Re: MATH/COMP/PHIL: "Omega Man"

Date: Mon Apr 02 2001 - 18:27:26 MDT

In a message dated 4/2/01 5:15:43 PM, writes:

> But I agree with you that some of the
>claims in the science article were hyped, and thanks
>for reminding people like me to approach even things
>others know a lot better with a bit of skepticism.

Sad, but true; Nature and Science publish lots of papers with excellent
science but outrageous claims for consequences, relevance, and meaning
in the discussion. Proving most statements can be neither proved nor
disproved doesn't "blow holes" in mathematics. It just proves most of the
time you need you may need experimental mathematics. Big deal.
Even then, you have 2 additional questions: how often are *interesting*
claims unsolvable, and how well can you approximate the truth with
genuine proof. For example, somebody proved some time ago that there
were a finite number of elementary solutions to Fermat's equation. Now
Fermat's turned out to be decidable and true; but I'd be pretty happy
with a proof that Goldbach's conjecture had a finite number of exceptions.

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