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Article 7633 of comp.ai.philosophy:
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>From: mh10006@cl.cam.ac.uk (Mark Humphrys)
Subject: Re: The Paradox of the Unexpected Hanging
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References: <2217@sdrc.COM> <BxHv6w.KJu@ns1.nodak.edu> <BxIrtx.B98@cs.vu.nl> <1992Nov11.073859.16764JPII@tygra.Michigan.COM>
Date: Fri, 13 Nov 1992 15:50:31 GMT
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In article <1992Nov11.073859.16764JPII@tygra.Michigan.COM>, dave@tygra.Michigan.COM (David Conrad) writes:
|> In article <BxIrtx.B98@cs.vu.nl> lbkruij@cs.vu.nl (Kruijswijk LB) writes:
|> >In article <BxHv6w.KJu@ns1.nodak.edu> vender@plains.NoDak.edu (Does it matter?) writes:
|> >>  Because human beings can solve the halting problem, etc.
|> >The last theorem of Fermat is a halting problem. Can you solve it?
|> >
|> 
|> Eh?  I have neither a proof for nor a counterexample to Fermat's Last 
|> Theorem, but I cannot see how it is equivalent to the Halting Problem.

No it's not *equivalent*, but its solution would *follow* from the solution of the
Halting Problem (as would the solutions of lots of other unsolved problems).

The algorithm to solve Fermat then would be the one that runs successively through 
all of the (x,y,z,n) quadruples (n>2) and checks for each (easy) if:
   n      n         n
 x    +  y     =   z   
If it gets a solution, it stops.
Otherwise it runs forever.
So if you can *prove* that this algorithm does not stop,
then Fermat's theorem is true.

No human so far has been able to tell if this algorithm ever stops.

Mark Humphrys
AI research, Computer Laboratory, University of Cambridge



