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.

quote by Henri Poincare
Added by Lucian Velea
Comment! | Vote! | Copy!

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.

quote by Henri Poincare
Added by Lucian Velea
Comment! | Vote! | Copy!

The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious. It is through it that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to fill up the gulf that separates the symbol from reality.

quote by Henri Poincare
Added by Veronica Serbanoiu
Comment! | Vote! | Copy!

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means....[A] machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

quote by Henri Poincare
Added by Lucian Velea
Comment! | Vote! | Copy!