FOM: Grothendieck universes; f.o.m. amateurism

Stephen G Simpson simpson at
Wed Apr 21 20:14:02 EDT 1999

Colin McLarty 21 Apr 1999 12:42:13 writes:
 > On another topic: it is a misunderstanding to say Grothendieck
 > >even attacks Bourbaki for failing to incorporate Grothendieck
 > >toposes into the Bourbakian foundational scheme, thereby giving up
 > >the Bourbakian ambition to provide *the* foundation for all of
 > >contemporary mathematics.
 > The issue with Bourbaki was not toposes. It was primarily
 > homological algebra which Bourbaki members routinely used but could
 > into get into their system. See Leo Corry MODERN ALGEBRA AND THE
 > RISE OF MATHEMATICAL STRUCTURES (esp. pp.376-383) on this debate in
 > Bourbaki.

It wasn't a misunderstanding.  It was based on the quote from
Grothendieck's unpublished writings attacking Bourbaki, which you
provided.  That quote mentioned toposes, i.e. Grothendieck toposes,
presumably, but it didn't mention homological algebra.  (Of course I
may not have the full context, because I don't have access to the
master's unpublished writings.)

In any case, you are not trying to suggest that homological algebra is
beyond the reach of Bourbaki's system, are you?  I'll get the Corry
book and have a look at it.

All this is interesting to me as what seems to be a case study in
f.o.m. amateurism.  Here we have a Fields medalist in algebraic
geometry, apparently getting all upset because Bourbaki and others did
not embrace his pet f.o.m. concept, ``the vast All'', which everybody
recognizes as being straightforwardly eliminable and/or avoidable.

-- Steve

More information about the FOM mailing list