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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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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
Makes
Function
Resemble
Littles
Mass
Functions
Little
Century
Bizarre
Honest
Forced
Sometimes
Seen
Monsters
Possible
Appear
Purpose
Logic
Half
Serve

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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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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
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How is error possible in mathematics?
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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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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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Just as houses are made of stones, so is science made of facts.
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In the old days when people invented a new function they had something useful in mind.
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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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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.
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One geometry cannot be more true than another it can only be more convenient.
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Mathematics is the art of giving the same name to different things.
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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.
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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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It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.
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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
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All of mathematics is a tale about groups.
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Every good mathematician should also be a good chess player and vice versa.
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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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