FOM: "The Ignorance of Bourbaki"

[Lou van den Dries]

Bourbaki needs no defense from me, but I cannot resist responding
to Simpson's latest production. (I'd be interested in getting
Mathias' article though, predictable as its contents are.)

Bourbaki's little paper in the JSL of 1948 is forgettable (as most
papers in that issue of the JSL) and has very little to do with
the main ideas of Bourbaki concerning mathematics. I would like
to write at some point at greater length on these issues, but
there are the usual time pressures. (And doing math is usually
more rewarding than writing about it, I mean intellectually
rewarding.)

I certainly regard Bourbaki as having had a very favorable influence
in mathematics, although they have certainly not given much attention
to certain aspects which seem to preoccupy some of the FOM-people.

As a student I found several of their volumes highly useful. It goes
without saying (although one still hears such things) that these
books does not represent at all the style in which mathematics is
created and discovered, it's merely a way to organize certain 
well-understood parts of it in a highly modular fashion. (This is
certainly not always the best way to present things, but sometimes
it is highly effective.)

A century ago there was something of a crisis in foundations
(although this has been exaggerated by those who write about
foundations), and that explains why these big names got into the act.
As to compartmentalization, from the FOM-point of view it is indeed
hard to understand what is going on in mathematics nowadays.
Of course mathematics is enormous (and a lot larger than 100 years ago),
and a certain amount of specialization is almost required if one
wants to make an effective contribution, but that does not prevent
the more accomplished mathematicians to have a fairly broad knowledge
of their subject. There are large scale interactions going on,
between fields of mathematics, and mathematics and physics, mathematics
and computer science, etc. The caricature that Steve paints
couldn't be more wrong. Regards,
                                Lou van den Dries