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In his famous address at the Royaumont Seminar in 1959, Jean Dieudonné famously called for the elimination of Euclidean geometry from the secondary school curriculum. In the published (English-language) version of his remarks ("New Thinking in School Mathematics", 1959), Dieudonné expressed this call with the slogan "Euclid must go!", and most subsequent references to this speech quote him with that.

But a different (and stronger) version of this slogan is quoted in Siobhan Roberts's book King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry. In that book (p. 157) Dieudonné is quoted as saying (in French) "A bas Euclide! Mort aux triangles!" ("Down with Euclid! Death to triangles!"). Roberts cites three sources for this quote -- but two of them are to books that include the other version ("Euclid must go!"), and the third seems to be to an unpublished interview the author conducted with Imre Toth.

So my question:

We know what Dieudonné wrote in the published version of his Royaumont address, but (apparently) Imre Toth remembers him saying something different. Does anybody know if there is any other published source, other than Roberts, that can shed light on what Dieudonné actually said at Royaumont?

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    $\begingroup$ Dieudonne expressed these ideas many times, with various wording. In the most comprehensive way in his preface to the book: Algèbre linéaire et géométrie élémentaire. Enseignement des Sciences, VIII Hermann, Paris 1964 223 pp. $\endgroup$
    – Alexandre Eremenko
    Commented Jul 23, 2015 at 6:02
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    $\begingroup$ See also Castelnuovo science.unitn.it/~fontanar/EMMA/educational_studies_1977.pdf $\endgroup$
    – user2255
    Commented Jul 23, 2015 at 17:12
  • $\begingroup$ @FranzLemmermeyer thank you for the Castelnuovo piece. Apparently it quotes Dieudonné's Royaumont address with yet a third variation: "A bas les triangles! A bas Euclide!" I wonder if there is any way to pin down what he actually said (and in particular if 'Mort aux triangles!' is reliable). $\endgroup$
    – mweiss
    Commented Jul 23, 2015 at 18:03
  • $\begingroup$ @AlexandreEremenko Thank you for the reference. I will check out that preface next chance I get to the library. But just to clarify the question, I am actually not interested in a comprehensive discussion of Dieudonné's position, but in the slogan / rallying cry that he used to encapsulate it. "Down with Euclid! Death to triangles!" is a lot more dramatic than "Euclid must go!", but I am not sure if that is what he really said. $\endgroup$
    – mweiss
    Commented Jul 23, 2015 at 18:05
  • $\begingroup$ Make sure to add the correct quotation to en.wikiquote.org/wiki/Jean_Dieudonn%C3%A9 :) $\endgroup$
    – Nemo
    Commented Oct 17, 2015 at 19:27

2 Answers 2

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I hope a version in French may shed some light on this question. In Le Séminaire de Royaumont 1959-1979, here is apparently a verbatim of the words of Jean Dieudonné. The previous link http://www.ssrdm.ch/mathecole/wa_files/Mathecole_90.pdf is not available anymore. However, here is anotehr source: Calame, A. (1979). L’enseignement de la géométrie, Math-école, 90 Le séminaire de Royaumont 1959-1979. Novembre 1979, 11-16. Here is Math-école, volume 90, Le Séminaire de Royaumont 1959-1979 in pdf, the full quote is on page 6. Part of it is mentioned in « À bas Euclide ! » Mathématique Moderne au Séminaire OECE de Royaumont:

C'est à Royaumont que Jean Dieudonné lança son cri de guerre « À bas Euclide ! » et qu'il y définit, avec la collaboration de conférenciers et de délégués issus de 16 Pays européens, des Etats-Unis et du Canada, les contours d'un nouveau curriculum pour les mathématiques

and quoted in Le sujet et l'objet, confrontations: Jean Dieudonné on Euclid

Jean Dideudonné was apparently in favor of the teaching of 2D and 3D vector spaces, instead of mere geometry:

Je pense que le temps de ce "ravaudage" est dépassé et que nous devons maintenant envisager une réforme beaucoup plus profonde, à moins que nous n'acceptions de laisser la situation empirer au point d'entraver sérieusement tout progrès scientifique ultérieur. Si je voulais résumer en une phrase tout le programme que j'ai dans l'esprit, ce serait par le ·slogan: "A bas Euclide". Cette affirmation paraîtra peut-être choquante à certains d'entre vous; je voudrais vous exposer en détail les puissants arguments qui militent en sa faveur. Permettez-moi de dire d'abord que j'ai la plus profonde admiration pour les· résultat obtenus par les Grecs en mathématiques. Je considère que leur création de la géométrie a peut-être été dans le domaine intellectuel le progrès le plus extraordinaire que l'humanité ait jamais réalisé. C'est grâce aux Grecs que l'imposant édifice de la science moderne a pu être bâti. Mais, au cours de cette évolution même, on a repris à la base, surtout depuis le milieu du XIXe siècle, les notions fondamentales de la géométrie: on a pu ainsi réorganiser la géométrie euclidienne, lui redonner des fondements simples et solides et réévaluer son importance par rapport aux mathématiques modernes, en séparant ce qui est essentiel d'un amas chaotique de résultats qui ne sont que les reliques éparses de méthodes maladroites ou de points de vues désuets.

So, more a mere "Down with Euclid", no mention of triangles so far.

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The book

Hersh, Reuben; John-Steiner, Vera Loving + hating mathematics. Challenging the myths of mathematical life. Princeton University Press, Princeton, NJ, 2011

on page 185 reports that in november 1959 at Centre Culturel de Royaumont, Dieudonne rose to his feet with the cry: "A bas Euclide! Mort aux triangles!"

There is an MO thread dedicated to this.

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  • $\begingroup$ Given that the Hersh & John-Steiner book, which came out in 2011, provides no source for the quote but uses the same version of it as Roberts's book, which came out in 2006, I'm inclined to suspect that the later book just got it from the earlier one. The original post in the MO thread also quotes Robert's book. $\endgroup$
    – mweiss
    Commented Aug 17, 2016 at 0:02
  • $\begingroup$ What I suspect happened is that d. in his oral presentation used the inflammatory terms like "death to triangles" and this was later widely reported by eyewitnesses but the written version of the speech was doctored and/or toned down. It would be interesting to find eyewitness accounts as to what d. actually said at the meeting but admittedly it is a bit late in the game to do so. I wasn't there :-) $\endgroup$
    – Mikhail Katz
    Commented Aug 17, 2016 at 6:59
  • $\begingroup$ Yes, that's my suspicion too -- but I would love to have some kind of independent confirmation of that. It's also possible that the reverse happened - that eyewitnesses have, in recalling the speech, made the proclamation more emphatic, because it makes for a better story. $\endgroup$
    – mweiss
    Commented Aug 17, 2016 at 16:23
  • $\begingroup$ m, try to ask some older colleagues! $\endgroup$
    – Mikhail Katz
    Commented Aug 18, 2016 at 7:03

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