be cultivated for its own sake, and I mean the theories which cannot be applied to physics just as much as the others.
— Henri Poincaré
(1897) From the original French, “Et surtout, leurs adeptes y trouvent des jouissances analogues á celles que donnent la peinture et la musique. Ils admirent la délicate harmonie des nombres et des formes; ils s’émerveillent quand une découverte nouvelle leur ouvre une perspective inattendue; et la joie qu’ils éprouvent ainsi n’a-t-elle pas le caractère esthétique, bien que les sens n’y prennent aucune part?...C’est pourquoi je n’hésite pas à dire que les mathématiques méritent d’être cultivées pour elles-mêmes et que les théories qui ne peuvent être appliquées á la physique doivent l’être comme les autres.” Address read for him at the First International Congress of Mathematicians in Zurich: '‘Sur les rapports de l’analyse pure et de la physique', in Proceedings of that Congress 81-90, (1898). Also published as 'L’Analyse et la Physique', in La Valeur de la Science (1905), 137-151. As translated in Armand Borel, 'On the Place of Mathematics in Culture', in Armand Borel: Œvres: Collected Papers (1983), Vol. 4, 420-421.
Science quotes on:  |  Admire (18)  |  Aesthetic (35)  |  Applied (16)  |  Character (118)  |  Cultivate (19)  |  Delicate (21)  |  Deserve (28)  |  Disciple (7)  |  Discovery (680)  |  Form (314)  |  Harmony (72)  |  Joy (88)  |  Marvel (28)  |  Mathematics (1205)  |  Music (106)  |  New (496)  |  Number (282)  |  Painting (43)  |  Physics (348)  |  Pleasure (133)  |  Sake (23)  |  Sense (321)  |  Theory (696)  |  Unexpected (36)  |  Vista (6)

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.
Science quotes on:  |  Birth (93)  |  Decimal Place (2)  |  Founder (16)  |  Grasp (60)  |  Happening (32)  |  Lateness (4)  |  Means (176)  |  Misfortune (8)  |  Moment (107)  |  Observation (450)  |  Perfection (89)  |  Physical Chemistry (5)  |  Science (2067)

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
…...
Science quotes on:  |  Age (178)  |  Attract (22)  |  Beautiful (144)  |  Both (81)  |  Course (84)  |  Delight (66)  |  Fact (733)  |  Follow (124)  |  Geological (11)  |  Giant (38)  |  Microscope (74)  |  Past (152)  |  Preference (21)  |  Prodigious (9)  |  Remoteness (7)  |  Scrutinize (5)  |  Seek (107)  |  Simple (178)  |  Simplicity (147)  |  Smallness (5)  |  Star (336)  |  Trace (53)  |  Vast (89)  |  Vastness (11)

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.
Science quotes on:  |  Discovery (680)  |  Intuition (57)  |  Logic (260)  |  Proof (245)

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
…...
Science quotes on:  |  Convenience (34)  |  Find (408)  |  Impose (22)  |  Nature (1223)  |  Time And Space (31)

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.
Science quotes on:  |  Experiment (602)  |  Hypothesis (252)  |  Idea (580)

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
…...
Science quotes on:  |  Chance (160)  |  Hypothesis (252)  |  Pass (93)  |  Simple (178)  |  Unnoticed (5)  |  Wary (3)

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
…...
Science quotes on:  |  Fill (61)  |  Gulf (11)  |  Intuition (57)  |  Mathematics (1205)  |  Pure Mathematics (65)  |  Real World (14)  |  Reality (190)  |  Recourse (12)  |  Remain (113)  |  Separate (74)  |  Symbol (73)  |  Touch (77)  |  World (898)

It is through science that we prove, but through intuition that we discover.
— Henri Poincaré
…...
Science quotes on:  |  Discover (199)  |  Intuition (57)  |  Prove (109)  |  Science (2067)

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.
Science quotes on:  |  Appropriateness (6)  |  Conviction (71)  |  Jest (4)  |  Law Of Nature (64)  |  Mathematician (384)  |  Mystery (153)  |  Physicist (161)  |  Quotation (8)  |  Statement (76)  |  Theorem (90)

