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

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

" How is an error possible in mathematics? "

" Hypotheses are what we lack the least. "

" 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. "

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

" What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? "

" To invent is to discern, to choose. "

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

" 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. "

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

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

" 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. "

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

" 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. "

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

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

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

" Mathematicians do not study objects, but relations between objects. "

" 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. "

" Mathematicians are born, not made. "

" Just as houses are made of stones, so is science made of facts. "

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

" Science is facts. "

" Geometry is not true, it is advantageous. "

" 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. "

" 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. "

" If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. "

" 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. "

" Facts do not speak. "