Editing Nicolas Bourbaki (section)

==The Bourbaki collective==

[[File:Integral as region under curve.svg|thumb|left|200px|Bourbaki was founded to produce a text in [[mathematical analysis]], a branch of mathematics entailing [[calculus]]]]

===Founding===
During their time together at Strasbourg, Weil and Cartan regularly complained to each other regarding the inadequacy of available course material for [[calculus]] instruction. In his memoir ''Apprenticeship'', Weil described his solution in the following terms: "One winter day toward the end of 1934, I came upon a great idea that would put an end to these ceaseless interrogations by my comrade. 'We are five or six friends', I told him some time later, 'who are in charge of the same mathematics curriculum at various universities. Let us all come together and regulate these matters once and for all, and after this, I shall be delivered of these questions.' I was unaware of the fact that Bourbaki was born at that instant."{{sfn|Aczel|p=81}} Cartan confirmed the account.{{sfn|Mashaal|p=4}}

The first, unofficial meeting of the Bourbaki collective took place at noon on Monday, 10 December 1934, at the Café Grill-Room A. Capoulade, Paris, in the [[Latin Quarter]].{{sfn|Aczel|pp=82–83}}{{sfn|Beaulieu|1993|p=28}}{{sfn|Mashaal|p=6}}<ref name="mactutor">{{cite web |url=http://mathshistory.st-andrews.ac.uk/HistTopics/Bourbaki_1.html |title=Bourbaki: the pre-war years |last1=O'Connor |first1=John J. |last2=Robertson |first2=Edmund F. |date=December 2005 |website=[[MacTutor History of Mathematics archive|Mactutor]]}}</ref>{{efn|The restaurant, which no longer exists, was at 63 Boulevard Saint-Michel.{{sfn|Beaulieu|1993|p=29}} }} Six mathematicians were present: [[Henri Cartan]], [[Claude Chevalley]], [[Jean Delsarte]], [[Jean Dieudonné]], [[René de Possel]], and [[André Weil]]. Most of the group were based outside Paris and were in town to attend the Julia Seminar, a conference prepared with the help of Gaston Julia at which several future Bourbaki members and associates presented.{{sfn|Beaulieu|1993|p=32}}{{sfn|Mashaal|pp=6–7, 102–03}}{{efn|The Julia Seminar was held every other Monday, in the afternoon.{{sfn|Mashaal|p=103}}  Bourbaki's early lunch meetings during 1934–1935 were typically held on the same Mondays, immediately before the Seminar.{{sfn|Beaulieu|1993|p=32}}<ref name="barchive">{{cite web |url=http://sites.mathdoc.fr/archives-bourbaki/ |title=Archives de l'Association des Collaborateurs de Nicolas Bourbaki}}</ref><ref name="timedate">{{cite web |url=https://www.timeanddate.com/calendar/?year=1935&country=5 |title=Calendar for Year 1935 (France) |website=Time and Date}}</ref> }} The group resolved to collectively write a treatise on analysis, for the purpose of standardizing calculus instruction in French universities. The project was especially meant to supersede the text of [[Édouard Goursat]], which the group found to be badly outdated, and to improve its treatment of [[Stokes' Theorem]].{{sfn|Mashaal|p=6}}{{sfn|Aczel|p=84}}{{sfn|Beaulieu|1999|p=233}}<ref name="numericana">{{cite web |url=http://www.numericana.com/fame/bourbaki.htm |title=The Many Faces of Nicolas Bourbaki |last=Michon |first=Gérard P. |website=Numericana}}</ref> The founders were also motivated by a desire to incorporate ideas from the [[University of Göttingen|Göttingen]] school, particularly from exponents [[David Hilbert|Hilbert]], [[Emmy Noether|Noether]] and [[Bartel van der Waerden|B.L. van der Waerden]]. Further, in the aftermath of World War I, there was a certain nationalist impulse to save French mathematics from decline, especially in competition with Germany. As Dieudonné stated in an interview, "Without meaning to boast, I can say that it was Bourbaki that saved French mathematics from extinction."{{sfn|Mashaal|pp=38-45}}

