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.

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.

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

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