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

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" Facts do not speak. "

" 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. "

" Geometry is not true, it is advantageous. "

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

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

" 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. "

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

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

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

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

" How is an error possible in mathematics? "

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

" 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. "

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

" If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws. "

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

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

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

" 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 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. "

" Hypotheses are what we lack the least. "

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

" 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. "

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

" 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. "

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

" Mathematicians are born, not made. "

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

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