Talk:Nicolas Bourbaki

Photo

I see the PlanetMath article in the external links has a photo. Could we use this?

Charles Matthews 09:38, 17 Dec 2004 (UTC)

PS Yes, I know that it would be better to have one of N.B. himself. Any French Wikipedian able to photo a relevant statue.

Hmmm...I seem to recall that there's a Bourbaki statue at Nancy. I'll look into getting a photo. --C S 07:15, Jan 5, 2005 (UTC)

Strife and signature

Very nice article. Especially the parts pointing out the biases/preferences of Bourbaki. There needs to be material on the clashes between Bourbaki and others though. I know there were some famous altercations. On a related note, Weil, I just read some time ago, would sign the Bourbaki letters himself. So something should be said about that. Maybe we can even get an image of his signature, "N. Bourbaki". --C S 07:10, Jan 5, 2005 (UTC)

Phrasing

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)

Non sequitur?

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)

Yes, in a better world Philopedia would be exactly right. But Charles is right in fact, and actually understates it. Back in the 1960s and 1970s lots of people thought the new math was exactly what Bourbaki was about.Colin McLarty (talk) 02:14, 14 December 2009 (UTC)

Allonym

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)

Neutrality

The section "The Bourbaki perspective and its limitations" contains rhetoric and reads like a criticism of Bourbaki, thus running afoul of NPOV policy. Specific offending passages:

• "problem solving is considered secondary to axiomatics" Why not say "mathematics is considered secondary to axiomatics"? I suppose because the rhetorical nature of the latter sentence is even more obvious. It should be noted, incidentally, that the Bourbaki texts contain problems to be solved after each chapter of exposition.
• "combinatorial structure is deemed non-structural": a type of "structure" is deemed "non-structural"? Definitely a case of smart-aleck rhetoric. A more neutral (and more accurate) statement would be: "combinatorial structure is considered less fundamental than other types of structure".
• "measure theory is coerced towards Radon measures": "coerced" is not a neutral word.
• "And, it goes without saying, no pictures. In fact geometry as a whole is slighted, where it doesn't reduce to abstract algebra and soft analysis." First of all, it is false that there are no pictures: see Topologie Générale. Secondly, it is the point of view of the Bourbaki group that geometry, as a whole, does in fact reduce to something like a combination of abstract algebra and "soft analysis"; cf. Dieudonné's remark "Everyone knows that Euclidean geometry is just a special case of the theory of Hermitian operators on Hilbert space". The author of this section is not neutral on this question, but rather takes the opposing view for granted by assuming that there exist parts of geometry that don't reduce to abstract algebra and soft analysis.
• "Mathematicians have always preferred folk-history and anecdotes. Bourbaki's history of mathematics, later gathered as a separate book, suffers in contrast not from lack of scholarship — but from the attitude that history should be written by the victors in the struggle to attain axiomatic clarity. It is inevitably partial, but also partisan." Here the author presumes to speak on behalf of all mathematicians in asserting (I suppose) that the latter "prefer" that the history of their subject not appear in organized, written form. Also, "suffers" is unquestionably a POV word. This paragraph (like most of this section) sounds more like a book review than an encyclopedia article.

Komponisto 05:04, 20 August 2006 (UTC)

"problem solving is considered secondary to axiomatics" - I understand this sentence as saying that if Bourbaki's texts are considered as textbooks then axiomatics is more emphasized then problem solving. I feel that this is true even though some texts contain some problems to be solved (though I read only a few of their books).

On the other hand, "mathematics is considered secondary to axiomatics" - doesn't make sense for me since axiomatics is a part of mathematics. So here I agree and would even say it is a rhetoric nonsense.

Mathematics is not synonymous with problem solving! The point (which should stay in the article) is that Bourbaki does not present or explain ideas through the solution of problems, as most mathematicians do. I think there are some grounds to dispute the claim that Bourbaki de-emphasizes problem-solving, but they rely on saying that the problems are implied and would occur naturally to the mathematically mature reader. And this claim is not clear-cut and is worth debating! 68.236.60.30 16:31, 7 December 2006 (UTC)

"combinatorial structure is deemed non-structural" - I agree this is a little ambiguous. However, I would understand it this way. The author believes that combinatorics is structural and in Bourbaki's view it is non-structural. In this sense, this not neutral. One could say just "combinatorics is deemed non-structural" but this has a meaning different from "combinatorial structure is considered less fundamental than other types of structure". I cannot make any reference to support my understanding, can you?

FWIW there's a Dieudonne quote that goes something like: "We haven't yet begun to understand the relationship between combinatorics and conceptual mathematics." (my emphasis) 2601:681:8002:9270:7413:8C0D:9A:FC2F (talk) 16:03, 31 July 2016 (UTC)

measure theory: "Coerced" is a really strange word here. Would "in measure theory Radon measures are preferred to the other topics" be better? Or did the author mean stronger "measure theory is restricted to Radon measures?"

geometry, history: I support your view here.

