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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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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
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Henri Poincare
Jules Henri Poincare
Poincare
Demonstrate
Thus
Neither
Necessary
Understood
Means
Theorem
Mean
Advantageous
Even
Theorems

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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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It is far better to foresee even without certainty than not to foresee at all.
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When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole it is to intuition that we must look for it.
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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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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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A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
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Mathematicians do not study objects, but relations among objects they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
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But for harmony beautiful to contemplate, science would not be worth following.
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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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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
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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.
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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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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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Geometry is not true, it is advantageous.
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The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.
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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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Analyse data just so far as to obtain simplicity and no further.
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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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Pure logic could never lead us to anything but tautologies it can create nothing new not from it alone can any science issue.
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