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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
Mathematics
Possible
Error
Mathematical
Errors

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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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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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The mind uses its faculty for creativity only when experience forces it to do so.
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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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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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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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Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?
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Mathematical discoveries, small or great are never born of spontaneous generation.
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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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If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.
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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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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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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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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 far better to foresee even without certainty than not to foresee at all.
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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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Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.
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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.
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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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