[FOM] Study of Mathematical Practice
Harvey Friedman
friedman at math.ohio-state.edu
Sun Apr 2 16:25:42 EDT 2006
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
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