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

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" Mathematicians are born, not made. "

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

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

" Hypotheses are what we lack the least. "

" 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. "

" How is an error possible in mathematics? "

" 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. "

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

" 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. "

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

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

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

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

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

" Facts do not speak. "

" Science is facts. "

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

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

" 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. "

" 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. "

" 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. "

" Geometry is not true, it is advantageous. "

" 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. "

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

" 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. "

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

" 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. "

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

" Point set topology is a disease from which the human race will soon recover. "