Jean Delsarte was particularly favorable to the collective aspect of the proposed project, observing that such a working style could insulate the group's work against potential later individual claims of [[copyright]].{{sfn|Aczel|p=84}}{{sfn|Mashaal|pp=7,14}}{{efn|Delsarte's favorable view of a collective project was not recorded in the minutes of the first meeting.  He is supposed to have expressed the view elsewhere, with Cartan and Weil eventually attributing the opinion to him.  However, the opinion is closely associated with the working style of Bourbaki which eventually emerged.{{sfn|Beaulieu|1993|pp=28–29}} }} As various topics were discussed, Delsarte also suggested that the work begin in the most abstract, axiomatic terms possible, treating all of mathematics prerequisite to analysis from scratch.{{sfn|Aczel|pp=85–86}}{{sfn|Aubin|p=303}} The group agreed to the idea, and this foundational area of the proposed work was referred to as the "Abstract Packet" (Paquet Abstrait).{{sfn|Aczel|p=86}}{{sfn|Beaulieu|1993|p=30}}{{sfn|Mashaal|p=11}} [[Working title]]s were adopted: the group styled itself as the '''Committee for the Treatise on Analysis''', and their proposed work was called the ''Treatise on Analysis'' (''Traité d'analyse'').{{sfn|Aczel|p=87}}{{sfn|Mashaal|p=8}} In all, the collective held ten preliminary biweekly meetings at A. Capoulade before its first official, founding conference in July 1935.{{sfn|Mashaal|p=8}}{{sfn|Beaulieu|1993|p=33}} During this early period, [[Paul Dubreil]], [[Jean Leray]] and [[Szolem Mandelbrojt]] joined and participated. Dubreil and Leray left the meetings before the following summer, and were respectively replaced by new participants [[Jean Coulomb]] and [[Charles Ehresmann]].{{sfn|Aczel|p=87}}{{sfn|Mashaal|pp=8–9}}

[[File:Nicolas Bourbaki naissance à Besse.jpg|thumb|left|Sign marking the official founding of Bourbaki in [[Besse-en-Chandesse]]]]

The group's official founding conference was held in [[Besse-en-Chandesse]], from 10 to 17 July 1935.{{sfn|Aczel|p=90}}{{sfn|Mashaal|p=10}} At the time of the official founding, the membership consisted of the six attendees at the first lunch of 10 December 1934, together with Coulomb, Ehresmann and Mandelbrojt. On 16 July, the members took a walk to alleviate the boredom of unproductive proceedings. During the malaise, some decided to [[Nude swimming|skinny-dip]] in the nearby [[Lac Pavin]], repeatedly yelling "Bourbaki!"{{sfn|Mashaal|p=22}} At the close of the first official conference, the group renamed itself "Bourbaki", in reference to the general and prank as recalled by Weil and others.{{sfn|Mashaal|p=11}}{{efn|The mathematician Sterling K. Berberian suggested another possible origin for the Bourbaki name: [[Octave Mirbeau|Octave Mirbeau's]] 1900 novel ''[[The Diary of a Chambermaid (novel)|The Diary of a Chambermaid]]'', which describes a hedgehog named Bourbaki that eats voraciously.  However Mashaal dismissed this connection as being unlikely since the founders never referred to the novel, but only to the general and the Husson anecdote.{{sfn|Mashaal|pp=25–26}} }} During 1935, the group also resolved to establish the mathematical [[personhood]] of their collective pseudonym by getting an article published under its name.{{sfn|Aczel|p=90}}{{sfn|Mashaal|pp=27–29}} A first name had to be decided; a full name was required for publication of any article. To this end, René de Possel's wife Eveline "baptized" the pseudonym with the first name of Nicolas, becoming Bourbaki's "godmother".{{sfn|Aczel|p=90}}<ref name="Mainard">{{Cite web|url=http://www.academie-stanislas.org/academiestanislas/images/Publications/TomeXVI/TomeXVI-Mainard01.pdf|title=Le Mouvement Bourbaki|last=Mainard|first=Robert|date=October 21, 2001|website=academie-stanislas.org}}</ref>{{sfn|Mashaal|p=27}}<ref name="mccleary">{{Cite web|url=http://www.math.vassar.edu/faculty/mccleary/Bourbaki.pdf|title=Bourbaki and Algebraic Topology|last=McCleary|first=John|date=December 10, 2004|website=math.vassar.edu|archive-url=https://web.archive.org/web/20061030215012/http://math.vassar.edu/faculty/McCleary/Bourbaki.pdf|archive-date=October 30, 2006}}</ref> This allowed for the publication of a second article with material attributed to Bourbaki, this time under "his" own name.<ref name="sur">{{cite journal |url=https://gallica.bnf.fr/ark:/12148/bpt6k31534/f1311.image |title=Sur un théorème de Carathéodory et la mesure dans les espaces topologiques |last=Bourbaki |first=Nicolas |journal=[[Comptes rendus de l'Académie des Sciences]] |volume=201 |pages=1309–11 |date=18 November 1935}}</ref> Henri Cartan's father [[Élie Cartan]], also a mathematician and supportive of the group, presented the article to the publishers, who accepted it.{{sfn|Mashaal|pp=27–29}}

