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    This answer was given to the question

    21 December 2013, 9:09pm UTC

    Second Edit : the message below is about the first version of the question, before it was deeply edited and changed by Todd Trimble. I have nothing serious to complain about the new question.

    Okay, let me weigh in by saying that this question is a disgrace for this site.

    I have nothing against question about mathematical education, and nothing against question whose answers are primarily opinion-based. But I have a strong hostility against opinion-based question that shows such a contempt for the facts, especially when the asker is "leading a campaign" (quoting his own words) for some cause, however legitimate, and seems more interested into advancing his cause than in searching for the truth. (Why? Probably it's my personal history, coming/fleeing from a country where the basic distinction between fact and opinion is even more forgotten tham elsewhere, but whatever).

    So the question of whether Euclidean geometry should be taught or not in Elementary/Middle/High school or their equivalent is legitimate. But as for a pure question of math, one should not rush to answer before the fact expressed in the set-up of the question are recognized as correct.

    The facts in question are the affirmation that there were, I quote, << a series of articles in France in the 1960s, authored by the Bourbaki's, preaching the abolition of Euclidean Geometry (EG), as the main mathematical area in high schools of France. Some of the titles of these articles were: "A bas Euclide", "Euclid is dead", "Euclidean Geometry must go" etc. >>

    Despite my asking for precisions or references, none was given. Now such an affirmation should be substantiated. While I am certainly ignorant of many things in the history of Bourbaki, what I know makes the OP's assertion highly unlikely. For one thing, Bourbaki as a group was never concerned with high school teaching. As for individual members (since I guess they are what the OP calls "the Bourbaki's"), the ones I can think of couldn't care less about high school program. And perhaps I didn't drink enough today, but even with the best will I can't imagine someone like Cartan, or Serre, or Koszul, signing an opinion in say "Le Monde" with title "A bas Euclide!".

    I am voting to close (again), obviously, until the facts are substantiated or retracted.

    edited after some comments by the OP. The OP has given some references, but they are just about one talk given by Jean Dieudonné, when he was not anymore a member a Bourbaki. Now there have been perhaps 100 Bourbaki members over the years, and it is probable that any opinion $o$ on any subject has been at some point of time held by one of them. This is of course not enough to conclude that "Bourbaki has made a campaign in favor of $o$" Examples: "Bourbaki has made a campaign against the financing of IHES by the ministry of defense". No, Grothendieck did.

    [Comments to follow]

  2. – smyrlis yesterday

    Joel: Good answer. -- I wondered as well why this question has been received well on MO, rather than being closed quickly. -- Voted to close as "primarily opinion-based". – Stefan Kohl yesterday

    @smyrlis I am sorry but that won't do it. I need a list of papers by Bourbaki's members, not a side remark (which is again completely unsubstantiated) in a paper about something completely different (Euclid in the XVII-century) by someone unrelated to Bourbaki. – Joël yesterday

    À bas Euclide ! Mort aux triangles ! — Jean Dieudonné, keynote address at the Royaumont Seminar (1959). – smyrlis yesterday… – smyrlis yesterday

    Encore raté! "Dieudonné was then over 50 and no longer a member of Bourbaki". – Joël yesterday

    Yes, the question would be much better if the first par would be removed; it only makes the question more provoking, but it is provoking anyway. On the other hand it is clear that smyrlis wants to know and why not to help. – Anton Petrunin yesterday

    "'s my personal history, coming/fleeing from a country..." - if you had another name, I would think that you came from Russia. :) This is indeed not good, but essentially nothing would change if the autours of these scoldings against Euclid would turn out to be others. In Russia the talks on "getting rid of proofs" in mathematical education are very serious since the fall of the iron curtain. – Sergei Akbarov

    @Sergei and Anton. You're right, I guess I have been too rude. But I don't like to see Bourbaki used as a scapegoat for everything's that went wrong in mathematics. And Dieudonné, especially after he retired, is definitely not interchangeable with Bourbaki. – Joël 23 hours ago

    Cher Joël, I think the accurate quotation from Tintin's adventure L'Oreille Cassée is: "Caramba, encore raté!" – Georges Elencwajg 23 hours ago

    @StefanKohl it was closed quickly but got reopened. Also, it has a huge number of views for such a young question. There ought to have been a lot of viewers (and possibly voters, up not open) that are not actually on MO. Though this might not account for everything. (Maybe due to this cross-site advertising, where MO is 'out' but only in the IMO essentially irrelevant direction, ie we do not get ads but still are advertised, AFAIK; or some other 'promotion' somewhere. (Sorry this should be likely on meta, but I am sort of tired at the moment so just a comment.) – quid 22 hours ago

    Georges, you're right. I had hesitated putting the whole quotation :-) – Joël 22 hours ago

    +1000. I'm pretty shocked that this question is still here. – Andy Putman 21 hours ago

    Joel, is it not true that Bourbaki, as a group, was hostile to any kind of geometric arguments, especially, those based on diagrams? Whether this was due to the influence of Dieudonne and other founding members, I cannot tell, but careful examination of the Elements of Mathematics supports this claim. Moreover, there was a backlash against this approach, let us call it "anti-geometric", for the lack of a better term, among other French mathematicians. See, in particular, the preface to Seminar Artur Besse 1978-79, which makes a clear reference to Bourbaki. – Victor Protsak 17 hours ago

    I am afraid, however, that Joël's response is not an answer to the question. It's more of a commentary on the suitability of this question, hence it properly belongs on meta. – Todd Trimble♦ 17 hours ago

