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

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" 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. "

" To invent is to discern, to choose. "

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

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

" Mathematicians are born, not made. "

" How is an error possible in mathematics? "

" 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. "

" 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. "

" 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 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. "

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

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

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

" 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. "

" 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. "

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

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

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

" Hypotheses are what we lack the least. "

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

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

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

" Geometry is not true, it is advantageous. "

" Facts do not speak. "

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

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

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

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