Editing Nicolas Bourbaki (section)

==Working method==

[[File:Finite coxeter.svg|thumb|right|400px|At [[Armand Borel]]'s urging, Bourbaki's treatment of Lie groups and Lie algebras included uncharacteristic illustrations, such as graphs of finite [[Coxeter systems]]<ref name="lie">{{cite book |last=Bourbaki |first=Nicolas |title=Lie Groups and Lie Algebras, Chapters 4–6 |publisher=Springer |date=2002 |isbn=978-3540691716 |pages=205–206}}</ref>]]

Bourbaki holds periodic conferences for the purpose of expanding the ''Éléments''; these conferences are the central activity of the group's working life. Subcommittees are assigned to write drafts on specific material, and the drafts are later presented, vigorously debated, and re-drafted at the conferences. Unanimous agreement is required before any material is deemed acceptable for publication.{{sfn|Aczel|p=92}}{{sfn|Borel|p=375}}{{sfn|Guedj|p=18}} A given piece of material may require six or more drafts over a period of several years, and some drafts are never developed into completed work.{{sfn|Borel|p=375}}{{sfn|Guedj|p=20}} Bourbaki's writing process has therefore been described as "[[Sisyphus|Sisyphean]]".{{sfn|Guedj|p=18}} Although the method is slow, it yields a final product which satisfies the group's standards for [[mathematical rigour]], one of Bourbaki's main priorities in the treatise. Bourbaki's emphasis on rigour was a reaction to the style of [[Henri Poincaré]], who stressed the importance of free-flowing mathematical [[intuition]] at the cost of thorough presentation.{{efn|"Bourbaki came to terms with Poincaré only after a long struggle. When I joined the group in the fifties it was not the fashion to value Poincaré at all. He was old-fashioned." —Pierre Cartier{{sfn|Senechal|pp=22–28}} }} During the project's early years, Dieudonné served as the group's scribe, authoring several final drafts which were ultimately published. For this purpose, Dieudonné adopted an impersonal [[writing style]] which was not his own, but which was used to craft material acceptable to the entire group.{{sfn|Aczel|p=116}}{{sfn|Borel|p=376}} Dieudonné reserved his personal style for his own work; like all members of Bourbaki, Dieudonné also published material under his own name,{{sfn|Mashaal|p=69}} including the nine-volume ''[[Treatise on analysis|Éléments d'analyse]]'', a work explicitly focused on analysis and of a piece with Bourbaki's initial intentions.

Most of the final drafts of Bourbaki's ''Éléments'' carefully avoided using illustrations, favoring a formal presentation based only in text and formulas. An exception to this was the treatment of Lie groups and Lie algebras (especially in chapters 4–6), which did make use of diagrams and illustrations. The inclusion of illustration in this part of the work was due to [[Armand Borel]]. Borel was minority-Swiss in a majority-French collective, and [[Self-deprecation|self-deprecated]] as "the Swiss peasant", explaining that [[visual learning]] was important to the Swiss national character.{{sfn|Senechal|pp=22–28}}{{sfn|Aczel|pp=111–12}} When asked about the dearth of illustration in the work, former member [[Pierre Cartier (mathematician)|Pierre Cartier]] replied:

{{blockquote|text=The Bourbaki were [[Puritan]]s, and Puritans are strongly opposed to pictorial representations of truths of their faith. The number of Protestants and Jews in the Bourbaki group was overwhelming. And you know that the [[Protestantism in France|French Protestant]]s especially are very close to Jews in spirit. |title=Pierre Cartier{{sfn|Senechal|pp=22–28}} }}

The conferences have historically been held at quiet rural areas.{{sfn|Beaulieu|1999|pp=225–26}} These locations contrast with the lively, sometimes heated debates which have occurred. Laurent Schwartz reported an episode in which Weil slapped Cartan on the head with a draft. The hotel's proprietor saw the incident and assumed that the group would split up, but according to Schwartz, "peace was restored within ten minutes."{{sfn|Mashaal|pp=112–13}} The historical, confrontational style of debate within Bourbaki has been partly attributed to Weil, who believed that new ideas have a better chance of being born in confrontation than in an orderly discussion.{{sfn|Borel|p=375}}{{sfn|Mashaal|pp=112–13}} Schwartz related another illustrative incident: Dieudonné was adamant that [[topological vector spaces]] must appear in the work before [[Integral|integration]], and whenever anyone suggested that the order be reversed, he would loudly threaten his resignation. This became an in-joke among the group; [[Roger Godement|Roger Godement's]] wife Sonia attended a conference, aware of the idea, and asked for proof. As Sonia arrived at a meeting, a member suggested that integration must appear before topological vector spaces, which triggered Dieudonné's usual reaction.{{sfn|Mashaal|pp=112–13}}

