mem-weil.qxp 2/12/99 10:46 AM Page 440 André Weil (1906–1998) Armand Borel, Pierre Cartier, Komaravolu Chandrasekharan, Shiing-Shen Chern, and Shokichi Iyanaga Shiing-Shen Chern a book where all the theorems had complete and rigorous proofs. It is difficult to make success of I believe Weil and I first met in Paris in the fall such a plan if it is to include all mathematics. For of 1936 at the Julia seminar “Sur les travaux sci- instance, there is no generally agreeable Stokes entifiques de M. Élie Cartan”. He soon went to theorem in differential geometry. But in any case, Princeton, and I must have left no impression on the Bourbaki volumes contain a large collection of him. rigorously proven fundamental mathematical the- Our first scientific encounter came when he orems. It is a great asset in mathematical literature. wrote in the newly started Mathematical Reviews a lengthy review of a short article of mine on in- Komaravolu Chandrasekharan tegral geometry. Although he was somewhat crit- ical, he generally liked my paper. André Weil’s passing brings back to memory We first really met in the fall of 1943 when I Samuel Johnson’s remark on the death of a close came to the Institute for Advanced Study and he friend: “Howmuchsoever I valued him, I now wish was teaching at Lehigh University and we became I had valued him more.” Weil was the first to in- good friends. At that time he had just published troduce me (1947) to Georges de Rham’s work on his proof of the high-dimensional Gauss-Bonnet differential forms and multiple integrals and to the formula. But our common mathematical interest work of Laurent Schwartz on distributions. He per- goes over the whole of mathematics, and I was al- sonally introduced me to the glories of Greek ways impressed by his vast knowledge and judg- sculpture at the Louvre in Paris on my first visit ment. there (May 1949). After his lecture at the Amster- We soon became colleagues at the University of dam Congress (ICM 1954), to which he was fetched Chicago in 1949–59 during the Stone period. Under by Kloosterman direct from the airport, we spent Stone’s leadership Chicago became an active math- the afternoon among the treasures of the Rijksmu- ematical center with excellent students. We had seum. He was supportive in concrete ways at the constant contact and took long walks along the turning points of my career, when I moved to Bom- south coast of Lake Michigan when it was still safe. bay (1949), and when I moved out of there (1965)— Weil was known as a leader of the Bourbaki always kindly, hospitable, and encouraging. Un- group. This started when a group of young French forgettable are the days we spent together at Pon- mathematicians planned to introduce modern tresina, in the high Swiss Alps (1967), admiring the mathematics to France. It was an extremely talented snow-clad peaks as well as Hecke’s mathematical group. Among their plans was the compilation of achievements. Shiing-shen Chern is professor emeritus of mathematics Komaravolu Chandrasekharan is an emeritus professor at the University of California, Berkeley, and director of mathematics at Eidgenössische Technische Hochschule emeritus of the Mathematical Sciences Research Institute. (ETH) in Zürich. 440 NOTICES OF THE AMS VOLUME 46, NUMBER 4 mem-weil.qxp 2/12/99 10:46 AM Page 441 He left what he wanted his fellow human beings nothing else did either be- to know about him in his corpus of published fore or since. He acquired work. All his work, however, was governed and uni- sufficient Sanskrit to be fied by his remarkable personality. His French was able to read the Gı¯ta in the pellucid. He was endowed with poetic sensibility original with the help of a and metaphysical insight. His creative élan and Sanskrit-French dictionary intellectual power will long be missed. He had that and an English translation. kind of charisma which demanded respect through He was taken in as much admiration. When someone characterized him as by the beauty of the poem cantankerous, someone else rejoined that his long as by the thought that in- and happy marriage showed that he could not be spired it. The Gı¯ta is per- all that cantankerous. Eveline and he were as close haps the most systematic as candlewick to candle flame. The distinctive hard spiritual statement of the shell of his personality was established at an as- “perennial philosophy”, tonishingly early age; he was confident, articulate, embodying those univer- and independent. He had a tireless curiosity about sal truths to which no one the world, which was “so various, so beautiful, so people or age can make ex- new,” in Matthew Arnold’s words, and he had the clusive