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

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" 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. "

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

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

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

" Mathematicians are born, not made. "

" Geometry is not true, it is advantageous. "

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

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

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

" 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. "

" 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. "

" 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. "

" 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. "

" 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. "

" 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. "

" To invent is to discern, to choose. "

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

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

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

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

" How is an error possible in mathematics? "

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

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

" Science is facts. "

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