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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

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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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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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Geometry is not true, it is advantageous.
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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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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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But for harmony beautiful to contemplate, science would not be worth following.
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The mind uses its faculty for creativity only when experience forces it to do so.
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In the old days when people invented a new function they had something useful in mind.
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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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Intuition is more important to discovery than logic.
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Mathematical discoveries, small or great are never born of spontaneous generation.
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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
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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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Zero is the number of objects that satisfy a condition that is never satisfied. But as never means in no case, I do not see that any progress has been made.
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It is far better to foresee even without certainty than not to foresee at all.
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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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Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer.
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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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It is through science that we prove, but through intuition that we discover.
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