<snip>
> The formalists were pretty upset; and, although I don't
> really like the metaphor, the image that does come to
> mind that fits the metaphor is The List of All True Math
> Relationships (listed in the appendix of God's Book,
> according to Paul Eotvos--- 'scuse the spelling, it's
> pronounced Ehrdish).... anyway, The List has lots of
His name is Pál Erdös -- not Paul Eotvos; I presume?
> Relationships that can't properly be called Theorems
> because they don't have proofs. Each such unprovable
> theorem WOULD indeed look like a gaping hole to a
> formalist.
<snip>
> Here is a puzzle that I formulated on this subject that's fun.
> A great mathematician is at a party, and two students come
> up to him. One says, "I have found a proof that Goldbach's
> Conjecture is unprovable!". The mathematician snorts, "Go
> away, you crackpot". Then the other student says, "I have
> found a proof that whether or not there exist infinitely
> many prime pairs is unprovable!", and the mathematician's
> eyes light up and he says "Oh, really!? Please tell me
> more!". Why was the mathematician eager to hear out the
> second student, but not the first?
To begin with, the Goldbach conjecture is one of the very most
crackpot-prone existing.
Furthermore, if it is unprovable whether there exists infinitely many prime
pairs, then the existence of an upper bond on the prime pairs is unprovable,
and thus -- perchance -- one might argue that the unprovability proves the
theorem.
This seems (to me) to be the case with any negative proposal; but not with
positive such -- if FLT would have been proven unprovable, we would know
that the theorem would hold, because any counterexample is a proof against
it -- a proof that we would have proven not to exist :-)
> Lee Corbin
// Mikael Johansson
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