[FOM] John Baez on David Corfield's book

Stephen G Simpson simpson at math.psu.edu
Thu Sep 25 18:39:54 EDT 2003

David Corfield writes:

 > By the pulse of contemporary mathematics I mean the development of the
 > kind of mathematics relating to Fields Medals: [...]

 > Presumably, we agree that your work on foundations has no bearing
 > on the way mathematicians view the proper organisation of
 > mathematical ideas.

I don't agree.

The vast majority of recent and contemporary mathematicians, including
Fields Medalists, choose to organize mathematical ideas in terms of a
logical, hierarchical structure of axioms, basic concepts,
definitions, lemmas, theorems, proofs.  Contemporary f.o.m. research,
including my own f.o.m. research, is a study of this logical,
hierarchical structure.  The purpose of such research is to develop
precise answers to fundamental questions such as: What are the basic
concepts of mathematics?  What are the appropriate axioms for
mathematics?  What is the role of definitions in mathematics?  Etc
etc.  So, yes, I would say there is some bearing.

We could turn the question around.  With your talk of "the pulse of
contemporary mathematics," are you claiming that your own work has
some bearing on how Fields Medalists organize their mathematical
ideas?  If so, what bearing?

But this is beside the point.  My real question for you is, why are
you apparently so hostile to "foundationalism"?  And, what exactly do
you mean by "foundationalism"?

Of course, I haven't read your book.  But presumably you ought to be
able to give some indication here on the FOM list.


Stephen G. Simpson
Professor of Mathematics
Pennsylvania State University

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