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" How is an error possible in mathematics? "

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

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

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

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

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

" 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. "

" 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 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. "

" Geometry is not true, it is advantageous. "

" 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. "

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

" 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. "

" 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. "

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

" Mathematicians are born, not made. "

" Science is facts. "

" To invent is to discern, to choose. "

" 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. "

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

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

" Facts do not speak. "

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

" 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. "

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

" 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. "