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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

#61

Post by rramadass »

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?

Assuming you are asking in general and not specifically Bourbaki authored;

* Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, Lavrentev

* The Princeton Companion to Mathematics by Timothy Gowers et al.

* The Princeton Companion to Applied Mathematics by Higham et al.

Re: The Secret Math Society Known as Nicolas Bourbaki

#62

Post by joycian »

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.

If only they could be read by robots! Their formulation is actually quite unwieldy and wasteful:

https://johncarlosbaez.wordpress.com/2020/04/13/bigness-part...

Re: The Secret Math Society Known as Nicolas Bourbaki

#63

Post by hurrynot »

dnpp123 wrote: post #41
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.

I think the group writing the HoTT book (https://en.wikipedia.org/wiki/Homotopy_type_theory ) probably come close, though.

Re: The Secret Math Society Known as Nicolas Bourbaki

#64

Post by andi999 »

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…

Somehow from the link it seems Arnold didnt manage to make his point in the Arnold Serra debate, and audience thought he is ranting. i find this quite disappointing, since I think he really has a point.

Re: The Secret Math Society Known as Nicolas Bourbaki

#65

Post by dnpp123 »

rq1 wrote: post #60
dnpp123 wrote: post #53

Earlier quoted context omitted.

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.

> 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.

If you could prove me that there were more brilliant mathematicians educated in France during the 60's/70's compared to other periods, I'd be interested.

Even if this is the case (which I'm not sure), at least it's pretty clear it lowered the median (whether this is good or not is another debate ;)

Re: The Secret Math Society Known as Nicolas Bourbaki

#66

Post by wbhart »

Jraf wrote: post #56
dnpp123 wrote: post #51

Earlier quoted context omitted.

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.

Everybody learns that at school, French or not (I certainly did in Australia). The set theory referred to here is very abstract.

Re: The Secret Math Society Known as Nicolas Bourbaki

#67

Post by pfortuny »

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.

Well that is certainly a way to put it.

I have learned from both Bourbaki and Stewart and to each his own. I enjoyed Bourbaki’s Topology a lot, and their Real Analysis is quite good.

Re: The Secret Math Society Known as Nicolas Bourbaki

#68

Post by radomir_cernoch »

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…

I'm Czech and this revolutionary method of teaching came here in the 90's, when I entered my grammar school. Probably, it had a political “east vs. west” motivation among others, shortly after the velvet revolution...

The first thing I learned in the 1st year of schools were basic concepts of set theory. We were drawing circles, ellipses and Venn diagrams (even though we didn't call them like that) filled with images of apples, plums and cherries. Teachers explained to us what an intersection, union and set differences are and we were supposed to draw items into one set, but not in another set, etc.

I recall these exercises as funny and playful. They were similar to IQ tests in the sense that the exercise is logical, slightly entertaining, but highly abstract and loosely related to the world you know.

And I think this was the main issue. The 2nd topic we learned was simple arithmetics as in standard educational systems. However, at that time, I didn't see any relationship with the concepts of set theory.

Was the system any good? Hard to say. AFAIK, it was dropped after a few years. Eventually, I obtained a PhD in computer science, so at least, the system wasn't a complete disaster for me. :-)

Re: The Secret Math Society Known as Nicolas Bourbaki

#69

Post by Syzygies »

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…

I hiked with Arnold once, in New Hampshire. He at one point described walking far enough out onto a frozen lake to watch the ice crack around him, to see if the pattern matched his intuition. He was very hands-on.

Re: The Secret Math Society Known as Nicolas Bourbaki

#70

Post by stoolpigeon »

The band Twenty One Pilots references Bourbaki as an integral part of their most recent album, "Trench". They created some pretty intricate puzzles for their fans leading up to the release of the album and it was fun to watch all these (mostly) young people work it out and learn more about math history at the same time.
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