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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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" 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. "

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

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

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

" Science is facts. "

" 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. "

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

" Mathematicians are born, not made. "

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

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

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

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

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

" 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. "

" 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. "

" How is an error possible in mathematics? "

" 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. "

" 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. "

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

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

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

" To invent is to discern, to choose. "

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

" Geometry is not true, it is advantageous. "

" Hypotheses are what we lack the least. "

" Facts do not speak. "

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

" 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. "