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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.

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
Progress
Zero
Numbers
Condition
Means
Satisfied
Mean
Case
Made
Number
Never
Objects
Conditions
Cases
Satisfy

More quotes by Henri Poincare

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Mathematicians are born, not made.
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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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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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We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.
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It is through science that we prove, but through intuition that we discover.
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All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.
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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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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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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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Intuition is more important to discovery than logic.
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Les faits ne parlent pas. Facts do not speak.
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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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Geometry is the art of correct reasoning from incorrectly drawn figures.
Henri Poincare
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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.
Henri Poincare
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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
Henri Poincare
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It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry the founders are hampered in their general grasp by third and fourth decimal places.
Henri Poincare
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Analyse data just so far as to obtain simplicity and no further.
Henri Poincare
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. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
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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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It is far better to foresee even without certainty than not to foresee at all.
Henri Poincare