RE: [math-fun] Most influential mathematician?
Such a computer program would be as intricate as the proofs it is expected to verify, and is subject to the same human error. There cannot be certainty of correctness of a proof without certainty of the correctness of the proof-checking software. Could the program check itself?
this reminds me to the halting-problem, which is known to be not solveable... --Chris
The proof of correctness could be given in holographic form, after which a human could check the first eighty bits or so and for all practical purposes it would be correct. See http://www.cs.bu.edu/fac/lnd/expo/holo.htm On 3/3/06, Pacher Christoph <Christoph.Pacher@arcs.ac.at> wrote:
Such a computer program would be as intricate as the proofs it is expected to verify, and is subject to the same human error. There cannot be certainty of correctness of a proof without certainty of the correctness of the proof-checking software. Could the program check itself?
this reminds me to the halting-problem, which is known to be not solveable...
--Chris
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-- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike
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Pacher Christoph