At the time of Bourbaki's founding, René de Possel and his wife Eveline were in the process of divorcing. Eveline remarried to André Weil in 1937, and de Possel left the Bourbaki collective some time later. This sequence of events has caused speculation that de Possel left the group because of the remarriage,{{sfn|Mashaal|p=17}} however this suggestion has also been criticized as possibly historically inaccurate, since de Possel is supposed to have remained active in Bourbaki for years after André's marriage to Eveline.<ref>{{cite web |url=http://www.neverendingbooks.org/the-bumpy-road-to-the-first-bourbaki-congress |title=The Bumpy Road to the First Bourbaki Congress |date=22 October 2009 |website=neverendingbooks.org}}</ref>

===World War II===

Bourbaki's work slowed significantly during the [[Second World War]], though the group survived and later flourished. Some members of Bourbaki were Jewish and therefore forced to flee from certain parts of Europe at certain times. Weil, who was Jewish, spent the summer of 1939 in Finland with his wife Eveline, as guests of [[Lars Ahlfors]]. Due to their travel near the border, the couple were suspected as Soviet spies by Finnish authorities near the onset of the [[Winter War]], and André was later arrested.<ref>{{cite web |url=https://www.icmihistory.unito.it/portrait/nevanlinna.php |title=Rolf Nevanlinna |website=icmihistory.unito.it}}</ref> According to an anecdote, Weil was to have been executed but for the passing mention of his case to [[Rolf Nevanlinna]], who asked that Weil's sentence be commuted.{{sfn|Aczel|pp=17–36}} However, the accuracy of this detail is dubious.<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 reached the United States in 1941, later taking another teaching stint in [[São Paulo]] from 1945 to 1947 before settling at the [[University of Chicago]] from 1947 to 1958 and finally the [[Institute for Advanced Study]] in [[Princeton, New Jersey|Princeton]], where he spent the remainder of his career. Although Weil remained in touch with the Bourbaki collective and visited Europe and the group periodically following the war, his level of involvement with Bourbaki never returned to that at the time of founding.

Second-generation Bourbaki member [[Laurent Schwartz]] was also Jewish and found pickup work as a math teacher in rural [[Vichy France]]. Moving from village to village, Schwartz planned his movements in order to evade capture by the [[Nazi]]s.{{sfn|Senechal|pp=22–28}} On one occasion Schwartz found himself trapped overnight in a certain village, as his expected transportation home was unavailable. There were two inns in town: a comfortable, well-appointed one, and a very poor one with no heating and bad beds. Schwartz's instinct told him to stay at the poor inn; overnight, the Nazis raided the good inn, leaving the poor inn unchecked.{{sfn|Aczel|p=40}}

Meanwhile, Jean Delsarte, a Catholic, was mobilized in 1939 as the captain of an audio reconnaissance battery. He was forced to lead the unit's retreat from the northeastern part of France toward the south. While passing near the Swiss border, Delsarte overheard a soldier say "We are the army of Bourbaki";{{sfn|Aczel|p=98}}{{sfn|Mashaal|pp=20–24}} the 19th-century general's retreat was known to the French. Delsarte had coincidentally led a retreat similar to that of the collective's namesake.

===Postwar until the present===

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Following the war, Bourbaki had solidified the plan of its work and settled into a productive routine. Bourbaki regularly published volumes of the ''Éléments'' during the 1950s and 1960s, and enjoyed its greatest influence during this period.{{sfn|Aczel|p=117}}{{sfn|Beaulieu|1999|p=237}} Over time the founding members gradually left the group, slowly being replaced with younger newcomers including [[Jean-Pierre Serre]] and [[Alexander Grothendieck]]. Serre, Grothendieck and Laurent Schwartz were awarded the [[Fields Medal]] during the postwar period, in 1954, 1966 and 1950 respectively. Later members [[Alain Connes]] and [[Jean-Christophe Yoccoz]] also received the Fields Medal, in 1982 and 1994 respectively.{{sfn|Mashaal|p=19}}

