FOM: unimpressed by reverse mathematics?

[Stephen G Simpson]

Charles Silver Tue, 27 Feb 2001 17:54:25:
 > I personally think reverse mathematics seems foundational, but
 > several mathematicians I've spoken to seem not to hold it in high
 > regard.  I don't know what exactly this implies, but I'm
 > speculating that they don't consider it either to be "interesting"
 > math logic or they think it has no foundational interest.

In order to confirm this speculation, you would have to know more
about the intellectual/academic perspective of the mathematicians in
question.  For instance, maybe the mathematicians you talked to have
no interest whatsoever in mathematical logic.  A large number of
mathematicians, probably the majority, are in this camp.  Or, it could
be that the mathematicians you talked to have little or no interest in
foundational issues.  A large number of logicians, maybe the majority,
are in this category.

On the other hand, I have found that certain other mathematicians,
especially top-ranked ones like Barry Mazur, find reverse mathematics
appealing.  In particular, they like the idea of reverse mathematics
as a classification program -- classifying a large number of
mathematical theorems into a small number of equivalence classes,
according to the axioms needed to prove them.

Also, for whatever reason, reverse mathematics seems to be getting
quite a bit of play lately in the mathematical logic community.  For
instance, I am organizing a special session and participating in a
panel discussion, both on reverse mathematics and both by invitation,
at meetings of the Association for Symbolic Logic this spring.  Also,
I am being invited to a number of other meetings to talk about reverse
mathematics, e.g., an upcoming meeting in Pisa on the Hilbert
problems.

-- Steve