Henri Poincare Quotes - Page 4

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• It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomena.

  Henri Poincare

  Errors, Differences, Finals

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• In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer.

  Henri Poincare

  Science, Experience, Observation

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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 Poincare

  Eye, Science, Past

  Henri Poincare (2012). “The Value of Science: Essential Writings of Henri Poincare”, p.328, Modern Library

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• Zero is the number of objects that satisfy a condition that is never
  satisfied. But as never means "in no case", I do not see that any progress has been made.

  Henri Poincare

  Zero, Mean, Numbers

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• Les faits ne parlent pas.
  Facts do not speak.

  Henri Poincare

  Facts, Speak

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• I entered an omnibus to go to some place or other. At that 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 non-Euclidean geometry.

  Henri Poincare

  Ideas, Feet, Steps

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• . . . 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 Poincare

  Math, Mind, World

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• 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 Poincare

  Moving, Math, Two

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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 Poincare

  Science, History, Wish

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• 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.

  Henri Poincare

  Life, Math, Abstract

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

  Henri Poincare

  Children, Moving, History

  "'La logique et l'intuition dans la science mathématique et dans l'enseignement' ('Logic and intuition in the science of mathematics and in teaching')". Book by Henri Poincare, 1899.

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• 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 Poincare

  Science, Ideas, Long

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• A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.

  Henri Poincare

  Nature, Work, Math

  "Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse". Book by Tobias Dantzig, p. 8, 1954.

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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 Poincare

  Reality, Views, Giving

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• 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 Poincare

  Mean, Math, Piano

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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 Poincare

  Truth, Men, Giving

  1904 TheValue of Science.

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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 Poincare

  Stars, Distance, Moving

  Henri Poincare (2012). “The Value of Science: Essential Writings of Henri Poincare”, p.905, Modern Library

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• 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 Poincare

  Leadership, Math, Law

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• [T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.

  Henri Poincare

  Ambition, Math, Different

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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 Poincare

  Science, Thinking, Law

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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 Poincare

  Success, Science, Ideas

  Henri Poincare (2012). “The Value of Science: Essential Writings of Henri Poincare”, p.649, Modern Library

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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 Poincare

  Freedom, Science, Understanding

  Henri Poincare (2012). “The Value of Science: Essential Writings of Henri Poincare”, p.547, Modern Library

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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 Poincare

  Inspiration, Hard Work, Science

  Henri Poincare (2012). “The Value of Science: Essential Writings of Henri Poincare”, p.660, Modern Library

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• But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.

  Henri Poincare

  Effort, Difficulty

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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 Poincare

  Powerful, Science, Law

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