Editing André Weil

{{Short description|French mathematician (1906-1998)}}
{{for|the English mathematician|Andrew Wiles}}

{{Use dmy dates|date=February 2020}}
{{Infobox scientist
| name              = André Weil
| image             = André Weil, 1968 (cropped).jpg
| image_size        = 
| caption           = Weil in 1968
| birth_date        = {{birth date|1906|05|06|df=y}}
| birth_place       = [[Paris]], France
| death_date        = {{death date and age|1998|08|06|1906|05|06|df=y}}
| death_place       = [[Princeton, New Jersey]], U.S.
| field             = [[Mathematics]]
| work_institutions = {{Ubl
  | [[Lehigh University]]
  | [[Universidade de São Paulo]] (1945–47)
  | [[University of Chicago]] (1947–58)
  | [[Institute for Advanced Study]]
  }}
| education         = {{Ubl
  | [[University of Paris]]
  | [[École Normale Supérieure]]
  }}
| doctoral_advisor  = {{Ubl
  | [[Jacques Hadamard]]
  | [[Charles Émile Picard]]
  }}
| doctoral_students = {{Plainlist|
* {{nowrap|[[Pierre Cartier (mathematician)|Pierre Cartier]]}}
* {{nowrap|[[Harley Flanders]]}}
* {{nowrap|[[William Alvin Howard|William A. Howard]]}}
* {{nowrap|[[Teruhisa Matsusaka]]}}
* {{nowrap|[[Peter Swinnerton-Dyer]]<ref name=mathgene>{{MathGenealogy|id=6385}}</ref>}}
* {{nowrap|[[:pt:Alexandre Rodrigues (matemático)|Alexandre Augusto Martins Rodrigues]]}}}}
| known_for         = {{Collapsible list
  | [[Bergman–Weil formula]]
  | [[Borel–Weil theorem]]
  | [[Chern–Weil homomorphism]]
  | [[Chern–Weil theory]]
  | [[De Rham–Weil theorem]]
  | [[Weil's explicit formula]]
  | [[Hasse's theorem on elliptic curves#Hasse–Weil Bound | Hasse–Weil Bound]]
  | [[Hasse–Weil zeta function]]
  | [[Hasse–Weil L-function]]
  | [[Mordell–Weil group]]
  | [[Mordell–Weil theorem]]
  | [[Oka–Weil theorem]]
  | [[Siegel–Weil formula]]
  | [[Shafarevich–Weil theorem]]
  | [[Taniyama–Shimura–Weil conjecture]]
  | [[Weil algebra]]
  | [[Weil–Brezin Map]]
  | [[Weil–Châtelet group]]
  | [[Weil cohomology]]
  | [[Weil conjectures]]
  | [[Weil conjecture on Tamagawa numbers]]
  | [[Weil's criterion]]
  | [[Weil–Deligne group scheme]]
  | [[Weil distribution]]
  | [[Weil divisor]]
  | [[Weil group]]
  | [[Weil height]]
  | [[Weil number]]
  | [[Weil pairing]]
  | [[Weil–Petersson metric]]
  | [[Weil reciprocity law]]
  | [[Weil representation]]
  | [[Weil restriction]]
  }}
| prizes            = {{Plainlist|
* [[Wolf Prize in Mathematics|Wolf Prize]] (1979)
* [[Leroy P. Steele Prize]] (1980)
* [[Barnard Medal for Meritorious Service to Science]] (1980)
* [[Kyoto Prize]] (1994)
* [[Fellow of the Royal Society|ForMemRS]] (1966)<ref name="frs" />
}}
}}

