FOM: "The Ignorance of Bourbaki"

[Stephen G Simpson]

Table of contents:

  1. "The Ignorance of Bourbaki"

  2. A historical observation

  3. A historical question

1. "The ignorance of Bourbaki"

  Dave Marker wrote:
   > My guess is that most mathematicians simply view the foundations as
   > "done". ZFC provides a strong enough system (which is probably
   > consistent) to prove any theorem which is currently accepted as
   > proven. If forced any result they want to prove can be traced back
   > to a formal proof in ZFC, so there is no need to worry about
   > foundational questions and they can carry on.
  
  Yes, this extremely unenlightened and dysfunctional viewpoint is very
  common among pure mathematicians.  It has been advocated explicitly by
  Bourbaki.  The reference is
  
    N. Bourbaki, Foundations of Mathematics for the Working
    Mathematician, Journal of Symbolic Logic 14 (1948), pp. 1-14.
  
  Obviously the intention of this silly article by Bourbaki is to
  liberate pure mathematicians from the need to think about the
  foundations of their subject.  How stupid!  How crass!  How
  blatantly anti-intellectual!
  
  This and other writings of Bourbaki are discussed in an article by
  Adrian Mathias entitled "The Ignorance of Bourbaki."  I have a
  preprint of this article, dated September 6, 1989.  Would anybody
  like a copy?  I believe the article was ultimately published in the
  Mathematical Intelligencer.

2. A historical observation

  In the first part of the 20th century, all of the great
  mathematicians such as Hilbert, Brouwer, Poincare, von Neumann, and
  Weyl were not only intensely interested in foundational issues, but
  also wrote meaty papers and books about them.  By contrast, consider
  today's atmosphere of narrow compartmentalization.  Today, most of
  the leading pure mathematicians (not to mention their followers) are
  narrowly focused and have virtually nothing to say about foundations
  of mathematics or the place of mathematics in human knowledge.  Pure
  mathematics today is a game played by specialists for an audience of
  specialists.
 
3. A historical question

  What is the cause of this intellectual degeneration?

-- Steve