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" Geometry is not true, it is advantageous. "

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" Science is built up of 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. "

" Thought is only a flash between two long nights, but this flash is everything. "

" 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. "

" Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination. "

" 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. "

" To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection. "

" No more than these machines need the mathematician know what he does. "

" Need we add that mathematicians themselves are not infallible? "

" Science is facts. "

" 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. "

" Thus, they are free to replace some objects by others so long as the relations remain unchanged. "

" If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment. "

" It is through science that we prove, but through intuition that we discover. "

" Facts do not speak. "

" The mind uses its faculty for creativity only when experience forces it to do so. "

" Mathematicians are born, not made. "

" 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. "

" It is far better to foresee even without certainty than not to foresee at all. "

" A small error in the former will produce an enormous error in the latter. "

" In the old days when people invented a new function they had something useful in mind. "

" How is an error possible in mathematics? "

" 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. "

" Hypotheses are what we lack the least. "

" It has adopted the geometry most advantageous to the species or, in other words, the most convenient. "

" To invent is to discern, to choose. "

" A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations. "

" Mathematical discoveries, small or great are never born of spontaneous generation. "

" 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. "

" Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. "

" Mathematics is the art of giving the same name to different things. "