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

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" Geometry is not true, it is advantageous. "

" 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. "

" 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. "

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

" Science is facts. "

" Hypotheses are what we lack the least. "

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

" 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. "

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

" To invent is to discern, to choose. "

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

" How is an error possible in mathematics? "

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

" Mathematicians are born, not made. "

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

" 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. "

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

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

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

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

" Facts do not speak. "

" 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. "

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

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

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

" 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. "

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

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

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