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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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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
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Giving
Demonstration
Elegance
Solution
Solutions
Indeed
Gives
Feeling
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More quotes by Henri Poincare

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Les faits ne parlent pas. Facts do not speak.
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Intuition is more important to discovery than logic.
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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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It is far better to foresee even without certainty than not to foresee at all.
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It is through science that we prove, but through intuition that we discover.
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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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But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.
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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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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.
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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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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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For a long time the objects that mathematicians dealt with were mostly ill-defined one believed one knew them, but one represented them with the senses and imagination but one had but a rough picture and not a precise idea on which reasoning could take hold.
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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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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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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.
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One geometry cannot be more true than another it can only be more convenient.
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Mathematicians are born, not made.
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Just as houses are made of stones, so is science made of facts.
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How is error possible in mathematics?
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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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