Law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise, or at least pretends to be. Experiment is made under conditions always complex, the enunciation of the law eliminates these complications. This is what is called ‘correcting the systematic errors’.
— Henri Poincaré
From La Valeur de la Science (1904), 142, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 77. From the French, “La loi sort de l’expérience, mais elle n’en sort pas immédiatement. L’expérience est individuelle, la loi qu’on en tire est générale, l’expérience n’est qu’approchée, la loi est précise ou du moins prétend l’élre. L’expérience se fait dans des conditions toujours complexes, l’énoncé de la loi élimine ces complications. C’est ce qu’on appelle ‘corriger les erreurs systématiques’.”
Science quotes on:  |  Approximate (10)  |  Call (128)  |  Complex (95)  |  Complication (24)  |  Condition (163)  |  Correct (85)  |  Deduce (25)  |  Eliminate (21)  |  Enunciate (2)  |  Error (277)  |  Experiment (602)  |  General (160)  |  Immediately (23)  |  Individual (221)  |  Law (515)  |  Least (74)  |  Precise (34)  |  Pretend (17)  |  Spring (71)

Logic sometimes breeds monsters.
— Henri Poincaré
In Science and Method (1952), 125.
Science quotes on:  |  Breed (22)  |  Logic (260)  |  Monster (24)  |  Sometimes (43)

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
…...
Science quotes on:  |  Afar (6)  |  Desire (142)  |  Destitute (2)  |  End (195)  |  Faculty (70)  |  Geometrician (6)  |  Grammar (14)  |  Idea (580)  |  Intuition (57)  |  Lead (160)  |  Logic (260)  |  Meet (31)  |  Necessary (154)  |  Obstacle (31)  |  Road (64)  |  See (369)  |  Teach (188)  |  Tell (110)  |  Writer (46)

Mathematical discoveries, small or great … are never born of spontaneous generation. They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
— Henri Poincaré
As given, without citation, in Eric Temple Bell, Men of Mathematics (1937), 548.
Science quotes on:  |  Born (31)  |  Conscious (45)  |  Discovery (680)  |  Great (534)  |  Knowledge (1306)  |  Labour (47)  |  Mathematics (1205)  |  Preliminary (5)  |  Prepare (35)  |  Presuppose (7)  |  Seed (63)  |  Small (163)  |  Soil (64)  |  Spontaneous Generation (5)  |  Subconscious (4)

Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. But this is exactly what yields great results, in fact the more we see this aggregate clearly and at a single glance, the better we perceive its analogies with other neighboring objects, consequently the more chances we have of divining the possible generalizations. Elegance may produce the feeling of the unforeseen by the unexpected meeting of objects we are not accustomed to bring together; there again it is fruitful, since it thus unveils for us kinships before unrecognized. It is fruitful even when it results only from the contrast between the simplicity of the means and the complexity of the problem set; it makes us then think of the reason for this contrast and very often makes us see that chance is not the reason; that it is to be found in some unexpected law. In a word, the feeling of mathematical elegance is only the satisfaction due to any adaptation of the solution to the needs of our mind, and it is because of this very adaptation that this solution can be for us an instrument. Consequently this esthetic satisfaction is bound up with the economy of thought.
— Henri Poincaré
In 'The Future of Mathematics', Monist, 20, 80. Translated from the French by George Bruce Halsted.
Science quotes on:  |  Accustomed (16)  |  Adaptation (49)  |  Aesthetic (35)  |  Aggregate (14)  |  Analogy (60)  |  Balance (55)  |  Complexity (91)  |  Comprehend (39)  |  Demonstration (86)  |  Diverse (17)  |  Elegance (30)  |  Fruitful (43)  |  Generalization (41)  |  Happy (46)  |  Harmony (72)  |  Importance (218)  |  Instrument (95)  |  Law (515)  |  Mathematician (384)  |  Mathematics (1205)  |  Meeting (20)  |  Method (239)  |  Mind (760)  |  Neighboring (5)  |  Object (175)  |  Order (242)  |  Problem (497)  |  Pure (103)  |  Result (389)  |  Satisfaction (56)  |  Simplicity (147)  |  Solution (216)  |  Study And Research In Mathematics (61)  |  Symmetry (37)  |  Unexpected (36)  |  Unforeseen (6)

