Talk:Nicolas Bourbaki

message: How should we phrase "not a real individual" or "fictional character"? ~ Dpr
:You can use either, provided that you first define them in terms of sets and prove them equivalent up to a natural transformation.
How should we refer to Bourbaki in other Wikipedia articles? I see Bourbaki referred to as "it" and "the Bourbaki group" or just "Bourbaki" in some articles, and "Nicolas Bourbaki" and "he/him/his" in other articles. -SamCLowe (talk) 04:56, 20 February 2024 (UTC)
thread_title:  Phrasing 

message: Very nicely done. Clear and concise. One point has me stumped though. In the last section we have:
The New Maths project of early maths teaching, on the other hand, had little directly to do with Bourbaki. It is certainly true, though, that the inception of the New Math coincided with the height of Bourbaki's prestige, and the feeling that mathematics could simply be 'modernised', by being 'structuralised'. The use of Venn diagrams, for example, goes back to the pedagogy of the nineteenth century, rather than connecting with the École Normale Supérieure. The furore involved might now be seen as a demarcation dispute along the calculus/discrete maths boundary.
This text surprised me. Who would come up with the idea that there could be a connection between Bourbaki and New Math? Bourbaki was a movement concerned with advanced topics in pure math, and the so called New Math was a fad in education for the youngest school goers. 
I am going to remove the text. If I'm missed the point, sorry. We can put it back.
--Philopedia 8 July 2005 11:56 (UTC)
:The point really is that Bourbaki is often 'blamed' for New Math. That may have been journalistic. It's all a bit like blaming Derrida for multiculturism in primary education. However the charges were not uncommon, I think. Charles Matthews 19:29, 27 July 2005 (UTC)
thread_title: Non sequitur?

message: I changed the text, because Bourbaki is an alloynm, not a pseudonym, but the link is redirected to still wind up at pseudonym, which is an entertaining but unfortunate fact, I think. Awad helper 17:12, 22 October 2005 (UTC)
thread_title:  Allonym 

message: Someone had put "Operads" as volume IX. I'm fairly sure that's not right, so I removed it! But in double checking I noticed that in the French wikipedia, , the numbering is different: they say differential varieties is VIII, Lie groups is IX. Is the numbering system official? - does anyone know who is right? Sam Staton (talk) 10:55, 29 November 2007 (UTC)
thread_title: Numbering of Éléments de mathématique

message: The second paragraph of the last section ("The Bourbachique influence: education, institutions, trends") contains unsourced and biased statements. The statement about Bonn Arbeitstagung is not supported by any evidence or reference. It is an arbitrary comparison of a collective author and editorial project (Bourbaki) and a series of meetings (the Bonn Arbeitstagung). Setting these up as "rivals" is any sense does not appear to make much sense (if for nothing else, take Serre's participation in both!).
As for the example of the Borel-Serre (again!) seminar on complex multiplication, it is nonsensical to suggest that as being contrary to a Bourbaki viewpoint. Complex multiplication as a topic was never classified as "non-core" by Bourbaki; rather their treatise did not reach sufficiently far to treat such a topic "too far from foundations". Same applies to number theory. To get an as official as possible view on what Bourbaki considered core, a look at the 1971 book by Dieudonné is sufficient to counter the claims now made in the paragraph.
I shall remove the paragraph in question unless supporting citations for these can be found in reasonable time. Stca74 (talk) 19:11, 1 January 2008 (UTC)
replies: text: With no objections appearing since January, removed the offending paragraph. Stca74 (talk) 18:55, 16 May 2008 (UTC)
replies: text:  The sourcing for this article still seems a little poor, but I am impressed at how much it has improved. JackSchmidt (talk) 15:53, 22 July 2008 (UTC)
thread_title:  Section on influence 

message: It would be interesting to have an explanation for the choice of the name.  As the article presently stands, there are oblique references to the reason(s) for the choice, but without any explanation.  173.16.252.154 (talk) 21:16, 15 September 2009 (UTC)
thread_title:  The name 

message: Substituted at 01:13, 30 April 2016 (UTC)
thread_title: Assessment comment

message: Recently I've made multiple large edits to the article, which haven't yet occasioned any pushback.  I intend to continue this process, relying heavily (not exclusively) on Mashaal and Aczel, to the point of ultimately rewriting the article one section at a time.  I create this talk section both to explain my plan for a future article structure, and also as an obvious spot for other editors to push back/suggest other improvements/express any concerns.  My 40,000 foot-view vision for the future article runs thus:
*Lead (hitting all major beats of article, done and live)
*Background (historical background leading into founding, done and live)
*Founding (1934/1935)
*Working method (rural conferences, argumentative, slow, unanimity)
*Works (Elements, Seminars, La Tribu)
*Membership (Nature of members, table of members)
*Influence and criticism (lengthy section at which point several cultural non-math references can be introduced: Oulipo, Lyotard, Deleuze and Guattari, etc.  Also stressing the negatives of Elements as described by Mashaal/Aczel.)
*See also (boilerplate)
*Notes (boilerplate)
*References (boilerplate)
*External links (boilerplate)
I also eventually want to address the "partisan" concern in the current article's complaint tag (with a view toward legitimately getting rid of same tag), but as I write I haven't seen about the details of this point. MinnesotanUser (talk) 06:25, 24 January 2020 (UTC)
thread_title: Rewrite, late '19/early '20

