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Mathematicians do not study objects, but the relations between objects.

Henri Poincare

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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
Astronomer
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Mathematician
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Philosopher Of Science
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Henri Poincare
Jules Henri Poincare
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More quotes by Henri Poincare

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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
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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.
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One geometry cannot be more true than another it can only be more convenient.
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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.
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Geometry is the art of correct reasoning from incorrectly drawn figures.
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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.
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Mathematical discoveries, small or great are never born of spontaneous generation.
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Intuition is more important to discovery than logic.
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Analyse data just so far as to obtain simplicity and no further.
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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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Just as houses are made of stones, so is science made of facts.
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Les faits ne parlent pas. Facts do not speak.
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Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
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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.
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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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...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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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.
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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
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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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In the old days when people invented a new function they had something useful in mind.
Henri Poincare