**André Weil** was a French mathematician who worked on algebraic geometry and number theory.

- Every year Weil won the mathematics prize and chose himself (with Hadamard's advice) books for his prize.
- He graduated from the Lycée Saint-Louis in 1922 and, later that year, Weil entered the École Normale Supérieure in Paris.
- Right from the time he entered the École Normale Supérieure, Weil attended Hadamard's seminar at the Collège de France.
- Weil chose not to follow his supervisor's advice.
- At this time military service was compulsory in France, so Weil undertook these duties in the year 1928-29, leaving with the rank of lieutenant.
- The war was a disaster for Weil who had decided before hostilities broke out that he would avoid military service by going to the United States.
- Weil was arrested in Finland in November 1939 and when letters in Russian were found in his room (they were actually from Pontryagin describing mathematical research) things looked pretty black.
- One day Nevanlinna was told that they were about to execute Weil as a spy, and he was able to persuade the authorities to deport Weil instead.
- The dangers of his predicament made Weil decide that being in the army was a better bet and he was able to argue successfully for his release on the condition that indeed he did join the army.
- Having used the army as a reason to get out of prison, Weil had no intention of serving any longer than he possibly could.
- In 1947 Weil returned to the United States and he was appointed to the faculty of the University of Chicago, a position he continued to hold until 1958.
- Weil's research was in number theory, algebraic geometry and group theory.
- Weil's work in this area was basic to work by mathematicians such as Shing-Tung Yau who was awarded a Fields Medal in 1982 for work in three dimensional algebraic geometry which has major applications to quantum field theory.
- Yau is not the only mathematician who received a Fields Medal for work which continued that begun by Weil.
- In 1978 Pierre Deligne was awarded a Fields Medal for solving the Weil Conjectures.
- These Weil conjectures, as they came to be called, grew out of his deep insight into the topology of algebraic varieties and provided guiding principles for subsequent developments in the field.
- Weil's work on bringing together number theory and algebraic geometry was highly fruitful.
- The foundations of many topics studied in depth today were laid by Weil in this work, such as the foundations of the theory of modular forms, automorphic functions and automorphic representations.
- However, Weil's work was of major importance in a number of other new mathematical topics.
- Together with Dieudonné and others, Weil wrote under the name Nicolas Bourbaki, a project they began in the 1930s, in which they attempted to give a unified description of mathematics.
- Weil made a major contribution through his books that include Arithmétique et géométrie sur les variétés algébriques Ⓣ(Arithmetic and geometry of algebraic varieties) (1935), Sur les espaces à structure uniforme et sur la topologie générale Ⓣ(On spaces of uniform structure and general topology) (1937), L'intégration dans les groupes topologiques et ses applications Ⓣ(Integration in topological groups and their applications) (1940), Foundations of Algebraic Geometry (1946), Sur les courbes algébriques et les variétés qui s'en déduisent Ⓣ(On algebraic curves and varieties which are deduced from them) (1948), Variétés abéliennes et courbes algébriques Ⓣ(Abelian varieties and algebraic curves) (1948), Introduction à l'étude des variétés kählériennes Ⓣ(Introduction to the study of Kähler varieties) (1958), Discontinuous subgroups of classical groups (1958), Adeles and algebraic groups (1961), Basic number theory (1967), Dirichlet Series and Automorphic Forms (1971), Essais historiques sur la théorie des nombres Ⓣ(Historical essays on the theory of numbers) (1975), Elliptic Functions According to Eisenstein and Kronecker (1976), (with Maxwell Rosenlicht) Number Theory for Beginners (1979), Adeles and Algebraic Groups (1982), Number Theory: An Approach Through History From Hammurapi to Legendre (1984), and Correspondance entre Henri Cartan et André Weil Ⓣ(Correspondance between Henri Cartan and André Weil) (1928-1991) (2011).
- Weil received many honours for his outstanding mathematics.
- Weil was an invited speaker at the International Congress of Mathematicians in 1950 at Harvard when he gave an address on Number Theory and Algebraic Geometry and again at the following International Congress in 1954 in Amsterdam when he gave the lecture Abstract versus Classical Algebraic Geometry.
- In 1979 Weil was awarded the Wolf Prize and, in the following year, the American Mathematical Society awarded him their Steele Prize.

Born 6 May 1906, Paris, France. Died 6 August 1998, Princeton, New Jersey, USA.

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Bourbaki, Number Theory, Prize Wolf

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive