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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

#41

Post by dnpp123 »

pattusk wrote: post #2

I wish more science, and generally more work was done this way. Dispense with ego-flattering prizes, narratives of discovery that put lone geniuses in the spotlight, turning PIs heroes and dictators at the expense of their team... I understand this is not practical for all fields, but it would alleviate much of the pettiness and unethical behaviors that have become so normalized in academia.

You have to put back the creation of the group in context though.

Back then philosophers/mathematicians were kinda popular (think Sartre, Beauvoir and so on) so making such a group draw a lot of more public attention than it would now.

Sadly, I doubt that such a group could be created now.

Re: The Secret Math Society Known as Nicolas Bourbaki

#42

Post by rq1 »

dnpp123 wrote: post #39
wbhart wrote: post #35

Earlier quoted context omitted.

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.

I had discussion about it with Cedric Villani once and he told me that was not a disaster because of the books or the material, but the teachers were not good enough.

Eg. when teaching set theory, teachers were debating what should be a perfect representation of a set (is it an ellipse or circle... etc.?) Children were completely lost because of this.

If you don’t draw a perfect ellipse to represent a set then you had a bad mark and so on and so forth.

Re: The Secret Math Society Known as Nicolas Bourbaki

#43

Post by totony »

This made me think; is there a collection of books or a volume that treats mathematic extensively from base to advanced?

Right now everything is divided in specialized books with little to no connection from one to the other. Is there a feynman equivalent for maths?

Re: The Secret Math Society Known as Nicolas Bourbaki

#44

Post by ojnabieoot »

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.

I’ve always viewed Bourbaki as something like the CRC Handbook for pure mathematics: an exceptional reference and a necessary collation of wide-ranging ideas and information, but dry by design, and a poor way for self-learners to understand any new topics.

I also think it’s going a little far to say “remove the beauty” - but it is true that if you don’t already have an appreciation for the specific subject, that beauty is awfully hard to find.

Re: The Secret Math Society Known as Nicolas Bourbaki

#45

Post by reikonomusha »

totony wrote: post #43

This made me think; is there a collection of books or a volume that treats mathematic extensively from base to advanced? Right now everything is divided in specialized books with little to no connection from one to the other. Is there a feynman equivalent for maths?

The books do have strong connections to one another. They usually list the prerequisites.

Math isn’t just one linear subject. The foundations have tons of branches, and the abstract stuff has lots of branches.

Re: The Secret Math Society Known as Nicolas Bourbaki

#46

Post by wbhart »

dnpp123 wrote: post #39
wbhart wrote: post #35

Earlier quoted context omitted.

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.

But how did Bourbaki influence elementary/middle school mathematics? Bourbaki mathematics is basically at the level of graduate school. Except in countries where a graduate degree is required to teach mathematics, I can't imagine how there would even be a connection between the two worlds. Is that the case in France?

Again, I'm not disputing what you are saying either, merely trying to understand what happened.

Is it still going on in French schools today? Or was it 60's/70's only?

Re: The Secret Math Society Known as Nicolas Bourbaki

#47

Post by andi999 »

BlueTemplar wrote: post #40
andi999 wrote: post #13

Earlier quoted context omitted.

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 ?

Could be. Although high school (at least where I am) only teaches a tiny drop of mathematics (so the other style is also difficult.). But generally the is an adaptation problem/challenge in the first two semesters of math students where usually only solving a lot of problem and getting them corrected helps.

But dont worry, these things can be overcome (do not fight them at your current stage if you are still a student). Just dont believe the 'hours needed' in the description of the modules (they are politically decided). Generously work around the clock for the first few years.....

edit: more seriously: although working hard is important: go to the office hours of your TA and/or prof and discuss the work you are doing. Usually no student does that and you will learn a lot.

Re: The Secret Math Society Known as Nicolas Bourbaki

#49

Post by bdauvergne »

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.

« Chauvinisme » ? :)

Re: The Secret Math Society Known as Nicolas Bourbaki

#50

Post by chewz »

dnpp123 wrote: post #39
wbhart wrote: post #35

Earlier quoted context omitted.

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.

In most countries the schoolbooks had been changed to teaching about sets and stuff in the first grade. Generally more abstract or top-down approach. Old school approach was more bottom-up.

In my country I have been still learning from old schoobooks while classes below had new schoolbooks - thats why I remember that well.

Recently I have been helping 11 year old with classes (remote learning now). And my impression is that this top-down approach is still present but the schoolbook was full of practical life examples (money issues, understanding newspaper articles with pecentages and percent points etc.)

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