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Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.

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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More quotes by Henri Poincare

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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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Point set topology is a disease from which the human race will soon recover.
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The mind uses its faculty for creativity only when experience forces it to do so.
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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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. . . 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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Les faits ne parlent pas. Facts do not speak.
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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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Doubting everything and believing everything are two equally convenient solutions that guard us from having to think
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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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Experiment is the sole source of truth. It alone can teach us something new it alone can give us certainty.
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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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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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How is error possible in mathematics?
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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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Every good mathematician should also be a good chess player and vice versa.
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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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...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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It is far better to foresee even without certainty than not to foresee at all.
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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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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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