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In the old days when people invented a new function they had something useful in mind.

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
People
Invented
Useful
Function
Days
Mind
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It is through science that we prove, but through intuition that we discover.
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Every good mathematician should also be a good chess player and vice versa.
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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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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.
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In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.
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How is error possible in mathematics?
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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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Mathematicians are born, not made.
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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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Mathematics is the art of giving the same name to different things.
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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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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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...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
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The mind uses its faculty for creativity only when experience forces it to do so.
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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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It is far better to foresee even without certainty than not to foresee at all.
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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
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Mathematicians do not study objects, but the relations between objects.
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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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