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Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic 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
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Jules Henri Poincaré
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Henri Poincare
Jules Henri Poincare
Poincare
Science
Instrument
Nature
Provide
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Instruments
Mathematics
Study
Purpose
Threefold
Natural
Aesthetic

More quotes by Henri Poincare

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It is far better to foresee even without certainty than not to foresee at all.
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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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. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
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Mathematics is the art of giving the same name to different things.
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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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Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
Henri Poincare
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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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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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Thought is only a flash between two long nights, but this flash is everything.
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
Henri Poincare
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Mathematicians do not study objects, but the relations between objects.
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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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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
Henri Poincare
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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.
Henri Poincare
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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.
Henri Poincare
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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
Henri Poincare
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Geometry is the art of correct reasoning from incorrectly drawn figures.
Henri Poincare
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Mathematical discoveries, small or great are never born of spontaneous generation.
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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.
Henri Poincare
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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.
Henri Poincare