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

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

" 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. "

" Mathematicians are born, not made. "

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

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

" 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. "

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

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

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

" Facts do not speak. "

" 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. "

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

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

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

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

" How is an error possible in mathematics? "

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

" 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. "

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

" Science is facts. "

" Hypotheses are what we lack the least. "

" 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. "

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

" 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. "

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

" 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. "

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

" Geometry is not true, it is advantageous. "