message: As part of rewriting the article, I removed the "Partisan sources" tag placed here, by Quantum Knot.  Reasons:
* Ongoing heavy editing is eventually meant to give even weight (pro and con) to article's subject (Bourbaki's supporters and detractors),
* no specific reason given in above edit summary,
* personal confidence to rephrase available material in neutral fashion.
I write this note to invite discussion if there's any concern about the tag removal. MinnesotanUser (talk) 08:04, 31 January 2020 (UTC)
thread_title: Partisan source tag removal

message: I reverted a change (that went back to an earlier version I had changed) claiming that Grothendieck's decision to leave the Bourbaki group was due to disagreement on categories versus sets. I think this does not accurately characterise the disputes of the time and oversimplifies the issue. I will explain below. I have also added as new reference Ralf Krömer's great article about precisely this issue; it has the benefit of access to primary sources not accessible to Corry (or Mashaal and Aczel).
Grothendieck (like many members of the group, notably Cartan and Lang) advocated very strongly that categories be introduced into the treatise as a tool of both organisation and technique of proof. It appears that this was opposed in particular by Weil, perhaps partly on the basis of "aesthetic" dislike and (speculatively) early misunderstanding of what kinds of distinctions would be allowed by categories (such as between strict and non-strict morphism of topological groups). Eventually the strong opposition of Weil prevailed (despite his having officially "retired" from the group by that time!) and Grothendieck decided to leave.
Now apart from stylistic and "aesthetical" differences, there were two major issue that stood against the possible incorporation of categories in the treatise. First, the group had after many attempts and through a torturous process just produced the promised Chapter 4 of the book on set theory to lay out a "theory of mathematical structures" announced much earlier. However, the concept of "structures" and the associated theory in the new chapter was essentially a complete failure and was not eventually used in any way (and hardly even referenced) in the other books of the treatise. This was perceived at the time within the group, and Jacques Dixmier went as far as initially use his veto to block the publication of the new chapter. Eventually (as evidenced by Bourbaki's internal Tribu 39), Dixmier was pressured to withdraw his veto "in order not to delay the publication of a chapter on which a lot of work has been spent". Since Bourbaki's "structures" were essentially an unsuccessful attempt to build something like category theory, it is clear that properly bringing categories into the treatise would have invalidated and replaced this convoluted new chapter, and there was resistance to abandon this failed result of hard work. (Curiously the same Tribu 39 however recorded a decision to write also a new Chapter 5 of Set Theory on Categories and Functors...)
The second issue was how to integrate categories within the set-theoretical foundations chosen by Bourbaki (essentially equivalent in strength with ZFC even if somewhat different in details). The question is  mainly about large categories (where objects do not form a set) and quantification over objects in "any" categories. Various solutions were discussed such as switching to Bernays-Gödel type set theory with explicit distinction between (proper) classes and sets as well as an attempt of resorting to mathematical logic and turning categories into a "metamathematical" tool. 
Eventually Grothendieck came up with the proposal of integrating categories within set theory 
extended with a new axiom that guarantees the existence of sufficient supply of "Grothendieck universes" (the new axiom amounts to asking for existence of strongly inaccessible cardinals). This proposal provisionally won the group's support (in a Bourbaki conference where Weil was not present...) and was apparently intended to be the chosen way forward until the Weil-influenced decision to drop categories a bit later. Grothendieck's treatment of large categories within (extended) set theory ended up as a appendix to the first volume of SGA 4 (curiously atrributed to N. Bourbaki...).
The crucial point here is that Grothendieck did not envisage a conflict of categories versus set theory, but instead intended to bring categories inside the set-theoretic foundations of Bourbaki (subject to modification by a new axiom). It is instructive to see what Grothendieck wrote in his report to Bourbaki after denouncing the proposals of the logician (Lacombe) consulted by the group:
::Pour conclure, il me semble donc point qu'on soit obligé de rien changer aux trois premiers chapitres du Livre I [Set Theory] [...] Il sera suffisant d'introduire au nouveau chapitre 4 (qui remplacera l'ancien inutilisable de toutes façons) les axioms supplémentaires de la théorie des ensembles, et y développer la théorie des catégories aussi loin qu'il semble désirable.
Thus Grothendieck does not intend to change anything in the first three chapters of Set Theory (the ones containing Bourbaki's version of ZFC and basic set theory), but instead wants to replace the "unusable" (true!) chapter 4 on "structures" with a new chapter on categories, including the universe axiom to be added to set theory that allows the development of categories (as far as desired) within set theory.
Thus Grothendieck's conflict with Bourbaki (or rather Weil...) was not a conflict between categories and set theory, but about incorporation of categories and about replacement of the (failed) "theory of structures" with properly developed categories. This point is important to make also to avoid imputing later ideas about categorical foundations of mathematics (that would replace sets as the basis) into the earlied debates leading to Grothendieck's leaving Bourbaki in 1960.
Obviously this rant is way too long and detailed for inclusion in the article (let alone an image caption...), but I think it makes sense to avoid suggesting potentially misleading interpretations of the situation up to 1960.
Stca74 (talk) 08:28, 16 July 2023 (UTC)
thread_title:  Bourbaki and categories: not simply categories vs sets