André Weil is responsible for important advances in algebraic geometry, group theory, and number theory and belonged to the group of French mathematicians who published many important works under the collective pseudonym of Nicolas Bourbaki. Many of his peers in the 1950s considered him the finest living mathematician in the world. In 1980, he was presented with the Barnard Medal by Columbia University; prior recipients of the medal, which is awarded every five years, include Albert Einstein , Ernest Rutherford , and Neils Bohr . The prize recognizes outstanding accomplishment in physical or astronomical science or a scientific application of great benefit to humanity.
Weil was born May 6, 1906, in Paris, France, to free-thinking Jewish parents. His father, Bernard, was a physician, and his mother, Selma Reinherz Weil, came from a cultured Russian family. His sister was the famous writer, social critic, and World War II French Resistance activist, Simone Weil. When he was eight years old, Weil happened upon a geometry book and began to read it for recreation. By the time he was nine, he was absorbed in mathematics and was solving difficult problems. In her biography of Weil's sister, Simone Pétrement quotes Weil's mother as saying that at nine years of age André "is so happy that he has given up all play and spends hours immersed in his calculations." Weil's father was drafted into the military in 1914, and the family accompanied him to various medical assignments around France during World War I. At age 16, Weil was accepted at the elite Ecole Normale Supérieure in Paris, where he received his doctorate in 1928. He also studied at the Sorbonne, the University of Göttingen, and the University of Rome. From 1930 to 1932, he taught at the Aligarh Muslim University in India. From 1933 to 1940, he was a professor of mathematics at the University of Strasbourg in France. In 1937, he married.
Weil was in Finland with his wife when France entered World War II. He believed that he could do France more good as a mathematician and refused to return to his home country and join the army. He was walking near an anti-aircraft gun emplacement when the Russians invaded Finland, and the Finns arrested him, thinking that he was a spy. The letters to Russian mathematicians in his room did not help his case, and for a while it appeared that he would be executed. The Finns, however, released Weil to the Swedes, who sent him to England, from where he returned to France to be imprisoned and tried for not reporting for military service. He was tried on May 3, 1940 and convicted, and he asked to be sent to the front. The court obliged, and he was to be sent to an infantry unit along the English Channel at Cherbourg. Weil's boat, however, wound up in a British port, and he made his way back to France later in 1940. He soon rejoined his wife, Eveline, and they escaped the war to the United States. Their daughter, Sylvie, was born on September 12, 1942. Weil taught at Haverford and Swarthmore colleges in the United States in 1941 and 1942, and at the University of São Paulo in Brazil from 1945 to 1947.
In 1947, Weil was recruited to the mathematics department at the University of Chicago, where he taught until 1958. One of his colleagues at Chicago was Irving Kaplansky, who gives a sense of Weil's personality in More Mathematical People: "There we were at Chicago, lucky enough to have André Weil, one of the greatest mathematicians in the world. There were several times in my life that I've, one way or another, got that feeling, my gosh, here is a tremendous mathematician.... He was very impatient with what he regarded as incompetence." Kaplansky added, "Then there is his extraordinary quickness.... You can take an area of mathematics that he presumably never heard of before and just like that he'll have something to say about it." From 1958 until his retirement, Weil taught at the Institute for Advanced Study at Princeton.
Reveals Discovery of "Uniform Space"
Weil's mathematical innovations are highly technical and involve complex formulas. One of his discoveries was the concept of "uniform space," a kind of mathematical space that cannot be readily visualized like the three-dimensional space that we occupy in our daily lives. The Science News Letter pronounced Weil's discovery of uniform space one of the most important mathematical discoveries of 1939. In 1947, Weil developed some formulas in the field of algebraic geometry, which are known as the "Weil conjectures." Weil's conjectures, as Ian Stewart explains in Scientific American, "give formulas for the number of solutions to an algebraic equation in a finite field. In particular they allow one to deduce that a given equation does or does not have solutions; this information can be transferred to analogous equations involving integers or algebraic numbers.... [They] are of fundamental importance in algebraic geometry."
Weil's algebraic and geometrical innovations of the first half of the 20th century were especially important for the technological innovations of the second half of the 20th century. Complex computer software that models black holes for astronomers, scientific graphics for research physicists, and special effects visualizations for Hollywood filmmakers all rely in part on mathematical innovations in algebra and geometry. As the Science News Letter said in 1939, in the decades to come, mathematical innovations like Weil's may lead to "some concept that will illumine the universe as glimpsed by the 200-inch telescope or the atom as created or smashed by the powerful cyclotron."
Becomes Involved with Influential Group
In the mid-1930s, Weil and other important young French mathematicians--among them Jean Dieudonné, Claude Chevallier, and Henri Cartan--began to write a series of mathematical works under the pseudonym of Nicolas Bourbaki. As Paul Halmos said in Scientific American, one writer called Bourbaki a "polycephalic mathematician." The group has varied in number from ten to twenty and has been composed, predominantly, of those of French nationality. Their purpose was quite serious: to write a series of books about such fundamental mathematical areas as set theory, algebra, and topology. The resulting series of books, which to date number over thirty, was called the Elements of Mathematics. As Halmos said, "The main features of the Bourbaki approach are a radical attitude about the right order for doing things, a dogmatic insistence on a privately invented terminology, a clean and economical organization of ideas, and a style of presentation which is so bent on saying everything that it leaves nothing to the imagination." Their work has been very thorough (for example, it took them two hundred pages to define the number "1") and influential. Among other things, they inspired the "new math" that was introduced into American schools in the 1960s.
While their purpose is serious, the Bourbakians cultivate an atmosphere of mystery about their identities: they attempt to keep their names secret, they like to make up stories about themselves, and they love pranks. One story about their origin, which could well be a hoax, is that they got the idea for their name from the annual visit of a character named Nicolas Bourbaki to the Ecole Normale Supérieure, where many of them were educated. This character was an actor who gave a mock-serious lecture on mathematics in double-talk. Some of their own double-talk consists of saying that the home institution of Nicolas Bourbaki is the "University of Nancago," a fusion of the Universities of Nancy and Chicago, where several members of the group teach. Another story reported is that the name was inspired by General Charles Denis Sauter Bourbaki, a colorful figure in the Franco-Prussian war. One of the group's pranks was to apply for a membership to the American Mathematical Society under the name of N. Bourbaki. They played another prank on Ralph P. Boas, the executive editor of Mathematical Reviews. Boas had said in one of the Encyclopedia Britannica's annual Book of the Year volumes that Nicolas Bourbaki did not exist. The Bourbakians sent a letter to the editors of the Britannica complaining about Boas's charge. Later, as Paul Halmos said in Scientific American, the Bourbakians "circulated a rumor that Boas did not exist. Boas, said Bourbaki, is the collective pseudonym of a group of young American mathematicians who act jointly as the editors of Mathematical Reviews."
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