Henri Poincare

“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?”

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

“Science is facts.”

“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.”

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

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

“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.”

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

“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.”

“Hypotheses are what we lack the least.”

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

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

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

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

“Mathematicians do not study objects, but relations between objects.”

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

“Need we add that mathematicians themselves are not infallible?”