--Gogino 04:57, 25 August 2006 (UTC)

I would certainly defend most of this. I doubt you'll find much graph theory there, though Dynkin diagrams, yes. The comment about measure theory can surely be supported by opinions I have read that the measure space approach is the natural one, and Bourbaki really does distort the subject. I think the comment on the history rather misses the point of what is being said (which is that the Bourbaki Elements d'histoire is not so much unprofessional as with an agenda.

I wrote all of this, I believe, some years ago. Then people were less picky, and rather liked writing that was a bit more punchy than the current norm. I find it a bit sad that lame habits of expression have come in. Charles Matthews 18:51, 30 August 2006 (UTC)

Perhaps the only problem here is with certain wording? I think all the ideas in this section should stay, and if anything I think we should add a little more content about how Bourbaki isn't quite "neutral". 68.236.60.30 16:31, 7 December 2006 (UTC)

I'd have thought most of this is good to stay if it can be sourced as criticism by someone. Maybe we should try to dig up published critcisms of the Bourbaki programme. A Geek Tragedy 18:07, 19 December 2006 (UTC)

I have taken down the NPOV tag, since there are now nine detailed notes to the section. Charles Matthews 22:30, 19 December 2006 (UTC)

The citations are helpful, and the section has improved somewhat, but it still falls short of encyclopedia style. Note that merely adding citations does not turn opinion into fact; one still needs to state an opinion as an opinion. I have removed the last paragraph (on the historical notes), which consisted of blatant editorializing, and I have adjusted the language in places to make it sound more like an encyclopedia. I'm not saying that what was there before was misguided opinion or bad writing, only that its content and style were more appropriate for a book review, as I said before, than a reference source.

In sum, there are still issues with this article, and I will continue trying to address them. Komponisto 22:34, 23 March 2007 (UTC)

I think the tag might still belong. Consider "Overly enthusiastic defenders of Bourbaki will say that this is not in fact accurate... They are assuming that you will not actually take the time to get this book". What defenders are being referenced here? 99.251.204.24 (talk) 19:09, 14 September 2009 (UTC)

Biased footnotes

The footnotes are almost entirely attacks on Bourbaki. This seems to me grossly POV, and disrespectful to the genuises who developed a unified terminology for mathematics---a Herculean task. The main article still seems biased against Bourbaki, but it's definitely much better than the footnotes.  Kiefer.Wolfowitz  (Discussion) 18:19, 2 April 2011 (UTC)

The choice really is to whether to allow critics of Bourbaki (who certainly were many, whatever the situation is now - I get the impression that some sort of equilibrium has been restored) to be seen in verbatim quotes, or paraphrase. The approach of verbatim quotes in footnotes has advantages, but maybe not everyone likes it.

Now on particular points there can of course be rebuttals: if we can find quotes that state that Bourbaki's approach to measure theory is not only perfectly fine, but actually advantageous, then those can appear. I don't honestly know whether that can be done - it seems more likely that experts in the field might regard that as a side issue.

I really don't think the article as a whole is anti-Bourbaki. In any case we are hardly here to administer "respect", but to report neutrally on controversy when it exists. I would say it reports fairly, and in more detail than usual, on what the fuss was about. But then I'm quite close to it all. Charles Matthews (talk) 18:33, 2 April 2011 (UTC)

Which footnotes are you objecting to exactly? Tkuvho (talk) 18:36, 2 April 2011 (UTC)

Numbering of Éléments de mathématique

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, [1], 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)

Section on influence

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)

With no objections appearing since January, removed the offending paragraph. Stca74 (talk) 18:55, 16 May 2008 (UTC)

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)

The name

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)

The reference to a Parisian grill room makes me wonder if perhaps there might be some reference to General Bourbaki nearby to where they met. Maybe a statue or a painting or a road name? Is the location of the Parisian grill room known any more specifically than just somewhere in Paris? Is the name of the conference known and where it was being held? Is, or was, there a grill room nearby? — Preceding unsigned comment added by 86.135.44.230 (talk) 11:03, 15 December 2016 (UTC)

There are more details in the French version of the article, if anyone feels like translating. 2A04:B2C2:809:C100:857A:E9B9:9449:881B (talk) 19:48, 24 September 2018 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Nicolas Bourbaki/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

== Bourbaki X == What about chapter 10? Algebre Homologique? This seems to have been left out.

Last edited at 18:03, 23 March 2009 (UTC). Substituted at 01:13, 30 April 2016 (UTC)

Rewrite, late '19/early '20

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)

Partisan source tag removal

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)

Bourbaki and categories: not simply categories vs sets

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)