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How is error possible in mathematics?

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
Error
Mathematical
Errors
Mathematics
Possible

More quotes by 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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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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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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Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
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.
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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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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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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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In the old days when people invented a new function they had something useful in mind.
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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
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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.
Henri Poincare
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But for harmony beautiful to contemplate, science would not be worth following.
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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.
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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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Pure logic could never lead us to anything but tautologies it can create nothing new not from it alone can any science issue.
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Mathematicians are born, not made.
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All of mathematics is a tale about groups.
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Mathematicians do not study objects, but relations among objects they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
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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