'''André Weil''' ({{IPAc-en|v|eɪ}};<ref>{{Cite Dictionary.com|Weil}}</ref> {{IPA|fr|ɑ̃dʁe vɛj|lang}}; 6 May 1906 – 6 August 1998) was a French [[mathematician]], known for his foundational work in [[number theory]] and [[algebraic geometry]].<ref>{{cite journal | last1 = Horgan | first1 = J | author-link=John Horgan (journalist) | year = 1994 | title = Profile: Andre Weil – The Last Universal Mathematician | journal = [[Scientific American]] | volume = 270 | issue = 6| pages = 33–34 | doi=10.1038/scientificamerican0694-33| bibcode = 1994SciAm.270f..33H}}</ref> 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 [[Paris]] to [[agnosticism|agnostic]] [[Alsatian Jew]]ish parents who fled the annexation of [[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 [[Doctor of Philosophy|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, [[Hinduism]] and [[Sanskrit literature]]: he had taught himself Sanskrit in 1920 at age 14.<ref name ="Aczel">Amir D. Aczel,[https://books.google.com/books?id=fRCH-at7wgYC&pg=PA25 ''The Artist and the Mathematician,''] Basic Books, 2009 pp. 17ff., p. 25.</ref><ref>{{Cite web|url=http://www.math.sunysb.edu/~aknapp/BorelOnWeil.pdf|title=Borel, Armand}}</ref> 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.<ref name="enlisant">{{cite web |last1=Ypsilantis |first1=Olivier |title=En lisant " Chez les Weil. André et Simone " |date=31 March 2017 |url=https://zakhor-online.com/?p=11876 |access-date=26 April 2020}}</ref>

Weil was in [[Finland]] when [[World War II]] broke out; he had been traveling in Scandinavia since April 1939. His wife Éveline returned to France without him. Weil was arrested in Finland at the outbreak of the [[Winter War]] on suspicion of spying; however, accounts of his life having been in danger were shown to be exaggerated.<ref>Osmo Pekonen: ''L'affaire Weil à Helsinki en 1939'', Gazette des mathématiciens 52 (avril 1992), pp. 13–20. With an afterword by André Weil.</ref> Weil returned to France via Sweden and the United Kingdom, and was detained at [[Le Havre]] in January 1940. He was charged with [[draft evasion|failure to report for duty]], and was imprisoned in Le Havre and then [[Rouen]]. It was in the military prison in Bonne-Nouvelle, a district of Rouen, from February to May, that Weil completed the work that made his reputation. He was tried on 3 May 1940. Sentenced to five years, he requested to be attached to a military unit instead, and was given the chance to join a regiment in [[Cherbourg-Octeville|Cherbourg]]. After the [[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 [[Rockefeller Foundation]] and the [[John Simon Guggenheim Memorial Foundation|Guggenheim Foundation]]. For two years, he taught undergraduate mathematics at [[Lehigh University]], where he was unappreciated, overworked and poorly paid, although he did not have to worry about being drafted, unlike his American students. He quit the job at Lehigh and moved to Brazil, where he taught at the [[Universidade de São Paulo]] from 1945 to 1947, working with [[Oscar Zariski]]. Weil and his wife had two daughters, [[Sylvie Weil|Sylvie]] (born in 1942) and Nicolette (born in 1946).<ref name="enlisant" />

