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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
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Jules Henri Poincaré
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Henri Poincare
Jules Henri Poincare
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More quotes by 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.
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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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Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer.
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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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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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It is through science that we prove, but through intuition that we discover.
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Mathematicians are born, not made.
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When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.
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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.
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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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All of mathematics is a tale about groups.
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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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It is far better to foresee even without certainty than not to foresee at all.
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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Henri Poincare
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Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
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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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
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.
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Mathematics is the art of giving the same name to different things.
Henri Poincare
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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
Henri Poincare