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Has anyone else read Bourbaki?

  1. Feb 25, 2005 #1
    I've started reading Bourbaki and I'm finding myself blown away. It seems to be like reading Linux source code, dry but extremely powerful and clear. I'm seriously thinking about reading the whole series from Theory of Sets to Commutative Algebra over the next year or two.

    Anyone else ever do this, or am I just a wierdo?
  2. jcsd
  3. Feb 25, 2005 #2

    matt grime

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    It was fashionable about 20-40 years ago to think the Bourbaki school was best, but the modern view of *teaching* mathematics is that it is better to prove it for the case "2" then to show it for the case "2=n".
    Personally, I've never been very interested, explicitly, in the Bourbaki School, but it is hard to judge the implicit effect of it in my work. Often, unless one understands a particular case very well, and what it is about that particular case that allows one to make the deductions one does, and unless you have a good intuition as to what can be omitted from the hypothesis, then Bourbaki isn't very useful. If, however, you have a sound grasp of the fact all that mattered was, say, the operation was binary, rather than associative, then thinking a la Bourbaki can help you translate results into other areas.

    I would rather teach particular cases first but very quickly and extract to the general, rather than prove a general theorem. It is only by studying the particular that we understand the general, perhaps is the anti-bourbaki line of reasoning and one that is necessary after a certain level.
  4. Feb 25, 2005 #3
    isn't bourbaki's stuff better as a reference(s)? i'm sure there are better books for learning stuff from
  5. Feb 25, 2005 #4


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    i did not learn from bourbaki, but i like it very much. it is so clear and precise, and absolutely on the point. but i also agree with matt that i like examples too.

    so there is this argument that one may not learn best from something that is too perfectly written. still, it is impressive and enjoyable.

    i have known some very good mathematicians who seem to have well thumbed copies of bourbaki.

    i don't think you can go wrong by reading bourbaki. in fact some of my friends are members of bourbaki. i would not set a goal of reading all of it. just read it as long as you enjoy it.

    i have a complete set of the commutative algebra.
  6. Feb 25, 2005 #5
    I think it's a shame that people only use Bourbaki as a reference and not as a backbone to their math studies. The way Bourbaki puts math together as a unified subject is something that so far I think everyone should see. This can be seen in the current "problem" in math. Everyone is now moaning about mathematicians getting too narrowly focused on their branch of mathematic and I think Bourbaki was a bit prescient of this problem.

    I've also been thinking about the pedagogical implications of Bourbaki. It seems very impractical to teach out of Bourbaki, but then again it's a powerful (and maybe even the right) way to learn mathematic. Maybe reserved to people serious about mathematic in the abstract sense and/or for doing math for its own sake.

    I don't like the trend away from Bourbaki in any way. Furthermore, there are certain areas of study that seriously needs a Bourbaki treatment. I would name physics first and foremost.

    Sorry if the use of mathematic bothered the readers of this post. I did it in honor of Bourbaki :).
  7. Feb 26, 2005 #6

    matt grime

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    I'm not sure it's the right way to *learn* mathematics, but it might be the right way to collate it, ie perhaps we should think of Boubaki as an encyclopedia. We try to train our students to implicitly adopt the Bourbaki idea (or my interpretation of what Bourbaki is) by making them question if all the hypotheses are needed - is this reallya statement about continuous functions on R or is it about something more general. Personally I favour the approach that in mathematics it is the definitions that are important - something is its properties, if you will. Though trying to get my students to understand that is proving hard: often they can't do a question because they simply haven't learned the meanings of the symbols. Perhaps Boubaki would be a good stick to beat them with?
  8. Feb 26, 2005 #7
    Yeah Bourbaki would be a good stick for those applied people lol.

    Applied people are soooo stupid. lol (Referring to UHF, beginners class in karate.)
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