"... 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."
André Weil was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is due
"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."
André Weil"An important point is that the p-adic field, or respectively the real or complex field, corresponding to a prime ideal, plays exactly the role, in arithmetic, that the field of power series in the neighborhood of a point plays in the theory of functions: that is why one calls it a local field."
André Weil"We should ask our fellow physicists to invent a principle of anti-interference, which would bring light out of two obscurities (Leray and Grothendieck)."
André Weil"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."
André Weil"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."
André Weil"God exists since mathematics is consistent, and the Devil exists since we cannot prove it."
André Weil"In the life of the mass-order, the culture of the generality tends to conform to the demands of the average human being. Spirituality decays through being diffused among the masses when knowledge is impoverished in every possible way by rationalisation until it becomes accessible to the crude understanding of all."
"I say this to you because we Spaniards are a forgetful people, because we are used to living for the moment, because we do not look back, because we do not know how to see the chain of heroes, because we do not contemplate the sum of sacrifices."
Francisco Franco"Sharon Tate was my best friend. Once, we were roommates. She introduced me to my husband. She was the godmother to my baby daughter who is named for her. In the six years time that I knew her, she never said an unkind word about anyone."
"Long time to see. (VS: Tapion)"
"Most mathematicians prove what they can, von Neumann proves what he wants." Once in a discussion about the rapid growth of mathematics in modern times, von Neumann was heard to remark that whereas thirty years ago a mathematician could grasp all of mathematics, that is impossible today. Someone asked him: "What percentage of all mathematics might a person aspire to understand today?" Von Neumann went into one of his five-second thinking trances, and said: "About 28 percent."
John von Neumann"Children must be free to think in all directions irrespective of the peculiar ideas of parents who often seal their childrens minds with preconceived prejudices and false concepts of past generations. Unless we are very careful, very careful indeed, and very conscientious, there is still great danger that our children may turn out to be the same kind of people we are."