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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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It is through science that we prove, but through intuition that we discover.
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It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.
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It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
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Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.
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