Re: Bourbaki and Categories

["Meredith Gregory" <lgreg.meredith@gmail.com>]

All,

i have been utterly delighted by this conversation. What i can't help but
think about, however, is that with the internet we have a different sort of
opportunity. Let me try to describe it.

   - What is missing in most mathematical presentations is a view into the
   often very human and very messy process of getting to the presentation. What
   young mathematicians need -- in my view -- is a view of mathematicians doing
   mathematics. They need to see very top-down orientations rubbing elbows with
   very bottoms-up orientations. They need to see highly inventive, unifying
   viewpoints come up against skeptical viewpoints armed with vast arrays of
   counter-examples. They need to see people desperately trying to organize
   while others are desperately trying to de-construct. This is where the life
   of mathematics is. This is how people bring mathematics to life.
   - With the internet we have the opportunity to record not just the final
   artifact, tractate or wiki, but the process. Ever since Andre Joyal
   mentioned a 2nd life for Bourbaki i can't stop thinking about a Bourbaki
   colloquium run in Second Life <http://secondlife.com/> -- so that
   whatever the outcome of a given process is in terms of artifact, people can
   go back and look at the process, itself. They can see how people argued and
   counter-argued. There is getting to be a precendent for this, from
   Harvard<http://www.joystiq.com/2006/09/12/harvard-class-invades-second-life/>to
   Intel <http://softwarecommunity.intel.com/articles/eng/1283.htm>, to run
   serious technical conversation in Second Life.

Perhaps this idea is too far out, but i would urge those who seriously
consider a second life for Bourbaki to remember to record the living part as
well as the outcome. After all, looking over the last many emails to
categories so much of it is an attempt to recover process -- how things got
to be where they are.

Best wishes,

--greg

On Sat, Sep 20, 2008 at 1:21 PM, Andre Joyal <joyal.andre@uqam.ca> wrote:

> On Fri, Sep 19, 2008, John Baez wrote:
>
> >Do we imagine this new Bourbaki as just systematizing and
> >presenting what we know already, or struggling to create
> >brand new mathematics?
>
> This is  an important question.
> We need to have a clear view of the goal of such an enterprise.
> From my point of view, the goal should be "educational":
> to help students and researchers to learn mathematics
> and cross the boundary between fields.
> Mathematics is vast, and every mathematician is a permanent student.
> The traditional way to learn is to read the litterature and to discuss with
> a master.
> I was told that Grothendieck had learned algebraic geometry by discussing
> with Serre.
> But few peoples have this chance.
> Obviously, Internet is opening new avenues for learning.
> Many peoples (and myself) have learned a lot by reading your bulletin
> "This Week's Finds in Mathematical Physics".
> You have a real talent to explain a subject by exposing the heuristic!
> A discussion forum like the "Categories list" is also very helpful.
> Wikipedia is a useful place to gather informations about a subject.
> But the Bourbaki Tractate was offering something more:
> a unified presentation of mathematics, including the proofs.
>
> The Bourbaki Tractate was the result of a sustained collaboration
> of many generations of mathematicians from different fields.
> Conflicts are inevitable and mathematics evolve quickly.
> A unified, final presentation seems impossible.
>