Timeline for Why did Bourbaki's Élements omit the theory of categories?
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25 events
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| Aug 15, 2019 at 23:24 | comment | added | Francois Ziegler | Yes, 26th page of Krömer. His thesis (2004, pages numbered 334–335, omitted from the translation) further records Weil’s presence at meetings 44 (March 1958) and 51 (June-July 1960) which was Grothendieck’s (and Weil’s?) last. This seems to clearly settle your above debate with quid. | |
| Aug 15, 2019 at 20:51 | history | edited | user44143 | CC BY-SA 4.0 |
added 147 characters in body
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| Aug 15, 2019 at 20:42 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Aug 15, 2019 at 19:36 | history | edited | Todd Trimble | CC BY-SA 4.0 |
added the references kindly supplied by Francois Ziegler
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| Aug 15, 2019 at 19:26 | comment | added | Todd Trimble | @FrancoisZiegler My command of French is not sufficient to read the text without some assistance, but it is very interesting and it does seem consonant with what I thought I understood from reading the essays by McLarty and Corry. And so I think I will make an edit to my answer, acknowledging your references. Just one note with regard to the commentary below my answer: it is noted that Weil was present at the 43rd meeting in 1957 (after he announced his retirement in 1956) in which they are discussing a possible Theory of Categories (for Bourbaki) -- see page 26 of 44 of the pdf. | |
| Aug 15, 2019 at 15:21 | comment | added | Todd Trimble | @FrancoisZiegler Thanks. I haven't looked into this reference, and thus I don't know whether it is consonant or not with the conclusions drawn by McLarty and Corry. If it is not, then I don't see how I would smoothly integrate it into my answer -- but I am happy meanwhile to upvote your comment for visibility's sake. | |
| Aug 15, 2019 at 2:51 | comment | added | Francois Ziegler | It would be worth mentioning (not just in this buried comment) that Krömer (2006; pdf) (subtitled Bourbaki and categories during the 1950s) thoroughly investigates the OP’s question using unpublished internal reports, correspondence and quotes of e.g. Eilenberg (p. 142), Cartier (p. 147), Grothendieck (p. 149), etc. | |
| May 28, 2013 at 14:22 | comment | added | Mikhail Katz | To elaborate on Leo Corry on Bourbaki's structures, my sense from reading Corry is that Bourbaki, and especially Weil, were albatrossed by their theory of "structures" which was hopelessly rooted in naive set theory, which created an obstacle for a rival foundational account given by category theory. | |
| May 26, 2013 at 0:22 | comment | added | user9072 | @Todd Trimble: since I just stumbled over it, in case you are interested, the letter of retirement of Weil (to Cartan with the request to read it at the next congress) is in the Cartan-Weil correspondence (June 26th, 1956). | |
| May 25, 2013 at 19:09 | comment | added | user9072 | @Colin McLarty: Thank you for the reply. Perhaps this is a good ending point for our discussion. (Also, I like the word 'acerbic', which I had not known before.) | |
| May 25, 2013 at 18:41 | comment | added | Colin McLarty | @quid Well, yes Weil was a huge influence on all of modern pure mathematics. But his most important contributions are very hard to grasp even today, and he is utterly underrated by people who only know his low level ideas as in Bourbaki. He was also a brilliant collaborator to people he respected. But I know myself that to call him acerbic is an understatement. He and Grothendieck eventually could not stand each other. | |
| May 25, 2013 at 17:37 | comment | added | user9072 | Let me also stress that this is really meant as a very personal and amateurish opinion of mine. Perhaps I am completely wrong. It is more meant as a justifcation of me reacting relatively sensitive here. | |
| May 25, 2013 at 17:29 | comment | added | user9072 | @Colin McLarty: Sorry, for the rhetorical question; I saw the reference and indeed calculated the timespan from it. I did not pay attention to my phrasing possibly suggesting the information was not present there. In some sense I would actually be interested to investigate certain things related to this in detail, but then I am a complete amateur as regards history and the question why at least in my opinion Weil is treated so relatively negatively at many places in contrast to Grothendieck might even be more sociology than history. Yet then maybe at some point in the distant future. | |
| May 25, 2013 at 17:03 | comment | added | Colin McLarty | @quid. You can research and write this history. As to when Grothendieck spoke of "Verflachung" you need no rhetorical question: I give the date with the quote, and I give a footnote saying where he got the term. In the Grothendieck Serre correspondence you must have noticed their complaints about Weil, and I will say I doubt that actually came from Serre though he goes along with it. Serre understood (and understands) Weil very well. I think it came from Grothendieck. I am sure you are right that Grothendieck was also pulled away by his own projects. | |
| May 25, 2013 at 15:49 | comment | added | user9072 | ...else knew better at that point in time. And this seems a bit implausible to me. In addition, but I might be over-sensitive here, to contributing to a in my opinion somewhat wide spread tendency of painting a generally negative picture of Weil. | |
