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The Secret Math Society Known as Nicolas Bourbaki

quantamagazine.org

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Re: The Secret Math Society Known as Nicolas Bourbaki

#31

Post by andi999 »

andi999 wrote: post #13
jacobolus wrote: post #10

Earlier quoted context omitted.

I am no expert but it is not my impression that adopting a group pseudonym eliminated politics or pettiness from the behavior of people inside or outside. But maybe makes the politics a bit less public/transparent? One criticism I have heard from professional mathematicians is that Bourbaki wasted a whole generation of French talent, pulling the best young mathematicians away from their own useful and interesting res…

This is really a good question. On the one hand the work of bourbaki was important, the foundation of math was shaky (I heard there were proof of some theorems and the negative of the same theorem). But then it somehow seems to destroy the spirit of mathematics. Arnold wrote about it: https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html#:... .

To add: I dont know what the solution to this is. So lets say there are two types of approaching math. Approach one is formal/rigid (caring about Axiom of Choice, Set theoretical foundations ..:-)) the other one still (partially) rigorous but more classical in spirit. A big question for me is, how is actually research done? Is it more the first or more the second approach? So what are possible solutions? I dont know. If you are trained in the first approach, you usually loose the ability to gloss over the gaps in the second approach. If you are trained in the second you cannot (or very difficult) come around the first one.

And then there is physics which uses the sloppy (and often not correct) version of the second approach. I once asked Serge Lang about this (phrasing:'what about physicist getting the right result with wrong mathematics' (thinking about renormalization)). Lang replied:'this is God's way of calculation'.

Re: The Secret Math Society Known as Nicolas Bourbaki

#32

Post by andi999 »

frank2 wrote: post #22
tasogare wrote: post #21

Earlier quoted context omitted.

> French has always seemed to me to be the language of mathematics, reason, logic For some reason I often find papers and thesis I read in French way more interesting, well thought and presented than most things I read in English. I have a few hypotheses on why I get this impression: 1) the publish or perish culture originated from the Anglo-Saxon world. Until recently the research written in the national language wa…

And yet the most impactful scientists, Newton and Darwin, spoke English, and the main way France industrialized was to copy developments in England.

Maybe Newton spoke English, but didnt he publish in Latin?

Re: The Secret Math Society Known as Nicolas Bourbaki

#33

Post by cedex12 »

lsh123 wrote: post #14

I have to admit that I did read a couple Bourbaki books. Or should I say “tried to read” because their texts are unreadable to put it mildly. They kill mathematics by removing the beauty of it and instead provide dry and boring texts that could be read by robots. Please don’t try to understand mathematics by reading Bourbaki texts. This is not what mathematics is about.

Personal experience: I came to like mathematics by way of computer science: so first got an understanding and appreciation for discrete maths, logic, etc, and only later on analysis and “phyisics” related mathematics. It's hard to say exactly why, but I'd wager it's the following: discrete maths is easy to formalize and axiomatize for first year student, so you quickly get a grasp of the “rules of the game”: what axioms you're allowed to use, how an argument works, etc. On the contrary, when you learn first year analysis, you see all those theorems talking about this (intuitively very simple but) quite complex object – the reals – of which you don't know the axioms (say linearly ordered field something something). Thus, when you learn about the basics results, you're faced with a kind of two-faced problem: on the one hand, all the basic results are intuitively obvious, while on the other, you have no idea how to build a proof because you don't know what facts you can safely use.

I don't really know how to phrase all that, but discarding the CS/axiomatic side of maths while praising the intuitive physics-inspired one is not the right approach imo.

Re: The Secret Math Society Known as Nicolas Bourbaki

#35

Post by wbhart »

chewz wrote: post #25
lsh123 wrote: post #14

I have to admit that I did read a couple Bourbaki books. Or should I say “tried to read” because their texts are unreadable to put it mildly. They kill mathematics by removing the beauty of it and instead provide dry and boring texts that could be read by robots. Please don’t try to understand mathematics by reading Bourbaki texts. This is not what mathematics is about.

