Re: Internet, Goldbach conjecture, cranks and anticranks.


Gene Ward Smith wrote:

Ah - so someone who expresses serious doubts (and I'm being
polite) about the validity of your work is "nothing to do
with a mathematician"?

My point was, if what the author says about his purported proof is
correct, then the proof itself cannot be correct.

There's another problem with the claims, which is that the "proof"
purports to show that the Goldbach Conjecture is unprovable in PA, ie,
first-order arithmetic. In which case, it is also a proof that
Goldbach's Conjecture is true with stronger assumptions, for example
second order arithmetic or ZFC. In which case, it should be called a
proof of Goldbach's Conjecture, along with a proof it is unprovable in
first order arithmetic. Instead, we have a claim GC is "contradictory",
which makes no sense. It can't be "contradictory". At best we might get
that it is false in a nonstandard model of first-order arithmetic, but
true in ZFC or something like that, which would seem to follow from the
above claims.

.

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