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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
Poincaré
Henri Poincare
Jules Henri Poincare
Poincare
Purpose
Threefold
Natural
Aesthetic
Instrument
Science
Provide
Nature
Philosophical
Must
Instruments
Mathematics
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More quotes by Henri Poincare

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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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The mind uses its faculty for creativity only when experience forces it to do so.
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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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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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The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.
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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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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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How is error possible in mathematics?
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Mathematics is the art of giving the same name to different things.
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In the old days when people invented a new function they had something useful in mind.
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Mathematicians do not study objects, but the relations between objects.
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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
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.
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When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole it is to intuition that we must look for it.
Henri Poincare
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...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
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Mathematical discoveries, small or great are never born of spontaneous generation.
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All of mathematics is a tale about groups.
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Geometry is not true, it is advantageous.
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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
Henri Poincare