claim. Eminent In- dologists like A. K. capacity to assimilate ideas, attitudes, and quali- Photograph by Lucien Gillet, provided courtesy of Sylvie Weil. Coomaraswamy have ex- ties, combined with the sharply defined sense of André Weil in the family apartment pressed the opinion that his own wants. Mathematics and poetry (Greek in Paris, 1952. and Sanskrit) afforded him a way into the sublime; it is “probably the most travel lent enchantment to the enterprise. important single work pro- He was a radical in the true sense who always duced in India.” The Gı¯ta remained Weil’s close com- tried to get to the root of things, though there panion all his life, through thick and thin, as it did were strains of traditionalism in him. This was so with Gandhi. whether he was considering departmental bud- Ka¯lida¯sa’s lyric poem Meghadu¯ta (the Cloud-mes- gets or diophantine equations, functional analysis senger) enraptured him—as it has at least fifty gen- on groups or zeta-functions, abelian varieties or erations of Indians—with its delicacy and grace, its the theory of correspondences on an algebraic mellifluous diction, its lyrical concision, and its sug- curve. It has been said that the only success which gestive power. Ka¯lida¯sa’s deceptively simple San- is man’s to command is to bring to his work a skrit is the despair of translators. Weil was struck by mighty heart. This he certainly did with his Foun- Ka¯lida¯sa’s mastery of the Sanskrit language, of its dations of Algebraic Geometry (1946), with “the pre- grammar and rhetoric and dramatic theory, “subjects cision of its language and the completeness of its which Hindu savants have treated with great, if some- proofs” in Harish-Chandra’s words. His famous times hair-splitting, ingenuity,” in the words of Arthur theorem (1940, 1948) on the Riemann hypothesis Ryder (Berkeley, 1912). He came upon the fact that for curves over finite fields was built on those in India, Pa¯n. ini’s invention of grammar (ca. fourth foundations and will remain a standing witness to century B.C.) had preceded that of the decimal no- his triumph as a mathematician, a triumph which tation and negative numbers. Pa¯n. ini’s As.t.a¯dhya¯yi stemmed from uncompromising self-reliance. “He (eight chapters) consists of nearly four thousand lighted himself up with the fuel of himself.” His aphorisms, the su¯tras, enumerating the technical radicalist approach to questions of administra- terms used in grammar and the rules for their in- tion did not always endear him to the authorities, terpretation and application. The Sanskrit term for some of whom resented his success and found grammar is Vya¯karan.a, which literally means “un- his chirpy personality and dry humour not exactly doing”, implying linguistic analysis. Weil could very ingratiating. He never courted popularity but was well say that “nothing he later came across in the writ- grateful when it came, as it did with the publica- ings of Chomsky and his disciples seemed unfamil- tion of his book on topological groups, with its ded- iar to him.” ication to Élie Cartan written in the confines of Having delved that deep into Sanskrit studies, he prison, or his last one on the years of his appren- was ready to jump at any offer of a chair in India, ticeship. He carried an air of quiet satisfaction which eventually turned out to be mathematics whenever his audience in a lecture overflowed the (1930–32). It was in Helsinki on the opening day of auditorium, as it did at the Helsinki Congress (ICM the Congress (ICM 1978), as we emerged from a re- 1978). ception given by our Finnish hosts, and the evening His precocious fascination for epic poetry began was spread against the sky, that he suddenly asked with Homer’s Iliad, in Greek, which in turn quick- me to recite the first line of the first stanza of ened his interest in Sanskrit, and led inevitably to Meghadu¯ta, which he so dearly loved. I had not then the great epic Maha¯bha¯rata. Its core, the Bha- known, as I did later, the intensity of the impact of gavad-Gı¯ta (the Song of God) stirred his blood as India on his personality. Joseph Brodsky has said: “A APRIL 1999 NOTICES OF THE AMS 441 mem-weil.qxp 2/12/99 10:46 AM Page 442 man is what he agreed with someone’s opinion, this would usually loves. That is why translate into an oral or written comment which he loves it; be- could be biting, sometimes even hurting, or sim- cause he is a part ply amusing, with little or no venom. I would like of it.” His col- to describe two examples in the latter vein, per- leagues at Prince- taining to incidents which occurred while he was ton, Gödel and on the faculty at the Institute for Advanced Study.