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A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

Henri Poincare

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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
Astronomer
Engineer
Mathematician
Philosopher
Philosopher Of Science
Physicist
Researcher
Topologist
University Teacher
Le Cateau
Jules Henri Poincaré
Poincaré
Henri Poincare
Jules Henri Poincare
Poincare
Logical
Mathematical
Guilty
Following
Demonstrations
Minds
Fallacy
Fine
Demonstration
Mind
Incapable
Sane

More quotes by Henri Poincare

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The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.
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Mathematicians are born, not made.
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Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer.
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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.
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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.
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In the old days when people invented a new function they had something useful in mind.
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But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.
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Thought is only a flash between two long nights, but this flash is everything.
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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.
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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
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Intuition is more important to discovery than logic.
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But for harmony beautiful to contemplate, science would not be worth following.
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Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.
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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.
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...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
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Mathematicians do not deal in objects, but in relations between objects thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.
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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 practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?
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Pure logic could never lead us to anything but tautologies it can create nothing new not from it alone can any science issue.
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Just as houses are made of stones, so is science made of facts.
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Every good mathematician should also be a good chess player and vice versa.
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