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
In Science and Hypothesis (1901, 1907). Translated by W.J.G. from the original French, “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.”
Science quotes on:  |  Alone (106)  |  Attention (121)  |  Change (364)  |  Engage (25)  |  Form (314)  |  Indifference (13)  |  Interest (237)  |  Mathematician (384)  |  Matter (343)  |  Object (175)  |  Provide (69)  |  Relation (154)  |  Replace (30)  |  Study (476)

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.
Science quotes on:  |  Art (294)  |  Different (186)  |  Give (201)  |  Mathematics (1205)  |  Name (170)  |  Same (156)

Newton has shown us that a law is only a necessary relation between the present state of the world and its immediately subsequent state. All the other laws since discovered are nothing else; they are in sum, differential equations.
— Henri Poincaré
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 87.
Science quotes on:  |  Differential Equation (13)  |  Discover (199)  |  Immediate (43)  |  Law Of Nature (64)  |  Necessary (154)  |  Sir Isaac Newton (333)  |  Nothing (395)  |  Present (176)  |  Relation (154)  |  State (137)  |  Subsequent (19)  |  Sum (41)  |  World (898)

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)

One would have to have completely forgotten the history of science so as not to remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.
— Henri Poincaré
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 79.
Science quotes on:  |  Constant (58)  |  Desire (142)  |  Development (289)  |  Forget (63)  |  Happy (46)  |  History Of Science (58)  |  Influence (140)  |  Know (556)  |  Mathematics (1205)  |  Nature (1223)  |  Remember (82)

Only the privileged few are called to enjoy it [mathematics] fully, it is true; but is it not the same with all the noblest arts?
— Henri Poincaré
From 'The Relation of Analysis and Mathematical Physics', Bulletin American Mathematical Society (1899), 4 (1899), 248. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 181.
Science quotes on:  |  Art (294)  |  Enjoy (39)  |  Mathematics (1205)  |  Mathematics And Art (8)  |  Noblest (5)  |  Privilege (26)

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
In George Bruce Halsted (trans.) Science and Hypothesis (1905), 101. From the original French, “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.”, in La Science et l’Hypothèse (1908), 168. 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 (733)  |  Science (2067)

Science is facts; just as houses are made of stones, so is science made of facts; but a pile of stones is not a house and a collection of facts is not necessarily science.
— Henri Poincaré
In Science and Hypothesis.
Science quotes on:  |  Collection (44)  |  Fact (733)  |  House (43)  |  Necessarily (30)  |  Pile (12)  |  Science (2067)  |  Stone (76)

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.
Science quotes on:  |  Energy (214)  |  Enormous (41)  |  Heat (100)  |  Inexhaustible (13)  |  Million (111)  |  Radium (20)  |  Sir William Ramsay (6)  |  Transformation (54)  |  Years (5)

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 intimate 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
From La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 3, giving translation "approximately" in the footnote of the opening epigraph in the original French: “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.” Another translation, with a longer quote, beginning “Without this language…”, is on the Henri Poincaré Quotes" page of this website.
Science quotes on:  |  Language (228)  |  Mathematics (1205)  |  Mathematics As A Language (20)  |  Physicist (161)  |  Reality (190)

Sociology is the science with the greatest number of methods and the least results.
— Henri Poincaré
…...
Science quotes on:  |  Great (534)  |  Least (74)  |  Method (239)  |  Number (282)  |  Result (389)  |  Science (2067)  |  Sociology (43)

Sometimes truth frightens us. And in fact we know that it is sometimes deceptive, that it is a phantom never showing itself for a moment except to ceaselessly flee, that it must be pursued further and ever further without ever being attained. … Yet truth should not be feared, for it alone is beautiful.
— Henri Poincaré
As translated by George Bruce Halsted, in 'The Value of Science', Popular Science Monthly (Sep 1906), 69 193.
Science quotes on:  |  Alone (106)  |  Attain (45)  |  Beautiful (144)  |  Ceaseless (6)  |  Deceptive (2)  |  Fact (733)  |  Fear (142)  |  Flee (7)  |  Fright (10)  |  Know (556)  |  Moment (107)  |  Phantom (9)  |  Pursue (23)  |  Show (93)  |  Truth (928)