He then returned to the United States and taught at the [[University of Chicago]] from 1947 to 1958, before moving to the [[Institute for Advanced Study]], where he would spend the remainder of his career. He was a Plenary Speaker at the [[International Congress of Mathematicians|ICM]] in 1950 in Cambridge, Massachusetts,<ref>Weil, André. [http://www.mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0090.0102.ocr.pdf "Number theory and algebraic geometry."] {{Webarchive|url=https://web.archive.org/web/20170830035538/http://mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0090.0102.ocr.pdf |date=30 August 2017 }} In Proc. Intern. Math. Congres., Cambridge, Mass., vol. 2, pp. 90–100. 1950.</ref> in 1954 in Amsterdam,<ref>{{cite book|author=Weil, A.|chapter=Abstract versus classical algebraic geometry|title=''In:'' Proceedings of International Congress of Mathematicians, 1954, Amsterdam|volume=3|pages=550–558|chapter-url=http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0550.0558.ocr.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0550.0558.ocr.pdf |archive-date=2022-10-09 |url-status=live}}</ref> and in 1978 in Helsinki.<ref>{{cite book|author=Weil, A.|chapter=History of mathematics: How and why|title=''In:'' Proceedings of International Congress of Mathematicians, (Helsinki, 1978)|volume=1|pages=227–236|chapter-url=http://www.mathunion.org/ICM/ICM1978.1/Main/icm1978.1.0227.0236.ocr.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.mathunion.org/ICM/ICM1978.1/Main/icm1978.1.0227.0236.ocr.pdf |archive-date=2022-10-09 |url-status=live}}</ref> Weil was elected [[List of Fellows of the Royal Society elected in 1966|Foreign Member of the Royal Society in 1966]].<ref name="frs" /> 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 [[algebraic geometry]] and [[number theory]]. This began in his doctoral work leading to the [[Mordell–Weil theorem]] (1928, and shortly applied in [[Siegel's theorem on integral points]]).<ref>A. Weil, ''L'arithmétique sur les courbes algébriques'', Acta Math 52, (1929) p.&nbsp;281–315, reprinted in vol 1 of his collected papers {{isbn|0-387-90330-5}}
.</ref> [[Mordell's theorem]] had an ''ad hoc'' proof;<ref>{{cite journal
| last1=Mordell |first1=L. J. |authorlink1=Louis Mordell
| title=On the rational solutions of the indeterminate equations of the third and fourth degrees
|journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]]
| volume=21
| year=1922
| pages=179–192
| url=https://archive.org/details/proceedingscambr21camb/page/178/mode/2up}}</ref> Weil began the separation of the [[infinite descent]] argument into two types of structural approach, by means of [[height function]]s 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 [[Weil conjectures|Riemann hypothesis for zeta-functions]] of curves over finite fields,<ref>{{Citation | last1=Weil | first1=André | author1-link=André Weil | title=Numbers of solutions of equations in finite fields | doi=10.1090/S0002-9904-1949-09219-4 | mr=0029393 | year=1949 | journal=[[Bulletin of the American Mathematical Society]] | issn=0002-9904 | volume=55 | pages=497–508 | issue=5| doi-access=free }} Reprinted in Oeuvres Scientifiques/Collected Papers by André Weil {{isbn|0-387-90330-5}}</ref> and his subsequent laying of proper [[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]],<ref>{{Citation | last1=Dwork | first1=Bernard | author1-link=Bernard Dwork | title=On the rationality of the zeta function of an algebraic variety | jstor=2372974 | mr=0140494 | year=1960 | journal=[[American Journal of Mathematics]] | issn=0002-9327 | volume=82 | pages=631–648 | doi=10.2307/2372974 | issue=3 | publisher=American Journal of Mathematics, Vol. 82, No. 3}}</ref> [[Alexander Grothendieck]],<ref>{{Citation | last1=Grothendieck | first1=Alexander | author1-link=Alexander Grothendieck | title=Proc. Internat. Congress Math. (Edinburgh, 1958) | publisher=[[Cambridge University Press]] | mr=0130879 | year=1960 | chapter=The cohomology theory of abstract algebraic varieties | pages=103–118|chapter-url=http://grothendieckcircle.org/}}
</ref><ref>{{Citation | last1=Grothendieck | first1=Alexander | author1-link=Alexander Grothendieck | title=Séminaire Bourbaki | chapter-url=http://www.numdam.org/item?id=SB_1964-1966__9__41_0 | publisher=[[Société Mathématique de France]] | location=Paris | mr=1608788 | year=1995 | volume=9 | chapter=Formule de Lefschetz et rationalité des fonctions L | pages=41–55|orig-year=1965}}
</ref><ref>{{citation
 | last = Grothendieck | first = Alexander | author-link = Alexander Grothendieck
 | doi = 10.1007/BFb0068688
 | isbn = 978-3-540-05987-5
 | mr = 0354656
 | publisher = Springer-Verlag
 | series = Lecture Notes in Mathematics
 | title = Groupes de monodromie en géométrie algébrique, I: Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 I)
 | volume = 288
 | year = 1972}}</ref> [[Michael Artin]], and finally by [[Pierre Deligne]], who completed the most difficult step in 1973.<ref>{{Citation | last1=Deligne | first1=Pierre | author1-link=Pierre Deligne | title=Séminaire Bourbaki vol. 1968/69 Exposés 347–363 | chapter-url=http://www.numdam.org/item?id=SB_1968-1969__11__139_0 | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Lecture Notes in Mathematics | isbn=978-3-540-05356-9 | doi=10.1007/BFb0058801 | year=1971 | volume=179 | chapter=Formes modulaires et représentations l-adiques }}
</ref><ref>{{Citation | last1=Deligne | first1=Pierre | author1-link=Pierre Deligne | title=La conjecture de Weil. I | url=http://www.numdam.org/item?id=PMIHES_1974__43__273_0 | mr=0340258 | year=1974 | journal=[[Publications Mathématiques de l'IHÉS]] | volume=43 | issn=1618-1913 | issue=43 | pages=273–307| doi=10.1007/BF02684373 | s2cid=123139343 }}
</ref><ref>{{citation
 |editor-last=Deligne 
 |editor-first=Pierre 
 |editor-link=Pierre Deligne 
 |title=Cohomologie Etale 
 |series=Lecture Notes in Mathematics 
 |publisher=[[Springer-Verlag]] 
 |place=Berlin 
 |year=1977 
 |isbn=978-0-387-08066-6 
 |language=fr 
 |url=http://modular.fas.harvard.edu/sga/sga/4.5/index.html 
 |doi=10.1007/BFb0091516 
 |volume=569 
 |issue=569 
 |url-status=dead 
 |archive-url=https://web.archive.org/web/20090515034906/http://modular.fas.harvard.edu/sga/sga/4.5/index.html 
 |archive-date=15 May 2009 
}}
</ref><ref>{{Citation | last1=Deligne | first1=Pierre | author1-link=Pierre Deligne | title=La conjecture de Weil. II | url=http://www.numdam.org/item?id=PMIHES_1980__52__137_0 | mr=601520 | year=1980 | journal=[[Publications Mathématiques de l'IHÉS]] | volume=52 | issn=1618-1913 | issue=52 | pages=137–252| doi=10.1007/BF02684780 | s2cid=189769469 }}
</ref><ref>{{Citation | last1=Deligne | first1=Pierre | author1-link=Pierre Deligne | last2=Katz | first2=Nicholas | author2-link=Nicholas Katz | title=Groupes de monodromie en géométrie algébrique. II | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Lecture Notes in Mathematics, Vol. 340 | isbn=978-3-540-06433-6 | doi=10.1007/BFb0060505 | mr=0354657 | year=1973 | volume=340}}</ref>

