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" Thus, they are free to replace some objects by others so long as the relations remain unchanged. "
Henri Poincare
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" No more than these machines need the mathematician know what he does. "
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" The mind uses its faculty for creativity only when experience forces it to do so. "
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" To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection. "
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" Thought is only a flash between two long nights, but this flash is everything. "
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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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" A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. "
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" A small error in the former will produce an enormous error in the latter. "
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" Facts do not speak. "
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" Mathematics is the art of giving the same name to different things. "
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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. "
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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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" Point set topology is a disease from which the human race will soon recover. "
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Disease
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Soon
" Mathematicians do not study objects, but relations between objects. "
Henri Poincare
Objects
Study
Mathematicians
" Geometry is not true, it is advantageous. "
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True
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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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" Mathematicians are born, not made. "
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" Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence. "
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" In the old days when people invented a new function they had something useful in mind. "
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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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Indeed
" The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. "
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Nature
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" Hypotheses are what we lack the least. "
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Least
Hypotheses
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" Just as houses are made of stones, so is science made of facts. "
Henri Poincare
Houses
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" Mathematical discoveries, small or great are never born of spontaneous generation. "
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" The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. "
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" Need we add that mathematicians themselves are not infallible? "
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Infallible
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" To invent is to discern, to choose. "
Henri Poincare
Discern
Choose
Invent
" It is through science that we prove, but through intuition that we discover. "
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Prove
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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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" 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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" If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing. "
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