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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
Le Cateau
Jules Henri Poincaré
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Henri Poincare
Jules Henri Poincare
Poincare
Nature
Provide
Must
Philosophical
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Mathematics
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Purpose
Threefold
Natural
Aesthetic
Science
Instrument

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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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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.
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The mind uses its faculty for creativity only when experience forces it to do so.
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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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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
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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.
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But for harmony beautiful to contemplate, science would not be worth following.
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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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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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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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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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Just as houses are made of stones, so is science made of facts.
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Point set topology is a disease from which the human race will soon recover.
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Mathematicians are born, not made.
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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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Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?
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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
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It is through science that we prove, but through intuition that we discover.
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It is far better to foresee even without certainty than not to foresee at all.
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