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" 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. "

Henri Poincare

Capable

Knowledge

Worthy

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

" 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. "

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

" How is an error possible in mathematics? "

" 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. "

" 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. "

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

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

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

" 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. "

Henri Poincare

Beautiful

Nature

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

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

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

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

" Geometry is not true, it is advantageous. "

Henri Poincare

True

Geometry

" 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. "

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

Henri Poincare

Machines

Need

" 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. "

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

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

" Hypotheses are what we lack the least. "

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

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

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

" Science is facts. "

Henri Poincare

Facts

Science

" 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. "

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

" To invent is to discern, to choose. "

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