Andre Weil

“Nothing is more fruitful than the cross-fertilization of mathematical theories.”

“Intuition is what makes the mathematician a poet.”

“Rigor is to the mathematician what morality is to man.”

“When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate its fossilization.”

“Every mathematician worthy of the name has experienced... the state of lucid exaltation in which one thought succeeds another as if miraculously.”

“God exists since mathematics is consistent, and the Devil exists since we cannot prove it.”

“What is crucial is to be in a state of grace. For this, it is necessary to apply yourself to a problem which you love, and which is at the limit of your understanding.”

“The great problems are those which are simple in their statement, but whose solutions require a long and difficult analysis.”