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.
Science quotes on:  |  Advance (165)  |  Century (131)  |  Change (364)  |  City (48)  |  Common (122)  |  Comparison (64)  |  Continuity (30)  |  Demolition (4)  |  Development (289)  |  Edifice (15)  |  End (195)  |  Evolution (535)  |  Expert (50)  |  New (496)  |  Old-Fashioned (5)  |  Past (152)  |  Pity (13)  |  Prior (5)  |  Replacement (8)  |  Science (2067)  |  Sight (48)  |  Sterility (5)  |  Theory (696)  |  Thinking (231)  |  Trace (53)  |  Type (52)  |  Vanity (19)  |  Work (635)  |  Zoology (31)

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.
Science quotes on:  |  Aim (89)  |  Dogmatist (4)  |  Imagine (76)  |  Relationship (71)  |  Science (2067)  |  Simplicity (147)

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.
Science quotes on:  |  Creation (242)  |  Genesis (17)  |  Intense (19)  |  Interest (237)  |  Mathematics (1205)  |  Problem (497)  |  Psychologist (15)

The genesis of mathematical invention is a problem that must inspire the psychologist with the keenest interest. For this is the process in which the human mind seems to borrow least from the exterior world, in which it acts, or appears to act, only by itself and on itself, so that by studying the process of geometric thought, we may hope to arrive at what is most essential in the human mind
— Henri Poincaré
As translated in Arthur I. Miller, Imagery in Scientific Thought Creating 20th-Century Physics (1984, 2013), 307. Opening of Paper delivered at Conference at the Institut Général Psychologique, Paris, 'L’Invention Mathématique', published in Enseignment Mathématique (1908), 10, 357. From the original French, “La genèse do l’Invention mathématique est un problème qui doit inspirer le plus vif intérêt au psychologue. C’est l’acte dans lequel l’esprit humain semble le moins emprunter au monde extérieur, où il n’agit ou ne paraît agir que par lui-même et sur lui-même, de sorte, qu’en étudiant le processus de la pensée géométrique, c’est ce qu’il y a de plus essentiel dans l’esprit humain que nous pouvons espérer atteindre.”
Science quotes on:  |  Act (117)  |  Appear (118)  |  Arrive (35)  |  Borrow (16)  |  Essential (117)  |  Exterior (6)  |  Genesis (17)  |  Geometry (232)  |  Hope (174)  |  Human Mind (82)  |  Inspire (51)  |  Interest (237)  |  Invention (324)  |  Keen (10)  |  Least (74)  |  Mathematics (1205)  |  Problem (497)  |  Process (267)  |  Psychologist (15)  |  Study (476)  |  Thought (546)  |  World (898)

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.
— Henri Poincaré
From Lecture to the Psychological Society, Paris, 'Mathematical Creation', translation collected in James Roy Newman The World of Mathematics (1956), Vol. 4, 2043.
Science quotes on:  |  Analogy (60)  |  Belief (504)  |  Capable (51)  |  Fact (733)  |  Kinship (4)  |  Know (556)  |  Knowledge (1306)  |  Lead (160)  |  Long (174)  |  Mathematics (1205)  |  Physical Law (8)  |  Reveal (52)  |  Stranger (15)  |  Study (476)  |  Worthy (34)  |  Wrongly (2)

The mind uses its faculty for creating only when experience forces it to do so.
— Henri Poincaré
From La Science et l’Hypothèse (1908), 43 as translated by George Bruce Halsted in Science and Hypothesis (1905), 25. From the original French, “L’esprit n’use de sa faculté créatrice que quand l’expérience lui en impose la nécessité”.
Science quotes on:  |  Create (153)  |  Experience (342)  |  Faculty (70)  |  Force (249)  |  Mind (760)

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
…...
Science quotes on:  |  Cease (39)  |  Dogma (32)  |  Fact (733)  |  Idea (580)  |  Interest (237)  |  Party (18)  |  Passion (71)  |  Preconceived (3)  |  Submit (18)  |  Themselves (44)  |  Think (347)

