# Tag: bourbaki

Next year I’ll be teaching a master course on the “History of Mathematics” for the first time, so I’m brainstorming a bit on how to approach such a course and I would really appreciate your input.

Rather than giving a chronological historic account of some period, I’d like this course to be practice oriented and focus on questions such as

• what are relevant questions for historians of mathematics to ask?
• having answers, how do they communicate their finds to the general public?

To make this as concrete as possible I think it is best to concentrate on a specific period which is interesting both from a mathematical as well as an historic perspective. Such as the 1930’s with the decline of the Noether boys (pictures below) and the emergence of the Bourbaki group, illustrating the shift in mathematical influence from Germany to France.

(btw. the picture above is taken from a talk by Peter Roquette on Emmy Noether, available here)

There is plenty of excellent material available online, for students to explore in search for answers to their pet project-questions :

There’s a wealth of riddles left to solve about this period, ranging from the genuine over the anecdotic to the speculative. For example

• Many of the first generation Bourbakis spend some time studying in Germany in the late 20ties early 30ties. To what extend did these experiences influence the creation and working of the Bourbaki group?
• Now really, did Witt discover the Leech lattice or not?
• What if fascism would not have broken up the Noether group, would this have led to a proof of the Riemann hypothesis by the Noether-Bourbakis (Witt, Teichmuller, Chevalley, Weil) in the early 40ties?

I hope students will come up with other interesting questions, do some excellent detective work and report on their results (for example in a blogpost or a YouTube clip).

In Belgium the hashtag-craze of the moment is #cestjoelle. Joelle Milquet is perceived to be the dark force behind everything, from the crisis in Greece, over DSK, to your mother-in-law coming over this weekend? #cestjoelle.

Sam Leith used the same meme in his book the coincidence engine.

A hurricane assembling a passenger jet out of old bean-cans? #cestGrothendieck

All shops in Alabama out of Chicken & Broccoli Rica-A-Roni? #cestGrothendieck

Frogs raining down on Atlanta? #cestGrothendieck

As this is a work of fiction, Alexandre Grothendieck‘s name is only mentioned in the ‘author’s note’:

“It is customary to announce on this page that all resemblances to characters living or dead are entirely coincidental. It seems only courteous to acknowledge, though, that in preparing the character of Nicolas Banacharski I was inspired by the true-life story of the eminent mathematician Alexandre Grothendieck.”

The name ‘Nicolas Banacharski’ is, of course, chosen on purpose (the old Bourbaki NB-joke even makes an appearance). The character ‘Isla Holderness’ is, of course, Leila Schneps, the ‘Banacharski ring’ is, of course, the Grothendieck circle. But, I’d love to know the name of the IRL-‘Fred Nieman’, who’s described as ‘an operative for the military’.

Sam Leith surely knows all the Grothendieck-trivia which shouldn’t come as a surprise because he wrote in 2004 a piece for the Spectator on the ‘what is a metre?’ incident (see also this n-category cafe post).

The story of ‘the coincidence engine’ is that Grothendieck did a double (or was it triple) bluff when he dropped out of academia in protest of military money accepted by the IHES. He went into hiding only to work for a weapons company and to develop a ‘coincidence bomb’. As more and more unlikely events happen during a car-ride by a young Cambridge postdoc though the US (to propose to his American girlfriend), the true Grothendieck-aficianado (and there are still plenty of them in certain circles) will no doubt begin to believe that the old genius succeeded (once again) and that Ana’s (Grothendieck’s mother) $\infty$-ring is this devilish (pun intended) device…

However,

“There was no coincidence engine. Not in this world. It existed only in Banacharski’s imagination and in the imaginations he touched. But there was a world in which it worked, and this world was no further than a metre from our own. Its effect spilled across, like light through a lampshade.

And with that light there spilled, unappeased and peregrine, fragments of any number of versions of an old mathematician who had become his own ghost. Banacharski was neither quite alive nor quite dead, if you want the truth of it. He was a displaced person again, and nowhere was his home.”

If you’ve downloaded recently the little booklet containing the collection of my posts on the Bourbaki code, either in pdf- or epub-format, cherish it. I have taken all Bourbaki-code posts offline (that is, changed their visibility from ‘Public’ to ‘Private’). Here’s why.

