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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
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Henri Poincare
Jules Henri Poincare
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Mathematics
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More quotes by 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.
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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.
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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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Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
Henri Poincare
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Mathematical discoveries, small or great are never born of spontaneous generation.
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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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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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
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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Geometry is not true, it is advantageous.
Henri Poincare
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The mind uses its faculty for creativity only when experience forces it to do so.
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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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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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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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.
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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Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
Henri Poincare
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Every good mathematician should also be a good chess player and vice versa.
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All of mathematics is a tale about groups.
Henri Poincare