Editing Nicolas Bourbaki (section)

===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>