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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
Thus
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Advantageous
Even
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Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
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Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?
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What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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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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Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
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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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Ideas rose in clouds I felt them collide until pairs interlocked, so to speak, making a stable combination.
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Geometry is the art of correct reasoning from incorrectly drawn figures.
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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 subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.
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Mathematical discoveries, small or great are never born of spontaneous generation.
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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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All of mathematics is a tale about groups.
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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.
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It is through science that we prove, but through intuition that we discover.
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Mathematicians are born, not made.
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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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It may happen that small differences in the initial conditions produce very great ones in the final phenomena.
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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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Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
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