Nicolas Bourbaki

https://en.wikipedia.org/wiki/Nicolas_Bourbaki

by SMAAART • 2 years ago

64 49 2 years ago

en.wikipedia.org

FabHK• 2 years ago

Bourbaki's textbooks are notoriously formal, rigorous, and plain difficult.

This gave rise to a cute inside joke in the Sokal hoax [0], where physicist Alan Sokal aimed to demonstrate the lack of intellectual rigour in contemporary post-modern cultural studies and produced a nonsensical "paper" (Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity) [1] that was promptly published in Social Text, an academic journal of cultural studies.

At any rate, in that article, there's a footnote (to the hilarious statement that "More recently, Lacan's topologie du sujet has been applied fruitfully to cinema criticism.") that reads:

For a gentle introduction to set theory, see Bourbaki (1970).

Any competent peer reviewer reading the paper carefully would have fallen of the chair laughing.

[0] https://en.wikipedia.org/wiki/Sokal_affair

[1] https://physics.nyu.edu/faculty/sokal/transgress_v2/transgre...

eigenket3• 2 years ago

Its worth mentioning that the journal originally refused to publish the Sokal paper, and eventually put it in a special non-peer reviewed issue they were making called "Science Wars". The aim of the Science wars issue was to have as many different points of view represented as possible.

I find it amusing, given the context of the discussion, that people often fail to point this out.

nicolas_t• 2 years ago

Thanks! I never knew that aspect of the Sokal story. Not surprised it's not repeated since it makes the story less entrancing.

pi-e-sigma6• 2 years ago

Lame cop out. The article was a complete nonsense. It wasnt something like an unortodox view of things or passable article that missed some citations or whatnot. It would be like Nature publishing ramblings of some schizofrenic and when called out on it explaining that it wasnt peer reviewed

hermitcrab• 2 years ago

"lack of intellectual rigour in contemporary post-modern cultural studies"

Is putting it rather kindly.

Koshkin• 2 years ago

It’s formal in places and certainly rigorous, but I don’t find it difficult.

arawde• 2 years ago

Only a bit related, but I recently learned that André Weil's sister Simone was a noted philosopher and fought in the Spanish Civil War

https://en.wikipedia.org/wiki/Simone_Weil

timeforcomputer4• 2 years ago

At a second-hand bookstore I bought a biography of Simone Weil and have overheard some conversations about her work, and it looks like her work is very popular. I said I was interested in the biography because of her brother Andre the famous number theorist, and they didn't know she had a brother. Different worlds combined :)

da-bacon• 2 years ago

"The Weil Conjectures" by Karen Olsson is an interesting read that connects Andre and Simone and the authors own experiences as a math major. I thought it did a good job capture the appeal of math, but it's definitely not about the conjectures or their proof.

aunetx• 2 years ago

I would say that in France, Simone Weil really is more known than André Weil! And I suggest anyone to read La Condition Ouvrière (I don't know the title in English), which is not only very instructive and moving, but also specially beautiful in my opinion.

ykonstant2• 2 years ago

her work is very popular

She was a great thinker and writer; I highly recommend her works.

yau8edq12i5• 2 years ago

Not to be confused with Simone Veil https://en.wikipedia.org/wiki/Simone_Veil (who also had an eventful life, to say the least).

adamtaylor_13• 2 years ago

You mean Nico and the Niners?

All jesting aside, I still haven’t put together the reference to Nicolas Bourbaki in twentyone pilots’ “Nico and the Niners”. Just a clever history pun or something?

tmabraham• 2 years ago

Nicolas Bourbaki is the name of a character in twenty one pilots' concept album

"He'll always try to stop me, that Nicolas Bourbaki He's got no friends close, but those who know him most know He goes by Nico"

It is indeed inspired by the actual pseudonym, not just a pun.

stoolpigeon• 2 years ago

The Bourbaki dangerous bend symbol is also a part of the lore and symbology for the band. I think that the use of the name is a 'clue' to the meaning of the symbol. The recent new release is the first time I think they've stated this explicitly.

simplyinfinity• 2 years ago

Google twenty one pilots lore explained. There's few hours worth of videos on the topic :)

kirubakaran• 2 years ago

We had our own for a while: https://news.ycombinator.com/threads?id=nickb

That user was extremely prolific and, at that time was believed to be a group of people blessed by pg.

gommm• 2 years ago

That brings back memories... I always wondered where they disappeared to.

defrost• 2 years ago

aka Satoshi Nakamoto V1.0

seanhunter5• 2 years ago

They have an official twitter account apparently[1] which canonically is run by the daughter of Nicolas.

[1] https://twitter.com/i/flow/login?redirect_after_login=%2Fbet...

