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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.
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
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University Teacher
Le Cateau
Jules Henri Poincaré
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Henri Poincare
Jules Henri Poincare
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More quotes by Henri Poincare
Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
Henri Poincare
Point set topology is a disease from which the human race will soon recover.
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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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Analyse data just so far as to obtain simplicity and no further.
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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Henri Poincare
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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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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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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Pure logic could never lead us to anything but tautologies it can create nothing new not from it alone can any science issue.
Henri Poincare
One geometry cannot be more true than another it can only be more convenient.
Henri Poincare
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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I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry.
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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.
Henri Poincare
We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
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Geometry is the art of correct reasoning from incorrectly drawn figures.
Henri Poincare
It is far better to foresee even without certainty than not to foresee at all.
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Geometry is not true, it is advantageous.
Henri Poincare
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.
Henri Poincare
Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
Henri Poincare
If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.
Henri Poincare