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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.

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
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Henri Poincare
Jules Henri Poincare
Poincare
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Mathematician
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Irrelevant
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Relations
Free
Content
Others
Thus
Form
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Unchanged
Long
Remain
Mathematicians
Interested
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Mathematics is the art of giving the same name to different things.
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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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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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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.
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In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.
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Les faits ne parlent pas. Facts do not speak.
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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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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.
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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 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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Just as houses are made of stones, so is science made of facts.
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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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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
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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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Thought is only a flash between two long nights, but this flash is everything.
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It is the simple hypotheses of which one must be most wary because these are the ones that have the most chances of passing unnoticed.
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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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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
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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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