Thought is only a gleam in the midst of a long night. But it is this gleam which is everything.
— Henri Poincaré
Concluding sentences from La Valeur de la Science (1904), 276, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 77. From the French, “La pensée n’est qu’un écliar au milieu d’une longue nuit. Mais c’est cet éclair qui est tout”. Also given as “Thought is only a flash between two long nights. But this flash is everything”, in Edwin Emery Slosson, Major Prophets of To-day (1914), 138, citing the oration given by Paul Painlevé, of the Academy of Sciences, at the Montparnasse cemetery after the funeral for Poincaré.
Science quotes on:  |  Everything (181)  |  Flash (34)  |  Gleam (12)  |  Long (174)  |  Night (118)  |  Thought (546)

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
— Henri Poincaré
From 'Les Mathématiques et la Logique', Science et Méthode (1908, 1920), Livre 2, Chap. 3, Sec. 2, 157. English as in Henri Poincaré and George Bruce Halsted (trans.), 'Mathematics and Logic', Science and Method collected in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method (1913), 451. From the French, “Ainsi, c’est bien entendu, pour démontrer un théorème, il n’est pas nécessaire ni même utile de savoir ce qu’il veut dire. On pourrait remplacer le géomètre par le piano à raisonner imaginé par Stanley Jevons; ou, si l’on aime mieux, on pourrait imaginer une machine où l’on introduirait les axiomes par un bout pendant qu’on recueillerait les théorèmes à l’autre bout, comme cette machine légendaire de Chicago où les porcs entrent vivants et d’où ils sortent transformés en jambons et en saucisses. Pas plus que ces machines, le mathématicien n’a besoin de comprendre ce qu’il fait”.
Science quotes on:  |  Advantageous (4)  |  Alive (49)  |  Assumption (58)  |  Demonstrate (53)  |  Geometer (24)  |  Ham (2)  |  Imagine (76)  |  Know (556)  |  Logic (260)  |  Machine (157)  |  Mathematician (384)  |  Meaning (113)  |  Necessary (154)  |  Need (287)  |  Piano (12)  |  Pig (8)  |  Prove (109)  |  Replace (30)  |  Sausage (2)  |  Theorem (90)  |  Transform (35)  |  Understand (340)

To-day we no longer beg of nature; we command her, because we have discovered certain of her secrets and shall discover others each day. We command her in the name of laws she can not challenge because they are hers; these laws we do not madly ask her to change, we are the first to submit to them. Nature can only be governed by obeying her.
— Henri Poincaré
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 85.
Science quotes on:  |  Ask (160)  |  Beg (5)  |  Certain (126)  |  Challenge (61)  |  Change (364)  |  Command (28)  |  Discover (199)  |  First (314)  |  Govern (29)  |  Law Of Nature (64)  |  Mad (25)  |  Name (170)  |  Nature (1223)  |  Obey (16)  |  Secret (131)  |  Submit (18)

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
Science quotes on:  |  Absurd (30)  |  Conception (92)  |  Count (49)  |  Existence (299)  |  Fact (733)  |  Infinite (130)  |  Occupation (41)  |  Opinion (176)  |  Sake (23)  |  Science (2067)  |  Selection (33)  |  Count Leo Tolstoy (16)  |  Utility (33)  |  Writing (81)

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.
Science quotes on:  |  Application (170)  |  Definition (192)  |  Education (347)  |  Logic (260)  |  Philosopher (166)  |  Pupil (36)  |  Rule (177)  |  Satisfy (27)  |  Scientist (522)  |  Understanding (325)

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.
— Henri Poincaré
From 'L’Avenir des Mathématiques', Science et Méthode (1908, 1920), Livre Premier, Chap. 2, 25. English as in Henri Poincaré and George Bruce Halsted (trans.), 'The Future of Mathematics', Science and Method collected in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method (1913), 372. From the French, “Qu’est-ce qui nous donne en effet dans une solution, dans une démonstration, le sentiment de l’élégance? C’est l’harmonie des diverses parties, leur symétrie, leur heureux balancement; c’est en un mot tout ce qui y met de l'ordre, tout ce qui leur donne de l’unité, ce qui nous permet par conséquent d’y voir clair et d’en comprendre l’ensemble en même temps que les détails”.
Science quotes on:  |  Balance (55)  |  Clearly (41)  |  Comprehend (39)  |  Demonstration (86)  |  Detail (87)  |  Diverse (17)  |  Elegance (30)  |  Ensemble (5)  |  Feeling (91)  |  Happy (46)  |  Harmony (72)  |  Introduce (42)  |  Order (242)  |  Part (222)  |  Permit (31)  |  Proof (245)  |  See (369)  |  Solution (216)  |  Symmetry (37)  |  Unity (54)  |  Word (302)

