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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
Philosopher
Philosopher Of Science
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Researcher
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Mathematicians
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Geometry is not true, it is advantageous.
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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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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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Just as houses are made of stones, so is science made of facts.
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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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It is through science that we prove, but through intuition that we discover.
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Zero is the number of objects that satisfy a condition that is never satisfied. But as never means in no case, I do not see that any progress has been made.
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Les faits ne parlent pas. Facts do not speak.
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Thought is only a flash between two long nights, but this flash is everything.
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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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But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.
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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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Intuition is more important to discovery than logic.
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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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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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Mathematical discoveries, small or great are never born of spontaneous generation.
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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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How is error possible in mathematics?
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The mind uses its faculty for creativity only when experience forces it to do so.
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