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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

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
Giving
Demonstration
Elegance
Solution
Solutions
Indeed
Gives
Feeling
Feelings
Idaho

More quotes by 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?
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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
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Zero is the number of objects that satisfy a condition that is never satisfied. But as never means in no case, I do not see that any progress has been made.
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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
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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.
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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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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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All of mathematics is a tale about groups.
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Analyse data just so far as to obtain simplicity and no further.
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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
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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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If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living
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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
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It is far better to foresee even without certainty than not to foresee at all.
Henri Poincare
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Les faits ne parlent pas. Facts do not speak.
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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. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
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Point set topology is a disease from which the human race will soon recover.
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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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Just as houses are made of stones, so is science made of facts.
Henri Poincare