Unfortunately Bourbakism polluted teaching of Mathematics in Europe c.a. 1960s. With visible effects. Except for Eastern Europe were it was opposed by Arnold. > These discoveries of connections between heterogeneous mathematical objects can be compared with the discovery of the connection between electricity and magnetism in physics or with the discovery of the similarity between the east coast of America and the wes…

That's interesting. I'd seen Arnold's work on teaching mathematics, and I'm very much aware of the dry formalism in Bourbaki books. However, I was not aware of the Arnold-Serre debate.

But the thing that really caught my eye here is your claim that there were visible effects of Bourbakism polluting mathematics.

Do you have any examples or specifics of that "visible effect". My question is a genuine one, not a challenge to what you are saying.

Re: The Secret Math Society Known as Nicolas Bourbaki

#37

Post by tasogare »

kortilla wrote: post #26
tasogare wrote: post #21

Earlier quoted context omitted.

> French has always seemed to me to be the language of mathematics, reason, logic For some reason I often find papers and thesis I read in French way more interesting, well thought and presented than most things I read in English. I have a few hypotheses on why I get this impression: 1) the publish or perish culture originated from the Anglo-Saxon world. Until recently the research written in the national language wa…

> For some reason I often find papers and thesis I read in French way more interesting, well thought and presented than most things I read in English. The much simpler explanation is that there are way more English as a foreign language PhD students than there are French as a foreign language PhD students.

I’m note sure why you bring foreign-speakers doing their PhD in French (the one who does have outstanding language abilities btw), I’m speaking about research output in general. The few thesis I looked from my immediate research entourage are quite weak compared to the few I’ve read from my home country. There is definitely something different in the writing and the expectations between Europe and the New World. To be clear, I don’t think it’s a language issue per se, but a result of the difference in requirements to graduate. For research papers, quality went down because of the rat course.

Re: The Secret Math Society Known as Nicolas Bourbaki

#39

Post by dnpp123 »

wbhart wrote: post #35
chewz wrote: post #25

Earlier quoted context omitted.

Unfortunately Bourbakism polluted teaching of Mathematics in Europe c.a. 1960s. With visible effects. Except for Eastern Europe were it was opposed by Arnold. > These discoveries of connections between heterogeneous mathematical objects can be compared with the discovery of the connection between electricity and magnetism in physics or with the discovery of the similarity between the east coast of America and the wes…

That's interesting. I'd seen Arnold's work on teaching mathematics, and I'm very much aware of the dry formalism in Bourbaki books. However, I was not aware of the Arnold-Serre debate. But the thing that really caught my eye here is your claim that there were visible effects of Bourbakism polluting mathematics. Do you have any examples or specifics of that "visible effect". My question is a genuine one, not a challen…

If you speak/read French, try to have a look at elementary/middle school math books from the 60's/70's in France. It was a disaster and forced a lot of kids to imagine they were bad at maths.

Re: The Secret Math Society Known as Nicolas Bourbaki

#40

Post by BlueTemplar »

andi999 wrote: post #13
jacobolus wrote: post #10

Earlier quoted context omitted.

I am no expert but it is not my impression that adopting a group pseudonym eliminated politics or pettiness from the behavior of people inside or outside. But maybe makes the politics a bit less public/transparent? One criticism I have heard from professional mathematicians is that Bourbaki wasted a whole generation of French talent, pulling the best young mathematicians away from their own useful and interesting res…

This is really a good question. On the one hand the work of bourbaki was important, the foundation of math was shaky (I heard there were proof of some theorems and the negative of the same theorem). But then it somehow seems to destroy the spirit of mathematics. Arnold wrote about it: https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html#:... .

Oh wow. So it looks like that the reason why I suddenly got 'bad' at math towards the end of high school might be due to the switch to this hyper-formal way of teaching mathematics, instead of using a more geometric/physic way ?
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