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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.

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
Sign
Appearance
Illumination
Firsts
Prior
First
Striking
Work
Subconscious
Long
Manifest
Sudden
Unconscious

More quotes by Henri Poincare

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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
Henri Poincare
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Analyse data just so far as to obtain simplicity and no further.
Henri Poincare
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Mathematicians do not study objects, but relations among objects they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
Henri Poincare
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
Henri Poincare
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What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them it is that which satisfies the rules of logic. But in education it is not that it is one that can be understood by the pupils.
Henri Poincare
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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.
Henri Poincare
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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
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Mathematical discoveries, small or great are never born of spontaneous generation.
Henri Poincare
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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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Mathematics is the art of giving the same name to different things.
Henri Poincare
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It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry the founders are hampered in their general grasp by third and fourth decimal places.
Henri Poincare
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Mathematicians are born, not made.
Henri Poincare
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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
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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?
Henri Poincare
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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
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One geometry cannot be more true than another it can only be more convenient.
Henri Poincare
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One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.
Henri Poincare
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A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.
Henri Poincare
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Geometry is not true, it is advantageous.
Henri Poincare
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In the old days when people invented a new function they had something useful in mind.
Henri Poincare