I always thought it was an homage to Nicolas Bourbaki by pg and his friends who were using that account as a sock puppet. It was disputed https://news.ycombinator.com/item?id=21825207 I guess we'll never know.
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.
I feel like Bourbaki set back teaching mathematics a great deal, by focusing too much on the abstraction rather than the concepts and intuition behind it.
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).
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.
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.
The group was a "Camerata"!
There was a great talk at Rubyconf 2019 by Jessica Kerr about groups like this all over history who move their respective fields forward much faster than their contemporaries. She draws parallels to John Von Neumann's group, Van Gogh and friends, and more.
She talks about how the groups work together for a time doing great things, and then, and perhaps more importantly, the members of the group go on to do amazing things on their own or even start "invisible colleges" of their own.
Fun fact about Nicolas Bourbaki in pop culture. A popular band, Twenty One Pilots, adopted the character of Nicolas Bourbaki in their concept album Trench. It's interesting since they commonly use the symbol Ø in their branding, which was introduced in mathematics by Nicolas Bourbaki to denote an empty set.
The pseudonym originated by combining the initials of the mathematicians' given names (Bill, Leonard, Arthur, and Cedric) to form BLAC. This was extended to BLAnChe. The surname Descartes was chosen as a play on the common phrase carte blanche.
What motivates a research mathematician to publish their work under a collective pseudonym? I can't imagine that something like that is good for one's career.
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.
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.
The name was recently referenced by a satellite of another pseudonymous group, Wu-Ming (previously "Luther Blissett"). Under the name "Nicoletta Bourbaki" * , they published a number of very detailed analysis of historic revisionism and disinformation efforts, focusing particularly on material peddled by right-wing activists from the Italian North-East border.
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.
I'm inclined to regard talk of judgement of who is a "great mathematician", who is the "greatest mathematician" and so on as mathematical criticism. And I'm inclined to regard mathematical critics in the same way G. H. Hardy did, as he explained in A Mathematician's Apology [1].
To put the matter more bluntly: if the pilots of Top Gun were in the business of criticism, there wouldn't be any left because they'd blow each other to bits.
I think mathematicians and other high achievers should rather consider their relation to the Mary Sue and their domain of expertise as a LARP. Nobody likes a Mary Sue, nobody likes a Spock. And everyone should remember what rock music has to say about the fortunate sons who can aspire to the Mary Sue, Fortunate Son by Creedence Clearwater Revival.
I always thought it was an homage to Nicolas Bourbaki by pg and his friends who were using that account as a sock puppet. It was disputed https://news.ycombinator.com/item?id=21825207 I guess we'll never know.