FOM: "The Ignorance of Bourbaki"
Stephen G Simpson
simpson at math.psu.edu
Mon Oct 13 21:26:34 EDT 1997
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
More information about the FOM
mailing list