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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
Mathematical
Errors
Mathematics
Possible
Error

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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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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
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But for harmony beautiful to contemplate, science would not be worth following.
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It is far better to foresee even without certainty than not to foresee at all.
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Thought is only a flash between two long nights, but this flash is everything.
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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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Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.
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All of mathematics is a tale about groups.
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One geometry cannot be more true than another it can only be more convenient.
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Every good mathematician should also be a good chess player and vice versa.
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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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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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Point set topology is a disease from which the human race will soon recover.
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Geometry is the art of correct reasoning from incorrectly drawn figures.
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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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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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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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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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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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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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