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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.

Henri Poincare

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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
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More quotes by Henri Poincare

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Mathematicians do not study objects, but the relations between objects.
Henri Poincare
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A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist his pleasure is as great and of the same nature.
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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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
Henri Poincare
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Point set topology is a disease from which the human race will soon recover.
Henri Poincare
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What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them it is that which satisfies the rules of logic. But in education it is not that it is one that can be understood by the pupils.
Henri Poincare
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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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In the old days when people invented a new function they had something useful in mind.
Henri Poincare
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A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.
Henri Poincare
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Mathematical discoveries, small or great are never born of spontaneous generation.
Henri Poincare
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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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How is error possible in mathematics?
Henri Poincare
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The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.
Henri Poincare
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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?
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.
Henri Poincare
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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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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
Henri Poincare
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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.
Henri Poincare
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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.
Henri Poincare
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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.
Henri Poincare