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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.

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
Purpose
Threefold
Natural
Aesthetic
Science
Instrument
Nature
Provide
Must
Philosophical
Instruments
Mathematics
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More quotes by Henri Poincare

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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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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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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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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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Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
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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.
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.
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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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. . . 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 mind uses its faculty for creativity only when experience forces it to do so.
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Every good mathematician should also be a good chess player and vice versa.
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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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
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But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.
Henri Poincare
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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.
Henri Poincare
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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.
Henri Poincare
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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.
Henri Poincare
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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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But for harmony beautiful to contemplate, science would not be worth following.
Henri Poincare
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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.
Henri Poincare