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Yesterday I came across the following one-paragraph summary of the history of the Law of Quadratic Reciprocity in Roger Godement's Analyse mathématique, IV, p.313 (perhaps the only treatise on Analysis which contains a statement of the Law in question).

Legendre a deviné la formule et Gauss est devenu instatanément célèbre en la prouvant. En trouver des généralisations, par exemple aux anneaux d'entiers algébriques, ou d'autres démonstrations a constitué un sport national pour la dynastie allemande suscité par Gauss jusqu'à ce que le reste du monde, à commencer par le Japonais Takagi en 1920 et à continuer par Chevalley une dizaine d'années plus tard, découvre le sujet et, après 1945, le fasse exploser. Gouverné par un Haut Commissariat qui surveille rigoureusement l'alignement de ses Grandes Pyramides, c'est aujourd'hui l'un des domaines les plus respectés des Mathématiques.

(English translation: Legendre guessed the formula [the quadratic reciprocity law] and Gauss instantly became famous by proving it. Finding generalizations, for example to rings of algebraic integers, or other proofs was a "national sport" for the German dynasty sparked by Gauss until the rest of the world, starting with the Japanese Takagi in 1920 and then Chevalley about ten years later, discovered the subject and, after 1945, made it "explode". Governed by a High Commission that rigorously monitors the alignment of its Great Pyramids, today it is one of the most respected areas of Mathematics.)

Which Haut Commissariat is he referring to ? Or is it just a joke ?

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    $\begingroup$ I would guess it's a joke, although Godement certainly must have something in mind when he used these words; perhaps he was simply referring to Langlands' program. $\endgroup$
    – Franz Lemmermeyer
    Commented Sep 21, 2013 at 7:05
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    $\begingroup$ BTW there are quite a few textbooks on complex analysis that state and prove the quadratic reciprocity law, $\endgroup$
    – Franz Lemmermeyer
    Commented Sep 21, 2013 at 7:06
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    $\begingroup$ Yes, he's surely referring to the Langlands Programme, but it is somewhat funny to call it the Haut Commissariat of something or the other. Godement is a good friend of Langlands, by the way, and one of the three people who are gratefully mentioned in the acceptance speech when Langlands received the Grande Médaille d'Or of the Académie des sciences : publications.ias.edu/sites/default/files/discours-ps.pdf $\endgroup$
    – Chandan Singh Dalawat
    Commented Sep 21, 2013 at 7:57
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    $\begingroup$ Langlands writes "... je veux nommer trois mathématiciens qui se donnèrent la peine de persuader le jeune homme [the young Langlands], bien plus modeste que moi, qu’il valait quelque chose: Salomon Bochner, né je crois à Cracovie en Pologne, Harish-Chandra, né à Kanpur en Inde, tous les deux devenus mathématiciens américains, et Roger Godement, mathématicien français. Il me serait impossible d’exprimer en quelques phrases courtes combien lui, il leur devait, et combien moi, je leur dois toujours." $\endgroup$
    – Chandan Singh Dalawat
    Commented Sep 21, 2013 at 8:05
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    $\begingroup$ For those who might have missed it, Roger Godement has graced MathOverflow once (thanks to Anton for helping find the link) : mathoverflow.net/questions/91385/… $\endgroup$
    – Chandan Singh Dalawat
    Commented Sep 22, 2013 at 4:48

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I disagree with Michael Grünewald's interpretation, which by the way doesn't answer the initial question: who Godement is he referring too? I think this is a joke made without acrimony. "Thought police", "innovation preventing", are much too strong phrases to translate Godement's light ironical quotation.

To a french-spaking ear, "Haut Commissariat" in this context evokes the "Commissariat Général au Plan", created by the administration led by de Gaulle in 1946 (and including a large political spectrum, from right wing to communists). It was an institution without real power but which was supposed to prepare non-compulsory "plans" to develop the economy for the next five years, the idea being to take advantage of whatever was thought efficient in soviet-like planning while staying essentially a free-market economy. (Of course there are other institutions with that name, like UN's "haut-commissariat aux réfugiés", but really that the plan one that comes to mind).

So back to quadratic reciprocity, I may be completely wrong but I imagine that the Haut-Commissaire in question might be R.P. Langlands and his huge program that has provided a non-compulsory, but hugely influential, planning for the research in "higher class field theory" since more than 40 years.

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    $\begingroup$ I read after writing my answer the comments under the questions, to which I agree. Godement was very close to this "haut-commissariat", perhaps he even considered himself a member of it :-). After all he was Jacquet's advisor. There was a touching fear in the groups of mathematicians to which Godement belonged: the fear to become what they called a "mandarin", an installed mathematician detaining (and this detained by) a large power on the developments. Self-irony (or irony aimed at friends and students) was seen as a way to protect oneself against such an evolution. $\endgroup$
    – Joël
    Commented Sep 21, 2013 at 14:40
  • $\begingroup$ I think this is a joke made without acrimony. I also do! "Thought police", "innovation preventing", are much too strong phrases to translate Godement's light ironical quotation. You are definitely right, but irony is one of the hardest thing to deal with for non native speakers. This is why I choosed to rephrase the exceirpt without any subtlety. $\endgroup$
    – Michaël Le Barbier
    Commented Sep 21, 2013 at 16:10

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