Jules H. Poincare Quotes

37 Jules H. Poincare quotes:

"A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations."
"A small error in the former will produce an enormous error in the latter."
"But even if it were the case that the natural laws had nolonger any secret for us, we could still know the situation approximately."
"Now, they invent them deliberately just to invalidate our ancestors' reasoning, and that is all they are ever going to get out of them."
"Hypotheses are what we lack the least."
"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."
"Thus, they are free to replace some objects by others so long as the relations remain unchanged."
"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."
"It has adopted the geometry most advantageous to the species or, in other words, the most convenient."
"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 through science that we prove, but through intuition that we discover."
"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."
"Mathematicians are born, not made."
"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."
"Geometry is not true, it is advantageous."
"No more than these machines need the mathematician know what he does."
"In the old days when people invented a new function they had something useful in mind."
"Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority."

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