4 ms·

I feel like Bourbaki set back teaching mathematics a great deal, by focusing too much on the abstraction rather than the concepts and intuition behind it. V.I.

by messe 6y ago

I feel like Bourbaki set back teaching mathematics a great deal, by focusing too much on the abstraction rather than the concepts and intuition behind it. V.I. Arnol'd does a better job of elucidating on this idea than I ever could in his "On Teaching Mathematics": https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html

enriquto 6y ago
It is a necessary "pendulum". I doubt that if Bourbaki hadn't existed, then the likes of Arnold would have not produced their beautiful (and useful) advice on mathematical pedagogy.
- rramadass 6y ago
  Nope; that's not an argument but a platitude.
  - drdeca 6y ago
    This comment seems to be self-describing. Edit: ok, that may be a stretch, but I thought it was amusing because my comment could also be interpreted as describing itself.
    - ves 6y ago
      I liked your comment! To substantiate this comment, I’ll say that words describing themselves are known as autonyms. So you marked out an autonomous comment.
JadeNB 6y ago
Teaching mathematics is a huge and important part of the mathematical endeavour, but that's not all that there is to it, and I don't think that's what Bourbaki was trying to do [0]. No one should learn, at least not initially, from a Bourbaki book—a sentiment with which I expect even his, uhm, constituents would agree [0]—but I suspect most professional mathematicians find the Bourbaki œuvre useful as a reference, both for facts they know that aren't otherwise written down, and for facts that are on the borders of their expertise and require only a spot check to confirm or dispute. Certainly I use it that way. [0] EDIT: I am wrong about this historical fact, although I believe it doesn't change my point about modern usage. Wikipedia says: > While teaching at the University of Strasbourg, Henri Cartan complained to his colleague André Weil of the inadequacy of available course material, which prompted Weil to propose a meeting with others in Paris to collectively write a modern analysis textbook. (https://en.wikipedia.org/wiki/Nicolas_Bourbaki https://en.wikipedia.org/wiki/Nicolas_Bourbaki).
rramadass 6y ago
Exactly right! Great article! People forget that generalization/abstraction is the end goal and should never be the first step. Unless and until you are sufficiently intellectually mature you should never start with general principles. Always start with a concrete example, motivate the arguments and slowly build/use the tools of Mathematics to work towards a solution. This is how Humans have learnt and developed for millennia but with the explosion of knowledge in the 19th/20th century we seem to have forgotten it and taken a completely wrong turn in the teaching of Mathematics. The result is that we have a lot of educated people (see in mirror :-) without any proper understanding.
QuesnayJr 6y ago
Bourbaki makes terrible introductory textbooks, but are great references when you are already motivated and just want an efficient presentation.
- curiousgal 6y ago
  I think that holds for all French math books. You literally have to be an expert before reading a book according to them. (I studied in France).
azepoi 6y ago
For french readers the french version in the Gazette of the Société Mathématique de France. http://math.unice.fr/~rchetrit/smf_gazette_78_19-29.pdf http://math.unice.fr/~rchetrit/smf_gazette_78_19-29.pdf

by messe 6y ago

enriquto 6y ago

It is a necessary "pendulum". I doubt that if Bourbaki hadn't existed, then the likes of Arnold would have not produced their beautiful (and useful) advice on mathematical pedagogy.

rramadass 6y ago
Nope; that's not an argument but a platitude.
- drdeca 6y ago
  This comment seems to be self-describing. Edit: ok, that may be a stretch, but I thought it was amusing because my comment could also be interpreted as describing itself.
  - ves 6y ago
    I liked your comment! To substantiate this comment, I’ll say that words describing themselves are known as autonyms. So you marked out an autonomous comment.

JadeNB 6y ago

Teaching mathematics is a huge and important part of the mathematical endeavour, but that's not all that there is to it, and I don't think that's what Bourbaki was trying to do [0]. No one should learn, at least not initially, from a Bourbaki book—a sentiment with which I expect even his, uhm, constituents would agree [0]—but I suspect most professional mathematicians find the Bourbaki œuvre useful as a reference, both for facts they know that aren't otherwise written down, and for facts that are on the borders of their expertise and require only a spot check to confirm or dispute. Certainly I use it that way. [0] EDIT: I am wrong about this historical fact, although I believe it doesn't change my point about modern usage. Wikipedia says: > While teaching at the University of Strasbourg, Henri Cartan complained to his colleague André Weil of the inadequacy of available course material, which prompted Weil to propose a meeting with others in Paris to collectively write a modern analysis textbook. (https://en.wikipedia.org/wiki/Nicolas_Bourbaki https://en.wikipedia.org/wiki/Nicolas_Bourbaki).

rramadass 6y ago

Exactly right! Great article! People forget that generalization/abstraction is the end goal and should never be the first step. Unless and until you are sufficiently intellectually mature you should never start with general principles. Always start with a concrete example, motivate the arguments and slowly build/use the tools of Mathematics to work towards a solution. This is how Humans have learnt and developed for millennia but with the explosion of knowledge in the 19th/20th century we seem to have forgotten it and taken a completely wrong turn in the teaching of Mathematics. The result is that we have a lot of educated people (see in mirror :-) without any proper understanding.

QuesnayJr 6y ago

Bourbaki makes terrible introductory textbooks, but are great references when you are already motivated and just want an efficient presentation.

curiousgal 6y ago
I think that holds for all French math books. You literally have to be an expert before reading a book according to them. (I studied in France).

azepoi 6y ago

For french readers the french version in the Gazette of the Société Mathématique de France. http://math.unice.fr/~rchetrit/smf_gazette_78_19-29.pdf http://math.unice.fr/~rchetrit/smf_gazette_78_19-29.pdf