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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
Solution
Solutions
Indeed
Gives
Feeling
Feelings
Idaho
Giving
Demonstration
Elegance

More quotes by Henri Poincare

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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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Analyse data just so far as to obtain simplicity and no further.
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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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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
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Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
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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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Geometry is the art of correct reasoning from incorrectly drawn figures.
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It is through science that we prove, but through intuition that we discover.
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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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Intuition is more important to discovery than logic.
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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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A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
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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.
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If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.
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How is error possible in mathematics?
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All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.
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Mathematics is the art of giving the same name to different things.
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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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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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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.
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