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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
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Mathematician
Philosopher
Philosopher Of Science
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Jules Henri Poincaré
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Henri Poincare
Jules Henri Poincare
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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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Point set topology is a disease from which the human race will soon recover.
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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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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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...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.
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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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Geometry is the art of correct reasoning from incorrectly drawn figures.
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How is error possible in mathematics?
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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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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
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Mathematicians are born, not made.
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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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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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But for harmony beautiful to contemplate, science would not be worth following.
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Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
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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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In the old days when people invented a new function they had something useful in mind. Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them.
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Mathematical discoveries, small or great are never born of spontaneous generation.
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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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