André Weil Quotes (1906-1998)

“I would read Lefschetz's book on analysis situs and algebraic geometry - the book about which Hodge used to say that all the important statements were true and all the others false.”

“As Eisenstein shows, his method for constructing elliptic functions applies beautifully to the simpler case of trigonometric functions. Moreover, this case provides not merely an illuminating introduction to his theory, but also the simplest proofs for a series of results, originally discussed by Euler.”

“I have no doubt that future historians of differential geometry will rank Chern as the worthly successor of Elie Cartan in that field.”

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

“He had such a keen sense of color, it was said, that he would pack a tie to match his pale complexion on days when he was seasick. In any case, one calm day he was kind enough to open up his portfolios, which were full of impressive drawings.”

“On my way home in May 1932, when I stopped in Rome to see Vito Volterra and explained my 92 Andre Weil formula to him, he jumped up out of his chair and ran to the back of the apartment, crying to his wife: "Virginia! Virginia! Il signor Weil ha dimostrato un gran bel teorema!" ("Mr. Weil has proved a very beautiful theorem!")”

“Riemann was the first; I read his inaugural dissertation and his major work on Abelian functions. Starting out thus was a stroke of luck for which I have always been grateful. These are not hard to read, as long as one realizes that every word is loaded with meaning: there is perhaps no other mathematician whose writing matches Riemann's for density.”

“In Hamburg, I was not able to find Artin. On the other hand, I did visit a large exhibit of Nolde's work, which left a lasting impression upon me. Later, back in Paris, I spoke enthusiastically of him to several friends who were devotees of modern painting. One of them, who ran a well-known art gallery, cut me short: "He has never been exhibited in Paris." Apparently, this settled his hash.”

“Hilbert was on the verge of retirement. He was the dignified chairman of the mathematical society's meetings, though he no longer came up with those caustic quips that people would repeat afterwards, imitating as best they could his Baltic accent. It is a pity these were not recorded before it was too late. The samples cited in English translation, in Constance Reid's biography of Hilbert, give only the palest idea of his biting wit.”

“All those who were acquainted with Hadamard know that until the end of his very long life, he retained an extraordinary freshness of mind and character: in many respects, his reactions remained those of a fourteen-year-old boy. His kindness knew no bounds. The warmth with which Hadamard received me in 1921 eliminated all distance between us. He seemed to me more like a peer, infinitely more knowledgeable but hardly any older; he needed no effort at all to make himself accessible to me.”

“When my neighbor, who spoke German tolerably well, introduced himself as a former Soviet general, I was somewhat surprised, even under these circumstances in which virtually nothing came as a surprise. ... He told me all kinds of stories, of which the best (one he claimed to have witnessed firsthand) was about Trotsky, who was irked by Voroshilov's arrogant behavior toward him. Trotsky took advantage of a council of war over which he was presiding in Petrograd and, raising his voice, addressed Voroshilov thus: "Commander of the Tsaritsyn front! Comrade Voroshilov!," then, as if giving orders, "ATTEN-TION!" At this, according to the story, Voroshilov, frozen on the spot, stood to attention, and this marked the end of his insolence. Se non è vero... ["Even if it's not true, it's a good story."]”

“Now it is time for us to realize that, in his Grundzüge, Kronecker did not merely intend to give his own treatment of the basic problems of ideal-theory which form the main subject of Dedekind's life-work. His aim was a higher own. He was, in fact, attempting to describe and to initiate a new branch of mathematics, which would contain both number-theory and algebraic geometry as special cases. This grandiose conception has been allowed to fade out of our sight, partly because of the intrinsic difficulties of carrying it out, partly owing to historical accidents and to the temporary successes of the partisans of purity and of Dedekind. It will be the main purpose of this lecture to try to rescue it from oblivion, to revive it, and to describe the few modern results which may be considered as belonging to the Kroneckerian program.”

“Alexandre Grothendieck was very different from Weil in the way he approached mathematics: Grothendieck was not just a mathematician who could understand the discipline and prove important results—he was a man who could create mathematics. And he did it alone.”

“In his thesis, Weil generalized Mordell's theorem on the finite generation of the group of rational points on an elliptic curve, to abelian varieties of any dimension. Weil then hoped to use this finite generation result for the rational points on the jacobian of a curve to go on to show that when a curve of genus > 1 is imbedded in its jacobian, only a finite number of the rational points of the jacobian can lie on the curve. Not finding a way to do this, he decided to call his proof of finite generation (the "theorem of Mordell-Weill") a thesis, despite Hadamard's advice not to be satisfied with half a result!”

“Sometimes my sister and I dream of having a run-of-the-mill father. He would make coffee and toss salads. He would not prefer his work to us, and he would tell us instead: "How pretty you look, my dear, tell me what you did today." He would speak to us with words of affectionate banality.”