RE: [Axiom-mail] Bourbaki as default pamphlet author name

[Page, Bill]

Bertfried,

Thank you very much for your comments on Bourbaki and your
support for the idea of continuing to attempt to associate
the name "Bourbaki" with AXIOM.

On Wednesday, July 30, 2003 2:09 AM Bertfried Fauser
[mailto:address@hidden wrote:

> 
> Hi dear all!
> 
>       as I said in my first mail, this was a subject for 
> amusement, now it got serious. I can try to make direct
> contact to some of the Bourbaki authors, e.g. Cartier, via
> my colleagues in France. I hope to be in Paris in Fall.
> In France the August is holiday month and nobody will be
> in the department currently anyway.

I will be in Paris for the week of 14 to 24 September for
a physics conference and a short vacation (Avignon). Do you
think it would be useful to attempt to meet with someone in
Paris and vicinity to discuss and promote the association
of Bourbaki with AXIOM?

> ... 
> f) Bourbaki and AXIOM.
> 
> I do lots of things with maple, and it was Bill Page who
> made me aware of AXIOM and its possible new availability.
> The mere structure of AXIOM as a strongly typed language
> and the names of the types, is a bourbakism par excellence.
> Suppose you are in a class and the system outputs a result
> '...' together with "type: FractionalInteger" or "Ring" or
> even more weird things. Indeed every student _will_ have
> to ponder about domain, codomain of a map etc. great! In
> this sense, AXIOM is the only CAS I know (there are a few
> exotic ones for category theory around too) which deserved
> the name badge Bourbaki on it.
>

I agree. Though AXIOM is not exactly category theory.
Indeed AXIOM (and the Aldor language) seems to predate
most of the current interest in category theory in computer
science in the same way that Bourbakism predates category
theory itself. For example

  http://pauillac.inria.fr/caml/

  http://www.cpsc.ucalgary.ca/Research/charity/home.html

etc. And meanwhile category theory is now almost taken
for granted in much of mathematics and advanced
mathematical physics. I think the task of "preserving"
(and reviving?) AXIOM that Tim Daly is leading is very
important. AXIOM is still in many ways ahead of it's
time as Saul Youssef points out

  http://nut001.bu.edu/~youssef

> 
> If you don't mind, I will try to contact the Bourbaki
> people to ask if the AXIOM pamphlet files can be written
> 'officially' (i.e. with permission) under the name of
> Bourbaki, I still like this idea very much....
>

I am not too optimistic that such an 'official'
sanction is possible. After all, there really is still
a large conceptual gap between the pure mathematicians
and computer scientists. But I do not agree with the
recent comments by Arthur Norman:

> As well as feeling that it could be pretentious to try
> to grab that mantle I note that Bourbaki is a mainly a
> French institution (yes I know that maths is universal
> and not tied to one country). But e.g. their annual
> sessions are mostly held in French.  E.g. see

http://www.iecn.u-nancy.fr/~eguether/bibliotheque/BOURBAKI/node2.html

> I know that nothing I do is in their league!

First, I think the goals of AXIOM certainly were/are
pretentious - just as pretentious as the young
Bourbaki's. In it's own context, one might also argue
that AXIOM was about equally successful in meeting it's
original goals. I don't think there is anything wrong
with that. The application and enhancement of AXIOM as
a computer algebra system deserves to continue in much
the same way as Bourbakism survives today.

About Bourbaki being "French". Also, I do not see any
problem with this. AXIOM is now open source. And in
many respects open source is strongest outside the
influence of corporate North America. I am still amazed
at the truly international flavour of almost all current
open source / free software projects.

Finally although humility is admirable, I disagree with
you Norman, when you say that that what you do is "not
in their league". Lisp, Reduce, Axiom many other projects
in which you have been involved are all enormous
intellectual achievements as far as I am concerned.
There is a sense in which mathematics done by computer
is harder (and much less forgiving) than any other
kind of mathematics!

Cheers,
Bill Page.