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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

#51

Post by dnpp123 »

wbhart wrote: post #46
dnpp123 wrote: post #39

Earlier quoted context omitted.

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…

AFAIK the idea at that time was to try to apply the Bourbaky method to teach kids elementary maths - e.g. try to explain the concept of sets before kids know how to add 2 numbers (I'm caricaturing but not that much - you had to explain to kids Peano before addition..). Someone else might have a better answer for that as I'm too young to know. Wikipedia French page on 'New Math' mentions it but not in details.

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

Unless you are in a reaally elitist high school in Paris with a really old teacher, this should'nt happen nowadays.

Re: The Secret Math Society Known as Nicolas Bourbaki

#52

Post by Jugurtha »

vector_spaces wrote: post #15
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…

We need formalism, and we need motivation, examples, and pictures. One isn't better than the other. In particular, formalism isn't about hazing (though I think some people abuse it this way). Books that claim to appeal more to intuition or rely on visual arguments certainly help a lot with motivating ideas and establishing context, but at a certain point we need to be clear about what exactly we are talking about. Wh…

>When learning a new topic in math, I personally prefer to start with a more formal, terse text. For me, the texts that focus too much on examples and motivation tend to be chattier

Soviet books (MIR Publishers) are notoriously terse and to the point. This is what we used in college, and it has made it difficult for me to read a different style, because the content tries my patience.

For example, I couldn't consume Andrew Ng's Coursera ML course, but I appreciated the CS229 recorded at Stanford because he dove directly into the maths part. I didn't want to see slides, I needed to see problem statement, pause the video, work through gradient descent, play the video, and check I got it right. Side note: doing this [pause, working on it, play] has its advantages, it helped avoid a confusion the instructor had in the course with notation, for example, which you had to be sorted out in the later part of the course.

As you said, it is a spectrum of content with different styles for different needs and people, but even for the same person, one might need a style at a certain point and the other at another point. I remember in my third year I used some MIT OCW resources because I felt my brain was shot and I needed to be spoon fed on a topic I was so far behind on.

Re: The Secret Math Society Known as Nicolas Bourbaki

#53

Post by dnpp123 »

rq1 wrote: post #42
dnpp123 wrote: post #39

Earlier quoted context omitted.

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 ha…

Sure but what good is an education method if the teachers don't understand it. I don't doubt that if you had a great teacher that would work, but considering how focused French education is on mathematics, this was one of the main reason why the social ladder broke.

Re: The Secret Math Society Known as Nicolas Bourbaki

#54

Post by chewz »

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…

The anectodal example in my country is the old (pre-WW2) math problems book that was used then and after war at middle education level (lycee).

Later on the problems from the book could be solved only by university students (engineering etc.) and nowadays only by math students.

This is anecdotal of course and there are still lots of bright kids eager to learn math today.

Re: The Secret Math Society Known as Nicolas Bourbaki

#56

Post by Jraf »

dnpp123 wrote: post #51
wbhart wrote: post #46

Earlier quoted context omitted.

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…

AFAIK the idea at that time was to try to apply the Bourbaky method to teach kids elementary maths - e.g. try to explain the concept of sets before kids know how to add 2 numbers (I'm caricaturing but not that much - you had to explain to kids Peano before addition..). Someone else might have a better answer for that as I'm too young to know. Wikipedia French page on 'New Math' mentions it but not in details. > Is it…

French here : As far as i remember, I've learned set, intersect, include, etc when i was 11-12 years old, in 1985-1986. Seems to be 6th Grade.

Re: The Secret Math Society Known as Nicolas Bourbaki

#57

Post by ever1 »

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.

It is well known that France never had impactful scientists...

Re: The Secret Math Society Known as Nicolas Bourbaki

#59

Post by amai »

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…

"By the way, in the 1960s I taught group theory to Moscow schoolchildren. Avoiding all the axiomatics and staying as close as possible to physics, in half a year I got to the Abel theorem on the unsolvability of a general equation of degree five in radicals (having on the way taught the pupils complex numbers, Riemann surfaces, fundamental groups and monodromy groups of algebraic functions). This course was later published by one of the audience, V. Alekseev, as the book The Abel theorem in problems." (Arnold - On teaching mathematics)

A english translation of this book is available here

https://staff.math.su.se/shapiro/Articles/AbelNew.pdf

Re: The Secret Math Society Known as Nicolas Bourbaki

#60

Post by rq1 »

dnpp123 wrote: post #53
rq1 wrote: post #42

Earlier quoted context omitted.

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 ha…

Sure but what good is an education method if the teachers don't understand it. I don't doubt that if you had a great teacher that would work, but considering how focused French education is on mathematics, this was one of the main reason why the social ladder broke.

I understand, but on the same period, France grew a whole generation of brilliant mathematicians. I don't think that the two are completely unrelated.

There is basically two solutions: reduce the quality of the material, or teach the teachers. I tend to prefer the second.

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