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. Also seen elsewhere translated with “invention” in place of “discovery”.
Science quotes on:  |  Combination (91)  |  Definition (192)  |  Discernment (3)  |  Discovery (680)  |  Interest (237)  |  Knowledge (1306)  |  Mathematics (1205)  |  Selection (33)  |  Usefulness (77)

When one talked with M. Hermite, he never evoked a sensuous image, and yet you soon perceived that the most abstract entities were for him like living beings.
— Henri Poincaré
From La Valeur de la Science (1904), 32, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 24. From the French, “Quand on causait avec M. Hermite; jamais il n’évoquait une image sensible, et pourtant vous vous aperceviez bientôt que les entités les plus abstraites étaient, pour lui comme des êtres vivants.” Also as epigraph, “Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures”, in Eric Temple Bell, Men of Mathematics, (1937), 448.
Science quotes on:  |  Abstract (86)  |  Being (41)  |  Concrete (32)  |  Creature (155)  |  Entity (31)  |  Evoke (7)  |  Charles Hermite (10)  |  Image (59)  |  Living (56)  |  Perceive (40)  |  Sensuous (5)  |  Talk (100)

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.
Science quotes on:  |  Correct (85)  |  Demonstration (86)  |  Elementary (45)  |  Indefinable (5)  |  Intuition (57)  |  Logic (260)  |  Logician (12)  |  Operation (121)  |  Reality (190)  |  Resolve (19)  |  Unity (54)  |  Whole (192)

While speaking, M. Bertrand is always in motion; now he seems in combat with some outside enemy, now he outlines with a gesture of the hand the figures he studies. Plainly he sees and he is eager to paint, this is why he calls gesture to his aid. With M. Hermite, it is just the opposite; his eyes seem to shun contact with the world; it is not without, it is within he seeks the vision of truth.
— Henri Poincaré
From La Valeur de la Science (1904), 14, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 16. From the French, “Tout en parlant, M. Bertrand est toujours en action; tantôt il semble aux prises avec quelque ennemi extérieur, tantôt il dessine d'un geste de la main les figures qu’il étudie. Évidemment, il voit et il cherche à peindre, c’est pour cela qu’il appelle le geste à son secours. Pour M. Hermite, c’est tout le contraire; ses yeux semblent fuir le contact du monde; ce n’est pas au dehors, c’est au dedans qu’il cherche la vision de la vérité.”
Science quotes on:  |  Joseph Bertrand (6)  |  Combat (13)  |  Contact (34)  |  Eager (15)  |  Enemy (65)  |  Eye (222)  |  Figure (69)  |  Gesture (4)  |  Hand (142)  |  Charles Hermite (10)  |  Inside (26)  |  Motion (160)  |  Opposite (50)  |  Outline (11)  |  Outside (48)  |  Paint (21)  |  See (369)  |  Seek (107)  |  Shun (4)  |  Speak (92)  |  Study (476)  |  Truth (928)  |  Vision (94)  |  World (898)

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.
Science quotes on:  |  Chance (160)  |  Eclipse (20)  |  People (390)  |  Prayer (23)  |  Rain (33)  |  Ridicule (17)  |  Shower (6)  |  Storm (30)  |  Weather (32)