Though all speculations and the few ‘discoveries’ in these posts are entirely my own work, I did benefit tremendously from background-information on the pre-war Bourbakis provided by experts in the field via email.

The great divide between myself and these historians is that to me the Bourbaki-story is merely a game and a pleasant time-waster, whereas to them it is the lifeblood of their research, and hence of their professional existence.

I value this interaction too much to jeopardize it by trowing potential useful tidbits of info in the public arena too quickly, before they are thoroughly researched or discarded.

I will continue the Bourbaki-code investigation offline, and, perhaps this will lead one day to something publishable. Here, we will switch back to mathematics, most of you will be relieved to hear.

As a matter of (open-access) principle, if you want to have your own copy of the Bourbaki-code booklet, please email me and specify the format (pdf or epub).

There were some great comments by Peter before this post was taken offline. So, here they are, once again.

In an interview with readers of the Guardian, December 3rd 2010, Julian Assange made a somewhat surprising comparison between WikiLeaks and Bourbaki, sorry, The Bourbaki (sic) :

“I originally tried hard for the organisation to have no face, because I wanted egos to play no part in our activities. This followed the tradition of the French anonymous pure mathematians, who wrote under the collective allonym, “The Bourbaki”. However this quickly led to tremendous distracting curiosity about who and random individuals claiming to represent us. In the end, someone must be responsible to the public and only a leadership that is willing to be publicly courageous can genuinely suggest that sources take risks for the greater good. In that process, I have become the lightening rod. I get undue attacks on every aspect of my life, but then I also get undue credit as some kind of balancing force.”

Analogies are never perfect, but perhaps Assange should have taken it a bit further and studied the history of the pre-war Bourbakistas in order to avoid problems that led to the eventual split-up.

Clearly, if Bourbaki=WikiLeaks, then Assange plays the role of Andre Weil. Both of them charismatic leaders, convincing the group around them that for the job at hand to succeed, it is best to work as a collective so that individual contributions cannot be traced.

At first this works well. Both groups make progress and gain importance, also to the outside world. But then, internal problems surface, questioning the commitment of ‘the leader’ to the original project.

In the case of the Bourbakis, Claude Chevalley and Rene de Possel dropped that bombshell at the second Chancay-meeting in 1937 with a 2 page pamphlet 7 theses de Chancay.

“Criticism on the state of affairs :

• in general, a certain aging of Bourbaki, which manifests itself in a tendency to neglect internal lively opposition in favor of pursuing visible external succes ((failed) completion of versions, artificial agreement among members of the group).
• in particular, often the working method appears to be that of suffocating any objections in official meetings (via interruptions, not listening, etc. etc.). This tendency didn’t exist at the Besse meeting, began to manifest itself at the Escorial-meeting and got even worse here at Chancay. Bourbaki-members don’t pay attention to discussions and the principle of unanimous decision-making is replaced in reality by majority rule.”

Sounds familiar? Perhaps stretching the analogy a bit one might say that Claude Chevalley’s and Rene de Possel’s role within Bourbaki is similar to that of respectively Birgitta Jónsdóttir and Daniel Domscheit-Berg within WikiLeaks.

This criticism will be neglected and at the following Bourbaki-meeting in Dieulefit (neither Chevalley nor de Possel were present) hardly any work gets done, largely due to the fact that Andre Weil is more concerned about his personal safety and escapes during the meeting for a couple of days to Switserland, fearing an imminent invasion.

After the Dieulefit-meeting, even though Bourbaki’s fame is spreading, work on the manuscripts is halted because all members are reserve-officers in the French army and have to prepare for war.

Except for Andre Weil, who’s touring the world with a clear “Bourbaki, c’est moi!” message, handing out Bourbaki name-cards or invitations to Betti Bourbaki’s wedding… That Andre and Eveline Weil are traveling as Mr. and Mrs. Bourbaki is perhaps best illustrated by the thank-you note, left on their journey through Finland.

If it were not for the fact that the other members had more pressing matters to deal with, Weil’s attitude would have resulted in more people dropping out of the group, or continuing the work under another name, a bit like what happens to WikiLeaks and OpenLeaks today.