Weil introduced the [[adele ring]]<ref>A. Weil, ''Adeles and algebraic groups'', Birkhauser, Boston, 1982</ref> in the late 1930s, following [[Claude Chevalley]]'s lead with the [[idele]]s, and gave a proof of the [[Riemann–Roch theorem]] with them (a version appeared in his ''[[Basic Number Theory]]'' in 1967).<ref>{{citation|mr=0234930 |last=Weil|first= André |title=Basic number theory.|series=Die Grundlehren der mathematischen Wissenschaften |volume=144 |publisher=Springer-Verlag New York, Inc., New York |date=1967 |isbn= 3-540-58655-5 }}</ref> His 'matrix divisor' ([[vector bundle]] ''avant la lettre'') Riemann–Roch theorem from 1938 was a very early anticipation of later ideas such as [[moduli space]]s of bundles. The [[Weil conjecture on Tamagawa numbers]]<ref>{{Citation | last1=Weil | first1=André | author1-link=André Weil | title=Exp. No. 186, Adèles et groupes algébriques | url=http://www.numdam.org/item?id=SB_1958-1960__5__249_0 | series=Séminaire Bourbaki | year=1959 | volume=5 | pages=249–257}}</ref> proved resistant for many years. Eventually the adelic approach became basic in [[automorphic representation]] theory. He picked up another credited ''Weil conjecture'', around 1967, which later under pressure<ref name="ShimuraTaniyama">{{cite web | title=Some History of the Shimura-Taniyama Conjecture | first=Serge | last=Lang | pages=1301–1307 | url=https://www.ams.org/journals/notices/199511/199511FullIssue.pdf | access-date=2025-03-30}}</ref> from [[Serge Lang]] (resp. of [[Jean-Pierre Serre]]) became known as 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.<ref>Lang, S. [https://www.ams.org/notices/199511/forum.pdf "Some History of the Shimura-Taniyama Conjecture."] Not. Amer. Math. Soc. 42, 1301–1307, 1995</ref>