Without this language [mathematics] most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world, which is the only true objective reality. …
This harmony … is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.
— Henri Poincaré
From La Valeur de la Science, as translated by George Bruce Halsted, in 'The Value of Science', Popular Science Monthly (Sep 1906), 69 195-196.
Science quotes on:  |  Analogy (60)  |  Attach (14)  |  Attain (45)  |  Beauty (248)  |  Better (192)  |  Difficult (121)  |  Enable (46)  |  Forever (60)  |  Harmony (72)  |  Ignorant (40)  |  Internal (25)  |  Intimate (15)  |  Know (556)  |  Little (188)  |  Mathematics (1205)  |  Mathematics As A Language (20)  |  Objective (66)  |  Price (34)  |  Progress (368)  |  Reality (190)  |  Remain (113)  |  Slow (56)  |  Sole (21)  |  Source (91)  |  True (208)  |  Truth (928)  |  Understand (340)  |  Universal (105)  |  Unknown (107)  |  World (898)

[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.

~~[No known source]~~ Later generations will regard Mengenlehre [set theory] as a disease from which one has recovered.
— Henri Poincaré
Webmaster finds zero support for the authenticity of this quote. Speculations on how it may have evolved include reference to a beau cas pathologique (a beautiful pathological case) in a very different quote which begins “I think, and I am not the only one…”. (See the Henri Poincaré Quotes web page of this site.) More details readily available with a Google search (for example): Did Poincaré say “set theory is a disease”. The quote is included here to provide this caution.
Science quotes on:  |  Disease (275)  |  Generation (141)  |  Later (17)  |  Recover (11)  |  Regard (95)  |  Set Theory (5)

… 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.
Science quotes on:  |  Chaos (77)  |  Condition (163)  |  Difference (246)  |  Phenomenon (278)



Quotes by others about Henri Poincaré (3)

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.
In Men of Mathematics (1937), 552.
Science quotes on:  |  Logic (260)  |  Mathematics (1205)

It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
Science quotes on:  |  A Priori (22)  |  Achievement (150)  |  Administrator (10)  |  Admit (45)  |  Affair (29)  |  Aid (42)  |  Alike (22)  |  Alone (106)  |  Analogous (5)  |  Analysis (166)  |  Anatomist (17)  |  Application (170)  |  François Arago (14)  |  Army (25)  |  Attain (45)  |  Author (62)  |  Balance (55)  |  Behold (18)  |  Bernhard Bolzano (2)  |  Calculation (100)  |  Calculus (51)  |  Call (128)  |  Lazare-Nicolas-Marguerite Carnot (4)  |  Celebrated (2)  |  Central (34)  |  Certainty (131)  |  Chair (11)  |  Civil (6)  |  Classic (10)  |  William Kingdon Clifford (21)  |  Commercial (26)  |  Comparative (13)  |  Compare (38)  |  Constantly (27)  |  Constitution (31)  |  Contemplate (17)  |  Creation (242)  |  Creator (55)  |  Current (54)  |  Baron Georges Cuvier (30)  |  Charles Darwin (301)  |  Deal (49)  |  Degree (82)  |  René Descartes (81)  |  Descriptive Geometry (3)  |  Devotee (5)  |  Devotion (25)  |  Direct (84)  |  Dissimilar (6)  |  Distinction (46)  |  Diverse (17)  |  Division (34)  |  Doctrine (75)  |  Due (20)  |  Eminent (17)  |  Empire (14)  |  Endless (28)  |  Engage (25)  |  Exercise (69)  |  Eye (222)  |  Fact (733)  |  False (99)  |  Fauna (13)  |  Field (171)  |  Finally (26)  |  Find (408)  |  Flora (9)  |  Flourish (16)  |  Baron Jean-Baptiste-Joseph Fourier (17)  |  Function (131)  |  Carl Friedrich Gauss (77)  |  General (160)  |  Genuinely (4)  |  Geometry (232)  |  Great (534)  |  Ground (90)  |  Group (72)  |  Hero (35)  |  Hide (53)  |  High (153)  |  Histology (2)  |  Host (16)  |  Idea (580)  |  Illuminate (24)  |  Immortal (19)  |  Industry (109)  |  Infinitesimal (15)  |  Inheritor (2)  |  Interest (237)  |  Intimate (15)  |  Invoke (6)  |  Judgment (101)  |  Kingdom (38)  |  Felix Klein (15)  |  Know (556)  |  Land (115)  |  Large (130)  |  Gottfried Wilhelm Leibniz (49)  |  Letter (51)  |  Logical (55)  |  Major (32)  |  Master (98)  |  Mathematician (384)  |  Mathematics (1205)  |  Matter (343)  |  Microscopic (11)  |  Mind (760)  |  Minute (44)  |  Monarch (4)  |  Gaspard Monge (2)  |  Sir Isaac Newton (333)  |  Office (22)  |  Operation (121)  |  Opinion (176)  |  Organize (20)  |  Part (222)  |  Blaise Pascal (80)  |  Peace (84)  |  Peer (11)  |  Philosophy (259)  |  Jean-Victor Poncelet (2)  |  Position (76)  |  Practical (133)  |  Prepare (35)  |  Probability (106)  |  Projective Geometry (2)  |  Public Service (5)  |  Pure (103)  |  Range (57)  |  Reality (190)  |  Recess (7)  |  Reduce (53)  |  Reducible (2)  |  Reflect (31)  |  Relate (20)  |  Render (33)  |  Require (85)  |  Bernhard Riemann (7)  |  Rightful (3)  |  Sagacious (4)  |  Say (228)  |  Scatter (6)  |  Science (2067)  |  Seldom (30)  |  Similarity (21)  |  Single (120)  |  Statesman (18)  |  Structure (225)  |  Surprise (71)  |  Survey (20)  |  Theory (696)  |  Tune (14)  |  Unfit (12)  |  Variety (71)  |  View (171)  |  Vision (94)  |  War (161)  |  Karl Weierstrass (9)  |  Wield (10)  |  Work (635)  |  World (898)

