Re: bourbaki_and_disdain

Re: bourbaki_and_disdain

[R Brown]

In this discussion I would like to mention some things about Alexander Grothendieck:

In 1958 at Edinburgh ICM (me very callow!) I happened to hear Raoul Bott say 2 things which expressed his own amazement about AG:

One was that AG could play with concepts and make something real of it. (Compare AG's comment to me much later: `The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps ...',) I like the idea that `childish steps' should still be possible in mathematics, and may be more fun than trying the famous problem line. In fact Saul Ulam told me at a conference in Sicily in 1964 that a young person may think that the most ambitious thing to do is to try for solving a famous problem; but this might distract them from developing the mathematics most appropriate to them. I was not in danger of the former, but I thought it interesting that someone so good as Ulam should make this comment, and think it worth  publicising, since it is relevant to aims.  

The other comment of Bott was that AG was prepared to work very hard to make things become tautologous. Should one say this is also (except in the exercises!) the intention of Bourbaki ? 

AG also mentioned to me that his initial direction at Paris was not viewed favourably until it proved the generalisation of the Riemann-Roch theorem! 

Ronnie








----- Original Message ----- 
From: "edubuc" <edubuc@dm.uba.ar>
To: "Categories list" <categories@mta.ca>
Sent: Thursday, September 18, 2008 4:42 PM
Subject: categories: bourbaki_and_disdain


> Hello
> 
> 1) I agree completely with Andre, or, more properly, with Samuel
> Eilemberg and Pierre Cartier (Andre just tel us what they said to him
> when he ask them the question)
> 
> So the problem is not wether to agree with Andre or not, but wether to
> agree with Eilemberg-Cartier or not. They said to Andre:
> 
> "Bourbaki had essentially two options: rewrite the whole treaty using
> categories,
> or just introduce them in the book on homological algebra,
> The second option won, essentially because of the enormity of the task
> of rewriting everything."
> 
> 2) We can see that this makes sense too, the  Bourbaki Tractate was
> already written, and Grothendieck's proposal was to entirely rewrite the
> thing !!
> 

...

bourbaki_and_disdain

[edubuc]

Hello

1) I agree completely with Andre, or, more properly, with Samuel
Eilemberg and Pierre Cartier (Andre just tel us what they said to him
when he ask them the question)

So the problem is not wether to agree with Andre or not, but wether to
agree with Eilemberg-Cartier or not. They said to Andre:

"Bourbaki had essentially two options: rewrite the whole treaty using
categories,
or just introduce them in the book on homological algebra,
The second option won, essentially because of the enormity of the task
of rewriting everything."

2) We can see that this makes sense too, the  Bourbaki Tractate was
already written, and Grothendieck's proposal was to entirely rewrite the
thing !!

3) Also, Bourbaki Tractate, as it is, is a masterful book. It is just
perfect, or as close to perfection as possible. It sets a way,
philosophy and style to write mathematics. I myself (as Andre) have
learned a lot by reading Bourbaki, and, more than that, I enjoyed the
reading (and the task to understand it) as much as I enjoy any reading
where I can see perfection in every sense (as in Borges for example).

4) So, it is a lost  for mathematics and for category theory that
category theory fit in Bourbaki's goal as a foundational theory (as set
theory is) , and not just as one more part of mathematics (as set theory
is not).

What a marvelous book just on category theory Bourbaki could have
written, can you imagine !!

A Boubaki book on category theory !!

We miss it  . . .

5) Concerning "desdain", I recall to all of you that most of the people
who show desdain for category theory, also show desdain for Bourbaki.

Eduardo.