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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.

Henri Poincare

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Henri Poincare
Age: 58 †
Born: 1854
Born: April 29
Died: 1912
Died: July 17
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More quotes by Henri Poincare

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Mathematicians do not study objects, but the relations between objects.
Henri Poincare
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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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But for harmony beautiful to contemplate, science would not be worth following.
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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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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.
Henri Poincare
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Point set topology is a disease from which the human race will soon recover.
Henri Poincare
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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
Henri Poincare
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Geometry is the art of correct reasoning from incorrectly drawn figures.
Henri Poincare
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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.
Henri Poincare
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It is through science that we prove, but through intuition that we discover.
Henri Poincare
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Geometry is not true, it is advantageous.
Henri Poincare
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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.
Henri Poincare
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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
Henri Poincare
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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
Henri Poincare
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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
Henri Poincare
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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
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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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.
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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
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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.
Henri Poincare