André Weil

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André Weil
École Normale Supérieure
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Awards
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Charles Émile Picard
Doctoral students

André Weil (/ˈveɪ/; French: [ɑ̃dʁe vɛj]; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry.[3] He was one of the most influential mathematicians of the twentieth century. His influence is due both to his original contributions to a remarkably broad spectrum of mathematical theories, and to the mark he left on mathematical practice and style, through some of his own works as well as through the

Bourbaki group
, of which he was one of the principal founders.

Life

André Weil was born in

Alsace-Lorraine by the German Empire after the Franco-Prussian War in 1870–71. Simone Weil, who would later become a famous philosopher, was Weil's younger sister and only sibling. He studied in Paris, Rome and Göttingen and received his doctorate in 1928. While in Germany, Weil befriended Carl Ludwig Siegel. Starting in 1930, he spent two academic years at Aligarh Muslim University in India. Aside from mathematics, Weil held lifelong interests in classical Greek and Latin literature, in Hinduism and Sanskrit literature: he had taught himself Sanskrit in 1920.[4][5] After teaching for one year at Aix-Marseille University, he taught for six years at University of Strasbourg. He married Éveline de Possel (née Éveline Gillet) in 1937.[6]

Weil was in

fall of France in June 1940, he met up with his family in Marseille, where he arrived by sea. He then went to Clermont-Ferrand
, where he managed to join his wife Éveline, who had been living in German-occupied France.

In January 1941, Weil and his family sailed from Marseille to New York. He spent the remainder of the war in the United States, where he was supported by the

Universidade de São Paulo from 1945 to 1947, working with Oscar Zariski. Weil and his wife had two daughters, Sylvie (born in 1942) and Nicolette (born in 1946).[6]

He then returned to the United States and taught at the

Foreign Member of the Royal Society in 1966.[1] In 1979, he shared the second Wolf Prize in Mathematics with Jean Leray
.

Work

Weil made substantial contributions in a number of areas, the most important being his discovery of profound connections between

infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology
, which would not be categorized as such for another two decades. Both aspects of Weil's work have steadily developed into substantial theories.

Among his major accomplishments were the 1940s proof of the

foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively). The so-called Weil conjectures were hugely influential from around 1950; these statements were later proved by Bernard Dwork,[14] Alexander Grothendieck,[15][16][17] Michael Artin, and finally by Pierre Deligne, who completed the most difficult step in 1973.[18][19][20][21][22]

Weil introduced the

Taniyama–Shimura conjecture (resp. Taniyama–Weil conjecture) based on a roughly formulated question of Taniyama at the 1955 Nikkō conference. His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.[26]

Other significant results were on

Norwegian alphabet (which he alone among the Bourbaki group was familiar with), to represent the empty set.[28]

Weil also made a well-known contribution in Riemannian geometry in his very first paper in 1926, when he showed that the classical isoperimetric inequality holds on non-positively curved surfaces. This established the 2-dimensional case of what later became known as the Cartan–Hadamard conjecture.

He discovered that the so-called

Weil representation, previously introduced in quantum mechanics by Irving Segal and David Shale, gave a contemporary framework for understanding the classical theory of quadratic forms.[29] This was also a beginning of a substantial development by others, connecting representation theory and theta functions
.

Weil was a member of both the National Academy of Sciences[30] and the American Philosophical Society.[31]

As expositor

Weil's ideas made an important contribution to the writings and seminars of Bourbaki, before and after World War II. He also wrote several books on the history of number theory.

Beliefs

Hindu thought had great influence on Weil.[32] He was an agnostic,[33] and he respected religions.[34]

Legacy

Asteroid

M.P.C. 87143).[36]

Books

Mathematical works:

  • Arithmétique et géométrie sur les variétés algébriques (1935)[37]
  • Sur les espaces à structure uniforme et sur la topologie générale (1937)[38]
  • L'intégration dans les groupes topologiques et ses applications (1940)
  • Weil, André (1946),
    MR 0023093[39]
  • Sur les courbes algébriques et les variétés qui s'en déduisent (1948)
  • Variétés abéliennes et courbes algébriques (1948)[40]
  • Introduction à l'étude des variétés kählériennes (1958)
  • Discontinuous subgroups of classical groups (1958) Chicago lecture notes
  • Weil, André (1967), Basic number theory., Die Grundlehren der mathematischen Wissenschaften, vol. 144, Springer-Verlag New York, Inc., New York,
    MR 0234930[41]
  • Dirichlet Series and Automorphic Forms, Lezioni Fermiane (1971) Lecture Notes in Mathematics, vol. 189[42]
  • Essais historiques sur la théorie des nombres (1975)
  • Elliptic Functions According to Eisenstein and Kronecker (1976)[43]
  • Number Theory for Beginners (1979) with Maxwell Rosenlicht[44]
  • Adeles and Algebraic Groups (1982)[45]
  • Number Theory: An Approach Through History From Hammurapi to Legendre (1984)[46]

Collected papers:

Autobiography:

Memoir by his daughter:

