"David C. Ullrich" <firstname.lastname@example.org> wrote in message news:email@example.com... > On Thu, 13 Jul 2006 09:43:42 -0500, "Robert J. Kolker" > <firstname.lastname@example.org> wrote: > >>Hatto von Aquitanien wrote: >> >>> >>> I know this was addressed to someone else, but I would also like to >>> offer my >>> thoughts on this matter. I contend that mathematics _is_ constrained by >>> physical reality. The underlying logic which determines mathematics is >>> a >>> manifestation of physical reality. I believe what you are asserting is >>> that mathematics should not be required to produce physically measurable >>> results as a test of its validity. I really have to wonder if such a >>> requirement is unrealistic. It's interesting to observe that some >>> people >>> are wont to point to the fact that formal proofs can be verified by >>> computer programs. >> >>But formal proofs generally cannot be discovered by finitary algorithmic >>means. > > That's nonsense. Given a formal theory, enumerate all finite strings > in a language suitable for describing formal proofs in that theory. > As each one appears, check to see whether it's a proof. Every proof > in the theory will eventually appear. > > If you meant to be talking about _efficient_ algorithms you > should say so. > >> We still need Inspiration. If you regard all, so-called "mental" >>processes, as really physical then your assertion may have some basis. >> >>Bob Kolker > > > ************************ > > David C. Ullrich
Wiles proof of FLT almost certainly appears somewhere in the decimal expansion of pi.