Despite the historical culture of heated argument, Bourbaki thrived during the middle of the twentieth century. Bourbaki's ability to sustain such a collective, critical approach has been described as "something unusual",<ref>{{cite book |last1=Sabelli |first1=Héctor |contribution=Foreword |contributor-last=Kauffman |contributor-first=Louis H. |contributor-link=Louis Kauffman |title=BIOS: a Study of Creation |year=2005 |publisher=[[World Scientific]] |location=Singapore |series=Series on Knots and Everything |volume=35 |page=423 |isbn=978-9812561039 }}</ref> surprising even its own members. In founder Henri Cartan's words, "That a final product can be obtained at all is a kind of miracle that none of us can explain."<ref name="Corry1997">{{cite journal |last=Corry |first=Leo |title=The Origins of Eternal Truth in Modern Mathematics: Hilbert to Bourbaki and Beyond |url=https://www.tau.ac.il/~corry/publications/articles/truth.html |journal=Science in Context |volume=10 |issue=2 |page=279 |date=1997 |doi=10.1017/S0269889700002659 |s2cid=54803469 }}</ref>{{sfn|Corry|2004|p=309}} It has been suggested that the group survived because its members believed strongly in the importance of their collective project, despite personal differences.{{sfn|Borel|p=375}}{{sfn|Aczel|p=115}} When the group overcame difficulties or developed an idea that they liked, they would sometimes say ''l'esprit a soufflé'' ("the spirit breathes").{{sfn|Borel|p=375}}{{sfn|Mashaal|p=112}} Historian Liliane Beaulieu noted that the "spirit"—which might be an [[avatar]], the group mentality in action, or Bourbaki "himself"—was part of an internal culture and mythology which the group used to form its identity and perform work.{{sfn|Beaulieu|1999|p=245}}

===Humor===

Humor has been an important aspect of the group's culture, beginning with Weil's memories of the student pranks involving "Bourbaki" and "Poldevia". For example, in 1939 the group released a wedding announcement for the marriage of "Betti Bourbaki" (daughter of Nicolas) to one "[[Hoist with his own petard|H. Pétard]]" (H. "Firecrackers" or "Hector Pétard"), a "lion hunter".{{sfn|Beaulieu|1999|pp=239–40}} Hector Pétard was itself a pseudonym, but not one originally coined by the Bourbaki members. The Pétard moniker was originated by [[Ralph P. Boas]], [[Frank Smithies]] and other [[Princeton]] mathematicians who were aware of the Bourbaki project; inspired by them, the Princeton mathematicians published an article on the "mathematics of lion hunting". After meeting Boas and Smithies, Weil composed the wedding announcement, which contained several mathematical puns.{{sfn|Mashaal|pp=30, 113–14}} Bourbaki's internal newsletter ''La Tribu'' has sometimes been issued with humorous subtitles to describe a given conference, such as "The Extraordinary Congress of Old Fogies" (where anyone older than 30 was considered a fogy) or "The Congress of the Motorization of the Trotting Ass" (an expression used to describe the routine unfolding of a mathematical proof, or process).{{sfn|Beaulieu|1999|p=226}}{{sfn|Mashaal|pp=110–11}}

During the 1940s–1950s,{{sfn|Beaulieu|1999|p=241}}{{sfn|Mashaal|pp=33–34}} the [[American Mathematical Society]] received applications for individual membership from Bourbaki. They were rebuffed by [[John Robert Kline|J.R. Kline]] who understood the entity to be a collective, inviting them to re-apply for institutional membership. In response, Bourbaki floated a rumor that Ralph Boas was not a real person, but a collective pseudonym of the editors of ''[[Mathematical Reviews]]'' with which Boas had been affiliated. The reason for targeting Boas was because he had known the group in its earlier days when they were less strict with secrecy, and he'd described them as a collective in an article for the ''[[Encyclopædia Britannica]]''.{{sfn|Aczel|pp=121–23}} In November 1968, a mock obituary of Nicolas Bourbaki was released during one of the seminars.{{sfn|Beaulieu|1999|pp=241–42}}<ref>{{cite web |url=http://www.neverendingbooks.org/according-to-groth-iv-22 |title=According to Groth. IV.22 |date=1 October 2016 |website=neverendingbooks.org |access-date=2018-10-24}}</ref>

The group developed some variants of the word "Bourbaki" for internal use. The noun "Bourbaki" might refer to the group proper or to an individual member, e.g. "André Weil was a Bourbaki." "Bourbakist" is sometimes used to refer to members<ref name="numericana" /> but also denotes associates, supporters, and enthusiasts.{{sfn|Beaulieu|1993|p=31}}{{sfn|Beaulieu|1999|p=227}} To "bourbakize" meant to take a poor existing text and to improve it through an editing process.{{sfn|Guedj|p=20}}

Bourbaki's culture of humor has been described as an important factor in the group's social cohesion and capacity to survive, smoothing over tensions of heated debate.{{sfn|Mashaal|p=115}} As of {{year}}, a [[Twitter]] account registered to "Betty_Bourbaki" provides regular updates on the group's activity.<ref name="betty">{{cite web |url=https://twitter.com/betty_bourbaki |title=Compte twitter officiel de l'Association des collaborateurs de N. Bourbaki |author=Betty_Bourbaki |website=Twitter}}</ref>