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Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some 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
Half
Serve
Makes
Function
Resemble
Mass
Functions
Littles
Century
Bizarre
Little
Honest
Forced
Sometimes
Seen
Monsters
Possible
Appear
Purpose
Logic

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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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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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It is far better to foresee even without certainty than not to foresee at all.
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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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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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Mathematics is the art of giving the same name to different things.
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
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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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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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...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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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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All of mathematics is a tale about groups.
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Les faits ne parlent pas. Facts do not speak.
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The mind uses its faculty for creativity only when experience forces it to do so.
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Geometry is the art of correct reasoning from incorrectly drawn figures.
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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
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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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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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Mathematicians are born, not made.
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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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