Virgil
Posts:
9,012
Registered:
1/6/11


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 24, 2013 3:26 PM


In article <999ef5cf82a54d96bee81ff12beffc0c@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Monday, 24 June 2013 00:18:55 UTC+2, Virgil wrote: > > > The Riemann hypothesis is generally thought to be provable, but no one has > > as yet managed to prove it. > > And no one is silly enough to assume the RiemannHypothesis as an axiom, in > order to do get some "results".
There you are wrong! Many mathematicians assume it true to see what sort of results follow from that assumption. > > > Fermat's last theorem was for a long time unproven though provable, and its > > proof, when found, was of considerable length and difficulty. > > > In real mathematics and in reality solution by axiom, like Zermelo's, are > known to be madness.
In real mathematics, explicitely stating ab initio what is being assumed, and sometimes also explicitely what is not being assumed, is considered good mathematical practice.
It is certainly a practice that WM would benefit from adopting as it would force him to think about how he derived what he claims to have proved. > > > there is a considerable difference between something being doable and its > > having been done. > > But in mathematics there is no difference between proving that something is > doable and showing something is doable.
There seems to considerable difference within WM's wild weird world of WMytheology between proving something is doable and merely claiming it.
We see a to of the latter from WM, but almost none of the former.
It is as if proper proofs give WM an allergic reaction of some sort. 