Other significant results were on [[Pontryagin duality]] and [[differential geometry]].<ref>{{cite journal|author=Borel, A.|title=André Weil and Algebraic Topology|journal=Notices of the AMS|year=1999|volume=46|issue=4|pages=422–427|url=https://www.ams.org/notices/199904/borel.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ams.org/notices/199904/borel.pdf |archive-date=2022-10-09 |url-status=live}}</ref> He introduced the concept of a [[uniform space]] in [[general topology]], as a by-product of his collaboration with [[Nicolas Bourbaki]] (of which he was a Founding Father). His work on [[sheaf theory]] hardly appears in his published papers, but correspondence with [[Henri Cartan]] in the late 1940s, and reprinted in his collected papers, proved most influential. He also chose the symbol [[null sign|∅]], derived from the letter [[Ø]] in the [[Norwegian alphabet]] (which he alone among the Bourbaki group was familiar with), to represent the [[empty set]].<ref>{{Cite web|first=Jeff|last=Miller|date=1 September 2010 |url=http://jeff560.tripod.com/set.html|title=Earliest Uses of Symbols of Set Theory and Logic|publisher=Jeff Miller Web Pages|access-date=21 September 2011}}</ref>

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 form]]s.<ref>{{cite journal |first=A. |last=Weil |title=Sur certains groupes d'opérateurs unitaires |language=fr|journal=Acta Math. |volume=111 |year=1964 |pages=143–211 |doi=10.1007/BF02391012|doi-access=free }}</ref> This was also a beginning of a substantial development by others, connecting [[representation theory]] and [[theta function]]s.

Weil was a member of both the [[National Academy of Sciences]]<ref>{{Cite web|title=Andre Weil|url=http://www.nasonline.org/member-directory/deceased-members/45882.html|access-date=2021-12-20|website=www.nasonline.org}}</ref> and the [[American Philosophical Society]].<ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?creator=Andr%C3%A9+Weil&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|access-date=2021-12-20|website=search.amphilsoc.org}}</ref>

==As expositor==
Weil's ideas made an important contribution to the writings and seminars of [[Nicolas Bourbaki|Bourbaki]], before and after [[World War&nbsp;II]]. He also wrote several books on the history of number theory.

==Beliefs==

[[Hindu philosophy|Hindu thought]] had great influence on Weil.<ref>Borel, Armand. [http://www.math.sunysb.edu/~aknapp/BorelOnWeil.pdf] (see also)[http://www.britannica.com/EBchecked/topic/638991/Andre-Weil]</ref> He was an agnostic,<ref>{{cite book|title=American National Biography: Supplement, Volume 1|year=2002|publisher=[[Oxford University Press]]|isbn=978-0-19-515063-6|author1=Paul Betz |author2=Mark Christopher Carnes, [[American Council of Learned Societies]]|page=676|quote=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,...}}</ref> and he respected religions.<ref>{{cite book|title=History of the Mathematical Sciences|year=2004|publisher=Hindustan Book Agency|isbn=978-81-85931-45-6|author=I. Grattan-Guinness|editor=I. Grattan-Guinness, Bhuri Singh Yadav|page=63|quote=Like in mathematics he would go directly to the teaching of the Masters. He read [[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]].|author-link=I. Grattan-Guinness}}</ref>

==Legacy==
Asteroid [[289085 Andreweil]], discovered by astronomers at the [[Saint-Sulpice Observatory]] in 2004, was named in his memory.<ref name="MPC-object" /> The official {{MoMP|289085|naming citation}} was published by the [[Minor Planet Center]] on 14 February 2014 ({{small|[[Minor Planet Circulars|M.P.C.]] 87143}}).<ref name="MPC-Circulars-Archive" />

