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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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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
Even
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Mathematical discoveries, small or great are never born of spontaneous generation.
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The mind uses its faculty for creativity only when experience forces it to do so.
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Mathematicians are born, not made.
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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.
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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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How is error possible in mathematics?
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All of mathematics is a tale about groups.
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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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One geometry cannot be more true than another it can only be more convenient.
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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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Point set topology is a disease from which the human race will soon recover.
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Analyse data just so far as to obtain simplicity and no further.
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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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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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In the old days when people invented a new function they had something useful in mind.
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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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Mathematics is the art of giving the same name to different things.
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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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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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It is far better to foresee even without certainty than not to foresee at all.
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