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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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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
Unconscious
Sign
Appearance
Illumination
Firsts
Prior
First
Striking
Work
Subconscious
Long
Manifest
Sudden

More quotes by Henri Poincare

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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
Henri Poincare
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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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Mathematics is the art of giving the same name to different things.
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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
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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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Every good mathematician should also be a good chess player and vice versa.
Henri Poincare
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But for harmony beautiful to contemplate, science would not be worth following.
Henri Poincare
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Mathematicians are born, not made.
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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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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But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.
Henri Poincare
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How is error possible in mathematics?
Henri Poincare
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Geometry is not true, it is advantageous.
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Thought is only a flash between two long nights, but this flash is everything.
Henri Poincare
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Mathematicians do not study objects, but the relations between objects.
Henri Poincare
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Intuition is more important to discovery than logic.
Henri Poincare
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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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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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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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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.
Henri Poincare