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

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" 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. "

" To invent is to discern, to choose. "

" 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. "

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

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

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

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

" 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. "

" Hypotheses are what we lack the least. "

" 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. "

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

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

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

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

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

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

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

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

" 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. "

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

" 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. "

" 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. "

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

" 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. "

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

" Mathematicians are born, not made. "

" Facts do not speak. "

" How is an error possible in mathematics? "

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