[FOM] Study of Mathematical Practice

[Harvey Friedman]

On 4/2/06 1:29 AM, "Gabriel Stolzenberg" <gstolzen at math.bu.edu> wrote:

>  In a list of five "questions" on which he proposes to concentrate,
> Harvey writes:
> 
>>> Examples where the known proof is nonconstructive, and where one
>>> can give a constructive proof, but all known constructive proofs are
>>> grotesque (e.g., extremely long, or extremely unpleasant, etc.).
> 
>  I don't see how the quality of proofs of a certain statement that
> some people happen to have made can be revelant to fom.  (By contrast,
> Harvey's examples in which "all known" is replaced by "it is known
> that all" seem to this layman to be of great interest for fom.)

The foundations of mathematics is, at least partly, a scientific study of
mathematical practice. So what mathematicians actually do and actually say
is of direct interest to the foundations of mathematics.

Harvey Friedman