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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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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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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
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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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.
Henri Poincare
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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
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Just as houses are made of stones, so is science made of facts.
Henri Poincare
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Mathematics is the art of giving the same name to different things.
Henri Poincare
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For a long time the objects that mathematicians dealt with were mostly ill-defined one believed one knew them, but one represented them with the senses and imagination but one had but a rough picture and not a precise idea on which reasoning could take hold.
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
Henri Poincare
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Intuition is more important to discovery than logic.
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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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.
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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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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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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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.
Henri Poincare
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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
Henri Poincare
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All of mathematics is a tale about groups.
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.
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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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