Thought is only a flash between two long nights, but this flash is everything.
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.
It has adopted the geometry most advantageous to the species or, in other words, the most convenient.
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.
No more than these machines need the mathematician know what he does.
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.
What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
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.
Henri Poincare — quotes and aphorisms
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.
Mathematicians do not study objects, but relations between objects.
Mathematicians are born, not made.
Mathematics is the art of giving the same name to different things.