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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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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
Chance
Wary
Simple
Unnoticed
Must
Hypothesis
Chances
Passings
Passing
Mathematics
Ones
Hypotheses

More quotes by Henri Poincare

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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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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.
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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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. . . 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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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.
Henri Poincare
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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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Just as houses are made of stones, so is science made of facts.
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Thought is only a flash between two long nights, but this flash is everything.
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One geometry cannot be more true than another it can only be more convenient.
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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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The mind uses its faculty for creativity only when experience forces it to do so.
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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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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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It is through science that we prove, but through intuition that we discover.
Henri Poincare
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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.
Henri Poincare
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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
Henri Poincare
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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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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
Henri Poincare
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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Henri Poincare
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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.
Henri Poincare