FOM: Cartier and the revolution (was A pro cat-fom argument)

[Olivier Gerard]

Traditional fom member digest:
Name: Olivier P. R. Gerard
Position: Researcher in Mathematics and Theoretical Computer Science
Institution: Marin Mersenne Institute and Paris-VII University - G.M.P.I.B.
Research interest: Combinatorics, Theoretical physics, Found. of math.
More information: (soon available)

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Colin McLarty wrote:
>     	I have not read the Cartier article yet, but I suppose
> his time periods come from a certain Bourbakiste perspective: The
> purpose of Bourbaki in the 50s was certainly to take the viewpoint
> they had begun creating in 1935 and make it universal in math.
>
>     	Cartier jumps right from the 60s to "now". If he means
> some revolution has begun since say 1990 I have no idea what it
> would be. But I do know that many Bourbakistes felt their project
> was breaking down by the 1960s (see Leo Corry "Nicolas Bourbaki
> and the concept of mathematical structure" in SYNTHESE 92, 1992
> pp.315-348). The reason Corry gives (using internal Bourbaki
> documents) is largely that they could not cope with homological
> methods as used by Eilenberg, Cartan, Serre, (I believe they were
> all members) and increasingly Grothendieck (who went to meetings
> but would not join). Dieudonne certainly came to believe that
> category theory, which he knew almost entirely through
> Grothendieck, turned out to be better than Bourbaki's theory
> of structures. I think that is the new revolution Cartier
> means--certainly its effects are not at all settled yet--but
> I would not claim to know.

Dear Colin,

For having heard this discussion often from Pierre Cartier, I can
precise you that the revolution he is talking about is not relative
to Bourbaki or its project. As Pierre has been instrumental in the
increasing relationships between physicists and mathematician, he
feels that the whole field is moving, even boiling. I have not read
this particular interview, but I am sure he has in mind things such
as quantum groups and quantum field theory, knot and string theory,
mathematization of Feynman integrals, non linear dynamics, algebraic
combinatorics, etc... and a general feeling of a "baroque" era as
he often says.
By the way, in many topics I have quoted the categorical framework is widely
used as a common tool. Also, while Pierre has always been a strong
supporter of category theory, work on toposes, etc... he has also
helped the recognizance in France of the interest of the use of
large or innaccessible cardinals.
As you hinted, many members or companions of Bourbaki were more
lucid as to the shortcomings of the group than the official attitude
could make one believe. Their personal works are a sufficient testimony.

regards,

Olivier