See also

References

  1. ^
    doi:10.1098/rsbm.1999.0034
    .
  2. ^ André Weil at the Mathematics Genealogy Project
  3. doi:10.1038/scientificamerican0694-33
    .
  4. ^ Amir D. Aczel,The Artist and the Mathematician, Basic Books, 2009 pp. 17ff., p. 25.
  5. ^ Borel, Armand
  6. ^ a b Ypsilantis, Olivier (31 March 2017). "En lisant " Chez les Weil. André et Simone "". Retrieved 26 April 2020.
  7. ^ Osmo Pekonen: L'affaire Weil à Helsinki en 1939, Gazette des mathématiciens 52 (avril 1992), pp. 13–20. With an afterword by André Weil.
  8. ^ Weil, André. "Number theory and algebraic geometry." Archived 30 August 2017 at the Wayback Machine In Proc. Intern. Math. Congres., Cambridge, Mass., vol. 2, pp. 90–100. 1950.
  9. ^ Weil, A. "Abstract versus classical algebraic geometry" (PDF). In: Proceedings of International Congress of Mathematicians, 1954, Amsterdam. Vol. 3. pp. 550–558. Archived (PDF) from the original on 9 October 2022.
  10. ^ Weil, A. "History of mathematics: How and why" (PDF). In: Proceedings of International Congress of Mathematicians, (Helsinki, 1978). Vol. 1. pp. 227–236. Archived (PDF) from the original on 9 October 2022.
  11. ISBN 0-387-90330-5
    .
  12. ^ L.J. Mordell, On the rational solutions of the indeterminate equations of the third and fourth degrees, Proc Cam. Phil. Soc. 21, (1922) p. 179
  13. ISBN 0-387-90330-5
  14. MR 0140494
  15. MR 0130879
  16. MR 1608788
  17. MR 0354656
  18. ISBN 978-3-540-05356-9
  19. S2CID 123139343
  20. ISBN 978-0-387-08066-6, archived from the original
    on 15 May 2009
  21. S2CID 189769469
  22. MR 0354657
  23. ^ A. Weil, Adeles and algebraic groups, Birkhauser, Boston, 1982
  24. MR 0234930
  25. ^ Weil, André (1959), Exp. No. 186, Adèles et groupes algébriques, Séminaire Bourbaki, vol. 5, pp. 249–257
  26. ^ Lang, S. "Some History of the Shimura-Taniyama Conjecture." Not. Amer. Math. Soc. 42, 1301–1307, 1995
  27. ^ Borel, A. (1999). "André Weil and Algebraic Topology" (PDF). Notices of the AMS. 46 (4): 422–427. Archived (PDF) from the original on 9 October 2022.
  28. ^ Miller, Jeff (1 September 2010). "Earliest Uses of Symbols of Set Theory and Logic". Jeff Miller Web Pages. Retrieved 21 September 2011.
  29. doi:10.1007/BF02391012
    .
  30. ^ "Andre Weil". www.nasonline.org. Retrieved 20 December 2021.
  31. ^ "APS Member History". search.amphilsoc.org. Retrieved 20 December 2021.
  32. ^ Borel, Armand. [1] (see also)[2]
  33. ISBN 978-0-19-515063-6. Although as a lifelong agnostic he may have been somewhat bemused by Simone Weil's preoccupations with Christian mysticism
    , he remained a vigilant guardian of her memory,...
  34. Vivekananda and was deeply impressed by Ramakrishna. He had affinity for Hinduism. Andre Weil was an agnostic but respected religions. He often teased me about reincarnation in which he did not believe. He told me he would like to be reincarnated as a cat. He would often impress me by readings in Buddhism
    .
  35. ^ "289085 Andreweil (2004 TC244)". Minor Planet Center. Retrieved 11 September 2019.
  36. ^ "MPC/MPO/MPS Archive". Minor Planet Center. Retrieved 11 September 2019.
  37. doi:10.1090/S0002-9904-1936-06368-8
    .
  38. doi:10.1090/s0002-9904-1939-06919-X. Archived
    (PDF) from the original on 9 October 2022.
  39. doi:10.1090/s0002-9904-1948-09040-1. Archived
    (PDF) from the original on 9 October 2022.
  40. doi:10.1090/s0002-9904-1950-09391-4
    .
  41. ISBN 978-3-540-58655-5
    .
  42. ISSN 0075-8434
  43. ISBN 978-3-540-65036-2
    .
  44. ISBN 978-0-387-90381-1
    .
  45. doi:10.1080/03081088308817546
    .
  46. doi:10.1090/s0273-0979-1985-15411-4. Archived
    (PDF) from the original on 9 October 2022.
  47. ^ Berg, Michael (1 January 2015). "Review of Œuvres Scientifiques - Collected Papers, Volume 1 (1926–1951)". MAA Reviews, Mathematical Association of America.
  48. ^ Audin, Michèle (2011). "Review: At Home with André and Simone Weil, by Sylvie Weil" (PDF). Notices of the AMS. 58 (5): 697–698. Archived (PDF) from the original on 9 October 2022.

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