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

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

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

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

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

" 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. "

" 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. "

" 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. "

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

" Geometry is not true, it is advantageous. "

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

" To invent is to discern, to choose. "

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

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

" Science is facts. "

" Facts do not speak. "

" How is an error possible in mathematics? "

" 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. "

" Hypotheses are what we lack the least. "

" 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. "

" 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. "

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

" 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. "

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

" 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. "

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

" Mathematicians are born, not made. "

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

" 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. "