    Victor, I am not sure what you're asking. Bourbaki was arguably not very favorable to soft arguments, like some that can be used in differential geometry, but we are talking about Euclidean geometry, which is the absolute contrary of soft, as the first domain of mathematics that was reduces to a formal system of axioms. Besides, this is beyond the point: I hope there is no debate on the fact that Euclidean Geometry, as far as current research is concerned, had been long died at the time Bourbaki was arguing. As Bourbaki was only interested in research, not teaching, I don't see how it... – Joël 17 hours ago


    can possibly disagree with anyone on the status of Euclidean Geometry in research. Now on the question of Euclidean Geometry as a pedagogical tool for high school student, which is the question here, I am pretty sure (until I receive evidence on the contrary, of which I have not seen an ounce) that Bourbaki expressed no opinion. About the different question of the importance of Euclid's work in the history of mathematics, Bourbaki was very clear: why do you think they called their treatise "elements" ? – Joël 17 hours ago

    Todd, I respectfully dissent. I am discussing the assertions on which the question is built up. If a question says "it is well known that all rings are noetherian, but how to prove that they are all principal?", would it belong to meta to point out that no, all rings are not noetherian? – Joël 17 hours ago

    Joël: okay. At this point I am interested in taking a more constructive approach to this troubled question, and so taking your comments into consideration, I have tried to reword the question. Please let me know if you still have objections to what is there now (please ping me directly if you respond). – Todd Trimble♦ 16 hours ago

    @Todd: I find it much better now. It's still not a good question in my opinion but you have remover what was plainly false and truly offensive in its preamble. (PS: I am not sure what you mean by "ping me") – Joël 15 hours ago

    Thanks. "Ping" = notify, which you did. – Todd Trimble♦ 14 hours ago

    Hi Joël, I also think that this answer does not belong here but to meta, and its wording is too offensive even for meta. (The AIDS example does not add anything to the argument and I deleted it.) I encourage deleting this answer from here, and moving it meta while using less offensive language. – Gil Kalai 4 hours ago

    @Gil, you are too strict, imo. I doubt that it is possible to completely remove emotions from topics like this. – Sergei Akbarov 3 hours ago

    Hi Gil, while I always respect your opinion, I will not follow our advice here. I have already explained to Todd why this answer belonged here and not to meta, and for the offensive language, I think I was actually too mild with a falsifier of history. – Joël 2 hours ago

    Joël, I bet your ancestors were Russians. :) So much expression on such an occation... – Sergei Akbarov 2 hours ago

    @GilKalai I think the example adds something. It shows that one should not take the opinion of mathematicians even great ones too seriously on subjects where they have no actual expertise, such as mathematics education perhaps. ;-) [This is not meant as 'attack' against you but a general remark; even more so as you did not even say anything on the question itself.] – quid 1 hour ago

    I completely agree with that general remark, quid. Specifically, on math education I also completely agree. (Regarding the AIDS example, I did not see how it adds anything useful here. and I dont remember a single case, whether I agreed or disagreed with you that I regarded a general comment by you as an attack against me.) – Gil Kalai 49 mins ago

    Thanks, Joël; Had I thought that people will follow my suggestions rather than just taking them into account, I would have stopped making any suggestions :) . – Gil Kalai 46 mins ago

    @Joël In view of your recent edit (where you say you have no major complaints), it seems your answer was both useful in terms of suggesting improvements to the question, and at the same time obsolete - now that the question has been edited. In the spirit of having answers stay strictly on topic, I plan on copying your answer and the comments below to, to have them on public record, and then clean up this thread and bring the noise level down, by whittling this answer down to a pointer to tea. – Todd Trimble♦ 38 mins ago


    Answer by 'seub' ( Is Euclid dead?, URL (version: 2013-12-20):

    Just a small "historical" note, altough I'm really no expert: I don't think Bourbaki as a group advocated to "kill Euclid" in French high school and lower education, although some of its members did get involved in the "maths modernes" ("new maths") reform. This reform was heavily criticized (including by Bourbaki members such as Laurent Schwartz) and quickly turned out to be a failure to a large extent. Euclid was back with a vengeance in high schools soon after and is still very present to this day in French primary, middle and high schools.

    [Comments to follow]

    They DID (the Bourbaki) advocate abolition of EG in high schools. Their moto was: "A bas Euclide" - See – smyrlis yesterday

    Your link shows nothing of the sort. And "À bas Euclide" was not Bourbaki's motto, it's a famous quote of one his members at one point, Dieudonné, there's a difference. Bourbaki was not interested in education, "he" was interested in mathematics (and history of mathematics). Some of its members, at some point, supported the "maths modernes". I'm just making the point that it's a bit simplistic and inaccurate to say that Bourbaki, as an entity, supported the "maths modernes" and "anti-Euclid" maths education. – seub yesterday

    This answer refers to an earlier formulation of the question. I am moving it to tea, for the public record. – Todd Trimble♦ 7 mins ago

    For those of you looking for context about the "AIDS example" mentioned in the comments, Gil Kalai edited the end of Joël's answer, deleting two examples of opinions $o$ held by members of Bourbaki that could not be reasonably viewed as campaigns by Bourbaki in favor of $o$.

    Deleted text follows:

    "Bourbaki has made a campaign for calling the conjecture that every elliptic curve over ℚ was modular "Taniyama-Weil"". No, Serre has defended such an opinion. "Bourbaki has made a campaign to defend the claim that the AIDS virus was artificial". No an ex-member of Bourbaki expressed, at least once, this opinion.