==Books==
Mathematical works:
* ''Arithmétique et géométrie sur les variétés algébriques'' (1935)<ref>{{cite journal |doi=10.1090/S0002-9904-1936-06368-8|title=Book Review: Arithmétique et Géométrie sur les Variétés Algébriques |year=1936 |last1=Ore |first1=Oystein |journal=Bulletin of the American Mathematical Society |volume=42 |issue=9 |pages=618–619 |doi-access=free }}</ref>
* ''Sur les espaces à structure uniforme et sur la topologie générale'' (1937)<ref>{{cite journal|author=Cairns, Stewart S.|title=Review: ''Sur les Espaces à Structure Uniforme et sur la Topologie Générale'', by A. Weil|journal=Bull. Amer. Math. Soc.|year=1939|volume=45|issue=1|pages=59–60|doi=10.1090/s0002-9904-1939-06919-X|url=https://www.ams.org/journals/bull/1939-45-01/S0002-9904-1939-06919-X/S0002-9904-1939-06919-X.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ams.org/journals/bull/1939-45-01/S0002-9904-1939-06919-X/S0002-9904-1939-06919-X.pdf |archive-date=2022-10-09 |url-status=live|doi-access=free}}</ref>
* ''L'intégration dans les groupes topologiques et ses applications'' (1940)
* {{Citation | last1=Weil | first1=André | author1-link=André Weil | title=Foundations of Algebraic Geometry | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=American Mathematical Society Colloquium Publications, vol. 29 | isbn=978-0-8218-1029-3 | mr=0023093 | year=1946| title-link=Foundations of Algebraic Geometry }}<ref>{{cite journal|author=Zariski, Oscar|author-link=Oscar Zariski|title=Review: ''Foundations of Algebraic Geometry'', by A. Weil|journal=Bull. Amer. Math. Soc.|year=1948|volume=54|issue=7|pages=671–675|doi=10.1090/s0002-9904-1948-09040-1|url=https://www.ams.org/journals/bull/1948-54-07/S0002-9904-1948-09040-1/S0002-9904-1948-09040-1.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ams.org/journals/bull/1948-54-07/S0002-9904-1948-09040-1/S0002-9904-1948-09040-1.pdf |archive-date=2022-10-09 |url-status=live|doi-access=free}}</ref>
* ''Sur les courbes algébriques et les variétés qui s'en déduisent'' (1948)
* ''Variétés abéliennes et courbes algébriques'' (1948)<ref>{{cite journal|author=Chern, Shiing-shen|author-link=Shiing-Shen Chern|title=Review: ''Variétés abéliennes et courbes algébriques'', by A. Weil|journal=Bull. Amer. Math. Soc.|year=1950|volume=56|issue=2|pages=202–204|doi=10.1090/s0002-9904-1950-09391-4|doi-access=free}}</ref>
* ''Introduction à l'étude des variétés kählériennes'' (1958)
* ''Discontinuous subgroups of classical groups'' (1958) Chicago lecture notes
* {{citation|mr=0234930
|last=Weil|first= André
|title=Basic number theory.
|series=Die Grundlehren der mathematischen Wissenschaften|volume=144 |publisher=Springer-Verlag New York, Inc., New York |year=1967 |isbn= 3-540-58655-5 }}<ref>{{Cite book|last=Weil|first=André|date=1974|title=Basic Number Theory|language=en-gb|doi=10.1007/978-3-642-61945-8|isbn=978-3-540-58655-5}}</ref>
* ''Dirichlet Series and Automorphic Forms, Lezioni Fermiane'' (1971) Lecture Notes in Mathematics, vol. 189<ref>{{citation|last=Weil|first=André|date=1971|title=Dirichlet Series and Automorphic Forms: Lezioni Fermiane|series=Lecture Notes in Mathematics|volume=189|doi=10.1007/bfb0061201|isbn=978-3-540-05382-8|issn=0075-8434}}</ref>
* ''Essais historiques sur la théorie des nombres'' (1975)
* [https://books.google.com/books/about/Elliptic_Functions_According_to_Eisenste.html?id=voR95sDdb_MC ''Elliptic Functions According to Eisenstein and Kronecker''] (1976)<ref>{{Cite book|last=Weil|first=André|date=1976|title=Elliptic Functions according to Eisenstein and Kronecker|language=en-gb|doi=10.1007/978-3-642-66209-6|isbn=978-3-540-65036-2}}</ref>
* ''Number Theory for Beginners'' (1979) with Maxwell Rosenlicht<ref>{{Cite book|last=Weil|first=André|title=Number Theory for Beginners|date=1979|publisher=Springer New York|isbn=978-0-387-90381-1|location=New York, NY|language=en|doi=10.1007/978-1-4612-9957-8}}</ref>
* ''Adeles and Algebraic Groups'' (1982)<ref>{{cite journal|author=Humphreys, James E.|author-link=James E. Humphreys|title=Review of ''Adeles and Algebraic Groups'' by A. Weil|journal=Linear & Multilinear Algebra|volume=14|issue=1|year=1983|pages=111–112|doi=10.1080/03081088308817546}}</ref>
* [https://books.google.com/books/about/Number_Theory.html?id=XSV0hDFj3loC ''Number Theory: An Approach Through History From Hammurapi to Legendre''] (1984)<ref>{{cite journal|author=Ribenboim, Paulo|author-link=Paulo Ribenboim|title=Review of ''Number Theory: An Approach Through History From Hammurapi to Legendre'', by André Weil|journal=Bull. Amer. Math. Soc. (N.S.)|year=1985|volume=13|issue=2|pages=173–182|doi=10.1090/s0273-0979-1985-15411-4|url=https://www.ams.org/journals/bull/1985-13-02/S0273-0979-1985-15411-4/S0273-0979-1985-15411-4.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ams.org/journals/bull/1985-13-02/S0273-0979-1985-15411-4/S0273-0979-1985-15411-4.pdf |archive-date=2022-10-09 |url-status=live|doi-access=free}}</ref>

