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

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Henri Poincaré
(29 Apr 1854 - 17 Jul 1912)

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


Henri Poincaré Quotes on Fact (14 quotes)

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Les faits ne parlent pas.
Facts do not speak.
— Henri Poincaré
Attributed. As quoted in Alan L. Mackay, The Harvest of a Quiet Eye.
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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.
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All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not.
— Henri Poincaré
The Value of Science (1905), in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method(1946), trans. by George Bruce Halsted, 332.
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Everybody firmly believes in it [Nomal Law of Errors] because the mathematicians imagine it is a fact of observation, and observers that it is a theory of mathematics.
— Henri Poincaré
…...
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Geometrical axioms are neither synthetic a priori conclusions nor experimental facts. They are conventions: our choice, amongst all possible conventions, is guided by experimental facts; but it remains free, and is only limited by the necessity of avoiding all contradiction. ... In other words, axioms of geometry are only definitions in disguise.
That being so what ought one to think of this question: Is the Euclidean Geometry true?
The question is nonsense. One might as well ask whether the metric system is true and the old measures false; whether Cartesian co-ordinates are true and polar co-ordinates false.
— Henri Poincaré
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 110.
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It is because simplicity and vastness are both beautiful that we seek by preference simple facts and vast facts; that we take delight, now in following the giant courses of the stars, now in scrutinizing the microscope that prodigious smallness which is also a vastness, and now in seeking in geological ages the traces of a past that attracts us because of its remoteness.
— Henri Poincaré
…...
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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.
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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.”
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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.
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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.
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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 Poincaré
From Lecture to the Psychological Society, Paris, 'Mathematical Creation', translation collected in James Roy Newman The World of Mathematics (1956), Vol. 4, 2043.
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Thinking must never submit itself, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, if not to facts themselves, because, for it, to submit would be to cease to be.
— Henri Poincaré
…...
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Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts since they are infinite in number. We must make a selection ... guided by utility ... Have we not some better occupation than counting the number of lady-birds in existence on this planet?
— Henri Poincaré
In Science and Method (1914, 2003), 15
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What, 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”.
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See also:
  • 29 Apr - short biography, births, deaths and events on date of Poincaré's birth.
  • The Value of Science: Essential Writings of Henri Poincaré, by Henri Poincaré. - book suggestion.

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