The later practice of accepting scientific awards contrasted with some of the founders' views.{{sfn|Guedj|p=19}} During the 1930s, Weil and Delsarte petitioned against a French national scientific "medal system" proposed by the [[Nobel prize|Nobel]] [[Nobel Prize in Physics|physics]] laureate [[Jean Perrin]]. Weil and Delsarte felt that the institution of such a system would increase unconstructive pettiness and jealousy in the scientific community.{{sfn|Mashaal|p=49}} Despite this, the Bourbaki group had previously successfully petitioned Perrin for a government [[Grant (money)|grant]] to support its normal operations.{{sfn|Mashaal|pp=14–16}} Like the founders, Grothendieck was also averse to awards, albeit for [[pacifism|pacifist]] reasons. Although Grothendieck was awarded the Fields Medal in 1966, he declined to attend the ceremony in Moscow, in protest of the Soviet government.<ref>{{cite web |url=http://www.icm2018.org/wp/2018/08/03/sir-michael-atiyah-shares-memory-of-fields-win/ |title=Sir Michael Atiyah shares memory of Fields win |date=3 August 2018 |publisher=[[International Congress of Mathematicians]] |access-date=15 February 2020 |archive-date=22 September 2019 |archive-url=https://web.archive.org/web/20190922045445/http://www.icm2018.org/wp/2018/08/03/sir-michael-atiyah-shares-memory-of-fields-win/ |url-status=dead }}</ref> In 1988, Grothendieck rejected the [[Crafoord Prize]] outright, citing no personal need to accept prize money, lack of recent relevant output, and general distrust of the scientific community.<ref name="crafoord">{{cite web |url=http://www.math.columbia.edu/~lipyan/CrafoordPrize.pdf |last=Grothendieck |first=Alexander |title=Crafoord Prize letter, English translation |access-date=2005-06-17 |url-status = bot: unknown|archive-url=https://web.archive.org/web/20060106062005/http://www.math.columbia.edu/~lipyan/CrafoordPrize.pdf |archive-date=6 January 2006 |df=dmy}}</ref>

Born to Jewish [[anarchist]] parentage, Grothendieck survived the [[Holocaust]] and advanced rapidly in the French mathematical community, despite poor education during the war.{{sfn|Aczel|pp=9–10}} Grothendieck's teachers included Bourbaki's founders, and so he joined the group. During Grothendieck's membership, Bourbaki reached an impasse concerning its foundational approach. Grothendieck advocated for a reformulation of the group's work using [[category theory]] as its theoretical basis, as opposed to set theory. The proposal was ultimately rejected{{sfn|Aubin|p=328}}{{sfn|Beaulieu|1999|pp=236–37}}{{sfn|Corry|2009|pp=38–51}} in part because the group had already committed itself to a rigid track of sequential presentation, with multiple already-published volumes. Following this, Grothendieck left Bourbaki "in anger".<ref name="numericana" />{{sfn|Senechal|pp=22–28}}{{sfn|Aczel|p=119}} Biographers of the collective have described Bourbaki's unwillingness to start over in terms of category theory as a missed opportunity.{{sfn|Senechal|pp=22–28}}{{sfn|Aczel|p=205}}{{sfn|Mashaal|pp=81–84}} However, Bourbaki has in 2023 announced that a book on category theory is currently under preparation (see below the last paragraph of this section).

During the founding period, the group chose the Parisian publisher [[Éditions Hermann|Hermann]] to issue installments of the ''Éléments''. Hermann was led by Enrique Freymann, a friend of the founders willing to publish the group's project, despite financial risk. During the 1970s, Bourbaki entered a protracted legal battle with Hermann over matters of copyright and [[royalty payment]]. Although the Bourbaki group won the suit and retained collective copyright of the ''Éléments'', the dispute slowed the group's productivity.{{sfn|Aczel|pp=205–206}}{{sfn|Mashaal|pp=7, 51–54}} Former member Pierre Cartier described the lawsuit as a [[pyrrhic victory]], saying: "As usual in legal battles, both parties lost and the lawyer got rich."{{sfn|Senechal|pp=22–28}} Later editions of the ''Éléments'' were published by [[Masson (publisher)|Masson]], and modern editions are published by [[Springer Science+Business Media|Springer]].<ref>[https://www.springer.com/series/47 Elements of Mathematics] series in Springer</ref> From the 1980s through the 2000s, Bourbaki published very infrequently, with the result that in 1998 ''[[Le Monde]]'' pronounced the collective "dead".{{sfn|Mashaal|p=146}}

However, in 2012 Bourbaki resumed the publication of the ''Éléments'' with a revised chapter 8 of algebra, the first 4 chapters of a new book on [[algebraic topology]], and two volumes on [[spectral theory]] (the first of which is an expanded and revised version of the edition of 1967 while the latter consist of three new chapters). Moreover, the text of the two latest volumes announces that books on [[category theory]] and [[modular forms]] are currently under preparation (in addition to the latter part of the book on algebraic topology).<ref>{{cite book |last1=Bourbaki |first1=Nicolas |title=Théories spectrales: Chapitres 1 et 2 — Seconde édition, refondue et augmentée|year=2019 |publisher=Springer |series=Éléments de mathématique |isbn=978-3030140632|page=II.299}}</ref><ref>{{cite book |last1=Bourbaki |first1=Nicolas |title=Théories spectrales: Chapitres 3 à 5 |year=2023b |publisher=Springer |series=Éléments de mathématique |isbn=978-3031195044|page=V.416}}</ref>