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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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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
Great
Conditions
Fortuitous
Ones
Initial
Differences
Initials
Happen
Phenomena
Small
Final
Science
Finals
Happens
Chaos
May
Produce

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Analyse data just so far as to obtain simplicity and no further.
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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.
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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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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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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
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The mind uses its faculty for creativity only when experience forces it to do so.
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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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It is far better to foresee even without certainty than not to foresee at all.
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Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
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Thought is only a flash between two long nights, but this flash is everything.
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Mathematics is the art of giving the same name to different things.
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When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.
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How is error possible in mathematics?
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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.
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All of mathematics is a tale about groups.
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.
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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.
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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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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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