An important point is that the p-adic field, or respectively the real — André Weil

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

"First rank scientists recruit first rank scientists, but second rank scientists tend to recruit third rank scientists, third rank scientists recruit fifth rank, and so on. If the director of the Department is genuinely interested in preserving the high quality of his Institute, he must exercise all of his power to put things in their right place, otherwise the deterioration process is destined to diverge indefinitely."

"We should ask our fellow physicists to invent a principle of anti-interference, which would bring light out of two obscurities (Leray and Grothendieck)."

"I began to combine this ordinary form of touring with a specifically mathematical variety. I had formed the ambition of becoming, like Hadamard, a "universal" mathematician: the way I expressed it was that I wished to know more than non-specialists and less than specialists about every mathematical topic. Naturally, I did not achieve either goal."

"Awaiting me upon my return to Strasbourg were Henri Cartan and the course on "differential and integral calculus," which was our joint responsibility. ... One point that concerned him was the degree to which we should generalize Stokes formula in our teaching. ... In his book on invariant integrals, Elie Cartan, following Poincare in emphasizing the importance of this formula, proposed to extend its domain of validity. Mathematically speaking, the question was of a depth that far exceeded what we were in a position to suspect. ... One winter day toward the end of 1934,1 thought of a brilliant way of putting an end to my friends persistent questioning. We had several friends who were responsible for teaching the same topics in various universities. "Why dont we get together and settle such matters once and for all, and you wont plague me with your questions any more?" Little did I know that at that moment Bourbaki was born."

"... the geometry over p-adic fields, and more generally over complete local rings, can provide us only with local data; and the main tasks of algebraic geometry have always been understood to be of a global nature. It is well known that there can be no global theory of algebraic varieties unless one makes them "complete", by adding to them suitable "points at infinity," embedding them, for example, in projective spaces. In the theory of curves, for instance, one would not otherwise obtain such basic facts as that the number of poles and zeros of a function are equal, of that the sum of residues of a differential is 0."