Nicolas Bourbaki: The greatest mathematician who never was (2019)

I wonder if there can be a public version of this by sharing passwords openly but in a twisted way.

1. Create an account.

2. To know the password, you visit a service that gives you the password.

3. The service changes the password immediately in 10 seconds before which you login.

4. You can now post stuff with the account but can't change the password allowing another user to chime in.

Now the service basically needs to not allow another user to login in 10 seconds. If the website doesn't allow multiple users to login then there needs to be an etiquette of one user at a time, although you can kick off the user after a definite amount of time if the website allows logout from all sessions.

It is a necessary "pendulum". I doubt that if Bourbaki hadn't existed, then the likes of Arnold would have not produced their beautiful (and useful) advice on mathematical pedagogy.

Teaching mathematics is a huge and important part of the mathematical endeavour, but that's not all that there is to it, and I don't think that's what Bourbaki was trying to do [0]. No one should learn, at least not initially, from a Bourbaki book—a sentiment with which I expect even his, uhm, constituents would agree [0]—but I suspect most professional mathematicians find the Bourbaki œuvre useful as a reference, both for facts they know that aren't otherwise written down, and for facts that are on the borders of their expertise and require only a spot check to confirm or dispute. Certainly I use it that way.

[0] EDIT: I am wrong about this historical fact, although I believe it doesn't change my point about modern usage. Wikipedia says: > While teaching at the University of Strasbourg, Henri Cartan complained to his colleague André Weil of the inadequacy of available course material, which prompted Weil to propose a meeting with others in Paris to collectively write a modern analysis textbook. (https://en.wikipedia.org/wiki/Nicolas_Bourbaki).

Exactly right! Great article!

People forget that generalization/abstraction is the end goal and should never be the first step. Unless and until you are sufficiently intellectually mature you should never start with general principles. Always start with a concrete example, motivate the arguments and slowly build/use the tools of Mathematics to work towards a solution. This is how Humans have learnt and developed for millennia but with the explosion of knowledge in the 19th/20th century we seem to have forgotten it and taken a completely wrong turn in the teaching of Mathematics. The result is that we have a lot of educated people (see in mirror :-) without any proper understanding.

Bourbaki makes terrible introductory textbooks, but are great references when you are already motivated and just want an efficient presentation.

For french readers the french version in the Gazette of the Société Mathématique de France. http://math.unice.fr/~rchetrit/smf_gazette_78_19-29.pdf

I came for the TOP reference and I was not disappointed.

Fun, collective work and love of mathematics’ for mathematics’ sake?

The group also got its start in the 1930s, the current “publish or perish” mindset was decades away. And new subfields were still getting discovered left and right so there was no lack of material anyway.

I don't think that anything published under Bourbaki's name is considered research work, though.

It was done for the advancement of mathematics, not something so trifling as an individual's career. Explaining this makes me feel incredibly old.

Most if not all of them were university teachers in France and former students of ENS (so they already were civil servants before their career even started). Their careers weren't really at stake.

Most of the members had very impressive career anyway. Obviously there are no Fields medalist amongst the founders - they were already too old but I think something like five of the later members got it (Schwartz, Serre, Grothendieck, Connes and Yoccoz). There are probably more if we could count the current members.

More info on this kind of thing in the cultural field: https://en.wikipedia.org/wiki/Luther_Blissett_(nom_de_plume)

It's not the same set of members, there has been many generations of Bourbaki.

They're pretty far from dead, they just published a textbook in 2016 on Algebraic Topology.

Satoshi isn't the greatest mathematician who never was. Satoshi is the greatest ancap who never was.

It's either that, or he's Nick Szabo.

'et al' may be the most published author. But ibidem gets way more citations.

> I mean, by conflating multiple people's work as one (by whatever criteria, in this case a common pseudonym), comparison becomes meaningless.

Meaningless in a strict sense. But good enough as a hook for an article.

Compare also https://en.wikipedia.org/wiki/Jakob_Maria_Mierscheid

Are you, by any chance, reading the subtitle as “The greatest mathematician, who never lived” (i.e. Bourbaki was the greatest mathematician, and he never lived) rather than as (what's written) “The greatest mathematician who never lived” (i.e. among the mathematicians who never lived, Bourbaki was the greatest)?

The latter is a common snowclone especially in headlines, like (from https://www.google.com/search?q=%22the+*+*+you+haven%27t+hea...) “The Most Important Filmmaker You Haven't Heard Of”, “The Coolest Apps You Haven't Heard Of”, “Meet Vulfpeck, the best band you haven't heard of yet” — e.g. the last one doesn't mean that Vulfpeck is the best band, just that among bands you (probably) haven't heard of, it's (according to the author) the best.

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