| May 25, 2013 at 15:39 | comment | added | user9072 | ...Grothendieck somehow left/did not contribute much to Bourbaki (already relatively early) Weil does not seem to be the reason, but quite simply he (Gr.) simply was busy with his own projects and preferred to pursue them (instead). Or, also you quoting Gr. with Verflachung. But when did he say this? Three/four decades later. As said right at the start it might well be that then an (in retrospect) unfortunate diecision was made and even it might well be that Weil was responsible. But the presentation to me paints the picture of Weil somehow stubornly insisting on something while everbody... | |
| May 25, 2013 at 15:19 | comment | added | user9072 | ...and also it suggests there being a conflict. But in particular for Cartier and Grothendieck specifically with 1951 this hardly can be true. And, I am somewhat sensistive to this, since for example (digressing a bit) in this 'Bourbaki biography' by Aczel a picture is drawn that Grothendieck so to say left Bourbaki because of Weil and in general Weil is portrayed as some sort of villain of that story. Now, I have not carried out any actual historical studies relatred to this, but I read the Grothendieck-Serre correspondence and while there is mention of reasons why... | |
| May 25, 2013 at 15:08 | comment | added | user9072 | @Colin McLarty: what I meant to point out is that there is a so to say post-Weil period of Bourbaki that started in about the mid/end 50s. After that there would have been plenty of time to change things for others. And, now you mention 1951, and then let me get to another point I found surprising, the quote says: "Members Cartier, Chevalley, Eilenberg, and Grothendieck championed categories, as did their visitor Mac Lane. But Weil [...]" This juxtaposition give the impression that so to say everybody championed something except Weil and this happening at the same time and... | |
| May 25, 2013 at 14:01 | comment | added | Colin McLarty | @quid. Why is it hard to reconcile Weil being (far) the strongest voice in the group with him following his own rule on retirement? Of course we have much more from the Bourbaki archives now than when I wrote what I did. But it remains that Bourbaki wrote up a theory of structures following what Weil said in 1951 he got from Mac~Lane, while the theory did not actually do what Mac~Lane (or Cartan or Chevalley or Grothendieck) wanted. I am not clear what position Eilenberg took on it. | |
| May 24, 2013 at 21:10 | comment | added | user9072 | The above comment was written before I saw yours. I will leave it for practical reasons for the moment but study your source. Added after studying said source: it does not seem to contradict the claim Weil retired, which is also confirmed by a credible source (as already provided). The birthday detail is from elsewhere; I think I could refind it but this additional detail seems not very relevant anyway. I think I will stop now, at least for some time. But perhaps Godement will visit MO a second time and inform us first hand. This would be great. :-) | |
| May 24, 2013 at 20:47 | comment | added | user9072 | Weil was the first (while not oldest!) to apply them to himself by letting a letter announcing his retirement be read at the 50th birthday party of Dieudonné (born in 1906, like Weil). [See eg footnote 10 in article mentioned by Martin.] So, at least officially he definitely retired, which is what I claimed. (To what extent his influence continued in a non-official way is not known to me; in case I find time I might reread parts of his correpondence with Cartan for hints.) [There are some other details about the quote I find surprising but I do not want to appear argumentative.] | |
| May 24, 2013 at 20:15 | comment | added | Todd Trimble | @quid: regarding "mandatory requirement at age 50", see also the article by Aubin: math.jussieu.fr/~daubin/publis/1997.pdf. In particular, footnote 3 reads: "The historian Liliane Beaulieu, who has worked the most extensively on Bourbaki, told me that she had never come across any written trace of this rule and that in any case it was breached many times." (My emphasis) | |
| May 24, 2013 at 20:04 | comment | added | Todd Trimble | It is indeed a strong description; this and the fact that it is perhaps a critical point of the discussion were reasons I singled it out. I'm not sure to what extent the usual rules of Bourbaki (retirement at age 50 etc.) applied to Weil, who I take to be something of a spiritus rector for the collective. I hope Colin will weigh in at some point; I emailed him before putting together this answer. | |
| May 24, 2013 at 19:18 | comment | added | user9072 | While I'd agree there is something to Weil having some responsibility here, it is not quite clear to me how to reconcile this strong description in particular "But Weil was a majority of one in the group [...]" with what is generally said regarding the workings of the group (unanimity and alike) and more importantly the fact that Weil (officially) retired from Bourbaki in 1956. (Addded: To stress this point of timeline let me recall that then Grothendieck was aged 28 and Cartier aged 24 [roughly] so they'd had plenty of time.) | |
| May 24, 2013 at 15:52 | history | answered | Todd Trimble | CC BY-SA 3.0 |