To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.
Science quotes on:  |  Accept (65)  |  Accrue (3)  |  Achieve (64)  |  Advance (165)  |  Appear (118)  |  Applicability (6)  |  Application (170)  |  Apply (77)  |  Associate (16)  |  Astronomy (204)  |  Belief (504)  |  Body (247)  |  Build (117)  |  Certainly (31)  |  Chief (38)  |  Choose (60)  |  Complex (95)  |  Condenser (4)  |  Connection (111)  |  Consideration (85)  |  Conspicuous (7)  |  Construction (83)  |  Current (54)  |  Deduce (25)  |  Deem (6)  |  Develop (107)  |  Development (289)  |  Difficult (121)  |  Discontinuous (5)  |  Discussion (48)  |  Domain (42)  |  Dominate (19)  |  Dynamics (9)  |  Elaborate (21)  |  Electrostatic (5)  |  Emphasize (12)  |  Equation (96)  |  Extension (31)  |  Extremely (15)  |  Far (154)  |  Fluid Motion (2)  |  Function (131)  |  Functional (10)  |  General (160)  |  Geometrical (10)  |  Guide (65)  |  Heavy (23)  |  Hydrodynamics (5)  |  Idea (580)  |  Important (205)  |  Initiate (6)  |  Instance (32)  |  Interest (237)  |  Interpret (19)  |  Introduce (42)  |  Investigation (176)  |  Issue (42)  |  Knowledge (1306)  |  Count Joseph-Louis de Lagrange (26)  |  Least (74)  |  Let (61)  |  Map (30)  |  Mathematician (384)  |  Mathematics (1205)  |  Merely (82)  |  Method (239)  |  Motion (160)  |  Natural (173)  |  Opinion (176)  |  Paper (83)  |  Particularly (21)  |  Phenomenon (278)  |  Physical (134)  |  Plan (87)  |  Portion (24)  |  Possible (158)  |  Practical (133)  |  Principle (292)  |  Property (126)  |  Pure Mathematics (65)  |  Purely (28)  |  Question (404)  |  Refine (5)  |  Regard (95)  |  Region (36)  |  Relation (154)  |  Representation (36)  |  Result (389)  |  Rotate (6)  |  Score (8)  |  Similar (35)  |  Sole (21)  |  Study And Research In Mathematics (61)  |  Subject (240)  |  Substantial (14)  |  Supreme (37)  |  Theory (696)  |  Thought (546)  |  Time (595)  |  Title (18)  |  Turned Out (4)  |  Unwise (4)  |  Variable (16)  |  Various (47)  |  Work (635)  |  Year (299)


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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.