Collected papers:
* ''Œuvres Scientifiques, Collected Works, three volumes'' (1979)
* {{Cite book|last=Weil|first=André|date=March 2009|title=Œuvres Scientifiques / Collected Papers|volume=1 (1926–1951)|edition=2nd printing|publisher=Springer|language=en, fr, de|isbn=978-3-540-85888-1|url=https://www.springer.com/mathematics/algebra/book/978-3-540-85888-1|series=Springer Collected Works in Mathematics}}<ref>{{cite web|author=Berg, Michael|title=Review of ''Œuvres Scientifiques - Collected Papers'', Volume 1 (1926–1951)|website=MAA Reviews, Mathematical Association of America|date=January 1, 2015|url=https://old.maa.org/press/maa-reviews/andr-weil-oeuvres-scientifiques-collected-papers-i-1926-1951}}</ref>
* {{Cite book|last=Weil|first=André|date=March 2009|title=Œuvres Scientifiques / Collected Papers|volume=2 (1951-1964)|edition=2nd printing|publisher=Springer|language=en, fr, de|isbn=978-3-540-87735-6|url=https://www.springer.com/mathematics/algebra/book/978-3-540-87735-6|series=Springer Collected Works in Mathematics}}
* {{Cite book|last=Weil|first=André|date=March 2009|title=Œuvres Scientifiques / Collected Papers|volume=3 (1964-1978)|edition=2nd printing|publisher=Springer|language=en, fr, de|isbn=978-3-540-87737-0|url=https://www.springer.com/mathematics/algebra/book/978-3-540-87737-0|series=Springer Collected Works in Mathematics}}

{{Anchor|autobiography|}}[[Autobiography]]:
* French: ''Souvenirs d'Apprentissage'' (1991) {{isbn|3-7643-2500-3}}. [https://www.jstor.org/stable/3619730 Review in English] by J. E. Cremona.
* English translation: [https://books.google.com/books/about/The_Apprenticeship_of_a_Mathematician.html?id=73REHmJ9JNUC ''The Apprenticeship of a Mathematician''] (1992), {{isbn|0-8176-2650-6}} [https://www.ams.org/notices/199904/rev-varadarajan.pdf Review] by [[Veeravalli S. Varadarajan]]; [https://www.ams.org/journals/bull/1993-28-01/S0273-0979-1993-00337-9/S0273-0979-1993-00337-9.pdf Review] by [[Saunders Mac Lane]]

Memoir by his daughter:
* [https://books.google.com/books/about/At_Home_with_André_and_Simone_Weil.html?id=OdeDlT9-GBUC ''At Home with André and Simone Weil''] by Sylvie Weil, translated by [[Benjamin Ivry]]; {{isbn|978-0-8101-2704-3}}, [[Northwestern University Press]], 2010.<ref>{{cite journal|author=Audin, Michèle|author-link=Michèle Audin|title=Review: ''At Home with André and Simone Weil'', by Sylvie Weil|journal=Notices of the AMS|year=2011|volume=58|issue=5|pages=697–698|url=https://www.ams.org/notices/201105/rtx110500697p.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ams.org/notices/201105/rtx110500697p.pdf |archive-date=2022-10-09 |url-status=live}}</ref>

==See also==
* [[List of things named after André Weil]]

==References==
{{reflist|30em|refs=

<ref name="frs">{{Cite journal
  |last1      = Serre
  |first1     = J.-P.
  |author-link = Jean-Pierre Serre
  |doi        = 10.1098/rsbm.1999.0034
  |title      = Andre Weil. 6 May 1906 – 6 August 1998: Elected For.Mem.R.S. 1966
  |journal    = [[Biographical Memoirs of Fellows of the Royal Society]]
  |volume     = 45
  |pages      = 519
  |date       = 1999
  |doi-access= free
  }}</ref>

