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" 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. "

Henri Poincare

Artist

Work

Same

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" Facts do not speak. "

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" Geometry is not true, it is advantageous. "

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True

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

" Mathematicians are born, not made. "

" 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. "

Henri Poincare

Problems

Physics

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

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

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Machines

Need

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

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

" 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. "

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

" 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. "

" To invent is to discern, to choose. "

" 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. "

" 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. "

Henri Poincare

Science

Stones

" How is an error possible in mathematics? "

" 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. "

" 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

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

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

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

" Science is facts. "

Henri Poincare

Facts

Science

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

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

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

" 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. "

" Hypotheses are what we lack the least. "

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