13 ms·

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 mathemat

by lsh123 6y ago

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.

drallison 6y ago
I used Bourbaki as a second text in an advanced math course I took when I was at UC Berkeley in the early 1960's. I remember with delight the spare clarity of the presentation of the material and organic, intuitive organization of the topic. French has always seemed to me to be the language of mathematics, reason, logic (and love).
- tasogare 6y ago
  > 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 was kinda shielded from it. In Japan for instance, where the higher education is modeled upon the US one, master students are expected to publish at least a conference paper. In France students generally don’t publish anything. 2) the PhD thesis are written differently. Where I’m studying it’s basically slapping three papers together with an introduction and a conclusion. This sometimes leads to awkward thesis and shallow work. Thesis (and HDR) written in Europe are more like a very well structured monograph. 3) the way to use the language is different as well. In French, any intellectual written work will use long and complex sentences (sometimes to a fault) that are cramming few ideas and their relationships. In English the style is to write short sentences, with at most one idea each. I sometimes feel I have to dumb down my writing and splitting sentences while in my native language a Proust-like sentence would be more appropriate.
  - frank2 6y ago
    And yet the most impactful scientists, Newton and Darwin, spoke English, and the main way France industrialized was to copy developments in England.
    - Kbelicius 6y ago
      Ah, yes. Newton and Darwin the greatest products of modern Anglo-Saxon education.
    - deleted 6y ago
      [deleted]
    - andi999 6y ago
      Maybe Newton spoke English, but didnt he publish in Latin?
    - bdauvergne 6y ago
      « Chauvinisme » ? :)
    - ever1 6y ago
      It is well known that France never had impactful scientists...
    - throwaway_pdp09 6y ago
      Ramanujan was a brit. So was Leibnitz. Ditto archimedes. Gauss lived in brixton his whole life. All true.
  - kortilla 6y ago
    > 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.
    - tasogare 6y ago
chewz 6y ago
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 west coast of Africa in geology. > The emotional significance of such discoveries for teaching is difficult to overestimate. It is they who teach us to search and find such wonderful phenomena of harmony of the Universe. > The de-geometrisation of mathematical education and the divorce from physics sever these ties. For example, not only students but also modern algebro-geometers on the whole do not know about the Jacobi fact mentioned here: an elliptic integral of first kind expresses the time of motion along an elliptic phase curve in the corresponding Hamiltonian system. Arnold - On teaching mathematics - V.I. Arnold, On teaching mathematics – https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html The Arnold – Serre debate - MathOverflow – https://mathoverflow.net/questions/153604/the-arnold-serre-debate https://mathoverflow.net/questions/153604/the-arnold-serre-d... Vladimir Arnold - Wikipedia – https://en.m.wikipedia.org/wiki/Vladimir_Arnold https://en.m.wikipedia.org/wiki/Vladimir_Arnold
- wbhart 6y ago
  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.
  - dnpp123 6y ago
    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.
joppy 6y ago
The Bourbaki volumes are fantastic references for experts, and as with most reference books they are a terrible from an introductory/teaching perspective.
cedex12 6y ago
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.
ojnabieoot 6y ago
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.
joycian 6y ago
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-1/ https://johncarlosbaez.wordpress.com/2020/04/13/bigness-part...
pfortuny 6y ago
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.
nineparts 6y ago
I thought that beauty is in the eye of the beholder and doesn't need to be forced down the throats of uncircumcised peasants.
okprod 6y ago
I would posit one can probably understand math without seeing "the beauty of it".

by lsh123 6y ago

drallison 6y ago

I used Bourbaki as a second text in an advanced math course I took when I was at UC Berkeley in the early 1960's. I remember with delight the spare clarity of the presentation of the material and organic, intuitive organization of the topic. French has always seemed to me to be the language of mathematics, reason, logic (and love).

tasogare 6y ago
> 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 was kinda shielded from it. In Japan for instance, where the higher education is modeled upon the US one, master students are expected to publish at least a conference paper. In France students generally don’t publish anything. 2) the PhD thesis are written differently. Where I’m studying it’s basically slapping three papers together with an introduction and a conclusion. This sometimes leads to awkward thesis and shallow work. Thesis (and HDR) written in Europe are more like a very well structured monograph. 3) the way to use the language is different as well. In French, any intellectual written work will use long and complex sentences (sometimes to a fault) that are cramming few ideas and their relationships. In English the style is to write short sentences, with at most one idea each. I sometimes feel I have to dumb down my writing and splitting sentences while in my native language a Proust-like sentence would be more appropriate.
- frank2 6y ago
  And yet the most impactful scientists, Newton and Darwin, spoke English, and the main way France industrialized was to copy developments in England.
  - Kbelicius 6y ago
    Ah, yes. Newton and Darwin the greatest products of modern Anglo-Saxon education.
  - deleted 6y ago
    [deleted]
  - andi999 6y ago
    Maybe Newton spoke English, but didnt he publish in Latin?
  - bdauvergne 6y ago
    « Chauvinisme » ? :)
  - ever1 6y ago
    It is well known that France never had impactful scientists...
  - throwaway_pdp09 6y ago
    Ramanujan was a brit. So was Leibnitz. Ditto archimedes. Gauss lived in brixton his whole life. All true.
- kortilla 6y ago
  > 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.
  - tasogare 6y ago

chewz 6y ago

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 west coast of Africa in geology. > The emotional significance of such discoveries for teaching is difficult to overestimate. It is they who teach us to search and find such wonderful phenomena of harmony of the Universe. > The de-geometrisation of mathematical education and the divorce from physics sever these ties. For example, not only students but also modern algebro-geometers on the whole do not know about the Jacobi fact mentioned here: an elliptic integral of first kind expresses the time of motion along an elliptic phase curve in the corresponding Hamiltonian system. Arnold - On teaching mathematics - V.I. Arnold, On teaching mathematics – https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html The Arnold – Serre debate - MathOverflow – https://mathoverflow.net/questions/153604/the-arnold-serre-debate https://mathoverflow.net/questions/153604/the-arnold-serre-d... Vladimir Arnold - Wikipedia – https://en.m.wikipedia.org/wiki/Vladimir_Arnold https://en.m.wikipedia.org/wiki/Vladimir_Arnold

wbhart 6y ago
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.
- dnpp123 6y ago
  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.

joppy 6y ago

The Bourbaki volumes are fantastic references for experts, and as with most reference books they are a terrible from an introductory/teaching perspective.

cedex12 6y ago

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.

ojnabieoot 6y ago

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.

joycian 6y ago

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-1/ https://johncarlosbaez.wordpress.com/2020/04/13/bigness-part...

pfortuny 6y ago

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.

nineparts 6y ago

I thought that beauty is in the eye of the beholder and doesn't need to be forced down the throats of uncircumcised peasants.

okprod 6y ago

I would posit one can probably understand math without seeing "the beauty of it".