<ref name="MPC-object">{{cite web
  |title      = 289085 Andreweil (2004 TC244)
  |work       = Minor Planet Center
  |url        = https://www.minorplanetcenter.net/db_search/show_object?object_id=289085
  |access-date = 11 September 2019}}</ref>

<ref name="MPC-Circulars-Archive">{{cite web
  |title      = MPC/MPO/MPS Archive
  |work       = Minor Planet Center
  |url        = https://www.minorplanetcenter.net/iau/ECS/MPCArchive/MPCArchive_TBL.html
  |access-date = 11 September 2019}}</ref>

}} <!-- end of reflist -->

==External links==
{{Wikiquote}}
* [https://www.ams.org/journals/bull/2009-46-04/S0273-0979-09-01264-6/home.html André Weil], by A. Borel, Bull. AMS 46 (2009), 661–666.
* [https://www.ams.org/notices/199904/index.html André Weil]: memorial articles in the ''[[Notices of the American Mathematical Society|Notices of the AMS]]'' by [[Armand Borel]], [[Pierre Cartier (mathematician)|Pierre Cartier]], [[K. S. Chandrasekharan|Komaravolu Chandrasekharan]], [[Shiing-Shen Chern]], and Shokichi Iyanaga
* [https://www.ams.org/images/weil-photo.gif Image of Weil]
* [https://www.ams.org/notices/200503/fea-weil.pdf A 1940 Letter of André Weil on Analogy in Mathematics]
* {{cite news|title=Andre Weil, Who Reshaped Mathematics, Is Dead at 92|newspaper=[[The New York Times]]|author=Ford Burkhart|date=10 August 1998|access-date=10 January 2008|url=https://www.nytimes.com/1998/08/10/nyregion/andre-weil-who-reshaped-mathematics-is-dead-at-92.html?exprod=permalink&partner=permalink}}
* {{cite news|title=The lives they lived: Andre Weil; Numbers Man|newspaper=[[The New York Times]]|author=Paul Hoffman|date=3 January 1999|access-date=23 January 2008|url=https://www.nytimes.com/1999/01/03/magazine/the-lives-they-lived-andre-weil-numbers-man.html|author-link=Paul Hoffman (science writer)}}
* [http://www.ias.ac.in/currsci/aug252003/526.pdf Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene] – [[M. S. Raghunathan]]
* {{cite journal |first=V.S. |last=Varadaraja |title=Book Review: The Apprenticeship of a Mathematician—Autobiography of André Weil |journal=Notices of the AMS |volume=46 |issue=4 |pages=448–456 |date=April 1999 |url=https://www.ams.org/notices/199904/rev-varadarajan.pdf }}
* La vie et l'oeuvre d'André Weil, by J-P. Serre, L'Ens. Math. 45 (1999),5–16.
* Correspondance entre Henri Cartan et André Weil (1928–1991), par Michèle Audin, Doc. Math. 6, Soc. Math. France, 2011.

{{Wolf Prize in Mathematics}}
{{FRS 1966}}
{{Authority control}}

{{DEFAULTSORT:Weil, Andre}}
[[Category:1906 births]]
[[Category:1998 deaths]]
[[Category:20th-century French mathematicians]]
[[Category:Jewish French scientists]]
[[Category:French historians of mathematics]]
[[Category:Jewish agnostics]]
[[Category:French agnostics]]
[[Category:French people of Jewish descent]]
[[Category:Institute for Advanced Study faculty]]
[[Category:Academic staff of Aligarh Muslim University]]
[[Category:Arithmetic geometers]]
[[Category:École Normale Supérieure alumni]]
[[Category:Nicolas Bourbaki]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Kyoto laureates in Basic Sciences]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Aligarh Muslim University alumni]]
[[Category:Academic staff of the University of São Paulo]]
[[Category:Foreign members of the Royal Society]]
[[Category:Foreign associates of the National Academy of Sciences]]
[[Category:Scientists from Paris]]
[[Category:Lycée Saint-Louis alumni]]
[[Category:20th-century French historians]]
[[Category:Members of the American Philosophical Society]]
[[Category:French expatriates in Brazil]]
[[Category:French expatriates in the United States]]