AceJohnny2• 2 years ago

which canonically is run by the daughter of Nicolas

Is there a joke I'm missing?

seanhunter5• 2 years ago

Nicholas Bourbaki is not a person. The Bourbaki group are a collective who work together (at a glacial pace) and publish under the pseudonym "Nicholas Bourbaki" when everyone in the group agrees that the work is done. They have lots of "in jokes" not least of which is the name Nicolas Bourbaki itself. Another of these in jokes that Nicolas has a daughter called Betty. They apparently published a wedding notice for her at some point also.

yau8edq12i5• 2 years ago

They've moved to ma(th)stodon after the twitter clusterfuck: https://mathstodon.xyz/@nbourbaki

timeforcomputer4• 2 years ago

As a counterpoint, my favourite mathematician: https://en.wikipedia.org/wiki/Vladimir_Arnold

yau8edq12i5• 2 years ago

How is this a "counterpoint"?

timeforcomputer4• 2 years ago

Arnold is very influential especially in "Russian math" pedagogy/philosophy, which could be contrasted a bit with "French math" where Bourbaki was very influential. I think anyone interested enough to read the Bourbaki article might be interested in reading about him since his wikipedia page has a few references pointing to interesting discussions about Bourbaki's influence. I should have mentioned a little details in the original comment, sorry!

seanhunter5• 2 years ago

As I understand it, the Bourbaki school was basically obsessed with the idea of making maths rigorous to the point where their published work is extremely difficult to understand and you basically already have to know the subject to read the stuff. Other people, Arnold in particular, felt that it was important to learning to gain a more intuitive understanding even if that meant sacrificing some rigour along the way, and that once you got there you could go back and sort of fill in the blanks.

That's why that wiki page says

   Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education, and then later on that of other countries as well.

So a pastiche of the Bourbaki type criticism of Arnold's works would be that they are elegant but skip over some of the foundational steps that are necessary to be fully rigourous and the equivalent critique of Bourbaki is that their stuff is dry, tedious and impossible to understand which just puts people off the subject entirely rather than teaching them.

seanhunter5• 2 years ago

For all that Bourbaki has been highly influential (and equally contentious) in maths, I don't actually know anyone who owns a copy of "Éléments". Is that just because I'm not French and it's actually huge among French mathematicians or perhaps because I'm just not "there" yet in my study of maths, having not got on to analysis in particular?

Obviously some ex-members of the group (Grothendieck and Serge Lang in particular) have published books that are more widely read.

Galanwe• 2 years ago

I guess there is a trend to consider, in which algebra and statistics tend to be picked and studied more in the last decade compared to e.g. analysis. Thus why we don't see all that many people studying advanced analysis books.

I would also argue that each country / culture teaches mathematics in a different way, which may not suit well with an outsider. From my experience US/UK tend to emphasize intuition first and rigor later, while French mainly focus on rigorous reasoning and proofs, leaving intuition as a by-product of experience that will be eventually picked up by the student on his own. That may discourage non-French students to further read such books.

yau8edq12i5• 2 years ago

Given that you're talking about your "study of maths", I presume that you're a student. Well, Bourbaki books aren't textbooks. They're reference books. They're great when you need a theorem and you know you can just pickup your copy of "Lie algebras" and find it exactly where you expect it to be. And you know the proof will be there, and you know the proof of every single lemma used will be there. But it's not a learning tool. Think more about a dictionary/encyclopedia than a school book. You wouldn't learn to speak English by reading an English dictionary.

ykonstant2• 2 years ago

Well, Bourbaki books aren't textbooks. They're reference books.

The Bourbaki group has repeatedly emphasized that point and explained their goal and rationale with the Elements; and yet, people still blame them for all sorts of developments in post-graduate mathematics education. I find it rather unbecoming.

seanhunter5• 2 years ago

Sounds awesome. It's worth saying that the Serge Lang textbooks I have are awesome for learning maths from. I really love them - they don't treat me like an idiot and they have lots of problems to practise on - from basic to pretty hard, so I'm not negative about the group as a whole. I was genuinely curious.

ajbt200128• 2 years ago

I actually own most of elements, in the original French and first edition! Found them on a used bookstore warehouse outside of DC for $5 each. They sell on eBay pretty regularly for >$100 (you have to search the French title). I don't speak French but it's cool to have them as a collectors item

toyg• 2 years ago

A group of Italian intellectuals recently used a similar approach, first going by "Luther Blissett" (who was an actual footballer) in the '90s, then "Wu Ming" (Chinese for "anonymous", initially suggested to be a legendary general like Sun Tzu), and later "Nicoletta Bourbaki". The three different collectives share some but not all participants, and focus on slightly different topics - or rather a different degree of focus, with Blissett being the most generic and Bourbaki the most specific (concerning herself only with fighting historic revisionism of WW2 in Italy).

histories• 2 years ago

I wholeheartedly recommend Luther Blissett's first novel, "Q"

https://en.wikipedia.org/wiki/Q_(novel)

Nicolas Bourbaki

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