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

[Bertfried Fauser]

Hi dear all!

        as I said in my firts 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 holliday month and nobody will be in
the department currently anyway.
        However, such things take time, as I am still hunting for the
Springer interactive book on AXIOM, some progress is going on there, since
I think I have now contact to relevant persons.

To the Bourbaki discussion, I may add a few comments on my own.

a) Bourbaki failed.

Indeed, the idea behind the bourbaki group was to write a unique and
standard textbook on the highes mathematical level, fixing the
mathematical knowledge of the time. There was a very strong referee system
and the idea to write under a pseudonym was to some extend revolutionary.
        As a background, these people had in mind, that mathematics can be
developed from an AXIOMATIC basis (set theory) in an almost unique and
natural way. Hence a bootom-up strategy. All chapters in the Bourbaki
books are organized as follows. Setting up the problem, giving the axioms,
proving increasingly complicated theorems based on the axiomatics
culminating in astonishing complicated theorems which end the chapters by
settling down 'all' questions about the subject.
        As e.g. matroid theory shows evidently, such an approch to
mathematics is doomed to fail, since mathematics (as it presents itself in
present days) is not a layered increasingly complicated subject like a
tree, but has circuits (as the algebra in AXIOM has currently too). The
amazing things are the so called 'cryptomorphisms' which allow to identify
a couple of axiomatizations (say of matriods). Whil such an isomorphy
seems to be trivial at a firts sight, it turns out, that the theorems
derived in one system of axioms quite easily may be extraordinary hard in
another and vice versa. Hence somehow the idea of a straightened
mathematics from scratch is spoiled.

b) Bourbaki is abstract.

The books of Bourbaki offended lots of mathematicians. There was an
attepmt (in false bourbakism) to proof even the trivial. In a certain way,
mathematics got lost in an infinite self recursion. More practially
thinking persons were totally upset about sayings like the following.
Bourbaki did some tratement in algebra(ic geometry), you learned about
ideals etc, hearing at the end a sentence like "and geometry follows as a
corollary". I know about lots of physicists and even mathematicians which
get red spots on their skin hearing the word   "bourbaki"

c) Bourbaki is influential and well known.

For sure, the influence of Bourbaki on contemporary mathematics cannot
be underestimated and progress in this direction is made steadily. Even
physics is on the way to enter such fields as Grothendieck bla bla bla.
For sure Bourbaki has a reputation and would have a quite reasonable PR
value for AXIOM, as Bill Page suggested.

d) Bourbaki is french.

Since science has turned to be anglo-saxonian in its tongue, it may look
odd that math is done in France in French. However, that route has never
ended and there are lots of well recognized journals and math is still a
bilingual science, french is therefore in this branch of culture of equal
weight (I have to say it even if I can read it only, mostly trained by
bourbaki books). In France there is a legal threat that you _have to_ use
french whenever is possible, hence also at meetings etc. [There are even
no computers, but 'ordinateurs', which is ethymologically odd, since thsi
means litterally 'God ans world steerer'] The particular strength of
French people in mathematics comes from a different educational system,
which emphasiszes mathematical knowledge. If you want to be an
professional in 'XY' in France, you need an education in XY or in
mathematics, e.g. if you want to be a 'nose' composing parfumes, odd isn't
it. Hence I see no problem with the frenchness of Bourbaki.

e) Seminaire Bourbaki.

As fare as I know, the seminaire bourbaki is still runing, and they
produce shelfes of output. The process was, that topics are trated in such
seminars as long as they show up to be polished and then have been
compiled into the bourbaki books. I think also that newer bourbaki books
have reorganized and updated content. In this sense, bourbaki is still
active and alive.
        I think a subject like mathematics is never 'finished', so its
unlikely that the bourbaki group disbanded for that reason. To organize
and steer such a vigorouse (and diverging) group of mathematicians need
charisma and institutional support. I am not sure if such a grouping
together could in the present IEHS happen, (which would be the natural
institution for a current N.N. Bourbaki to be located)

f) Bourbaki and AXIOM.

I do lots of things with maple, and it was Bill Page who made me avare 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
excellecne. Suppose you are in a class and the system outputs a result
'...' together with "type: FractionalInteger" or "Ring" or even more
weired 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.



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....

cheers
BF.

% |   | PD Dr Bertfried Fauser    Fachbereich Physik    Fach M 678  |
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