[FOM] Proving FLT in PA

[joeshipman@aol.com]

Crowell:

>3. They're convinced that the proof could be reworked so that it would
>only use ZFC, but they see it as a waste of time to carry out the
>routine steps that would be necessary. This would be like publishing
>a proof using infinitesimals, knowing that it could be rewritten
>using limits, and not feeling that anything would be gained by
>the rewrite.


The essential difference is that in the case of a proof using 
infinitesimals, WE HAVE A METATHEOREM so the mathematician doesn't need 
to do any additional work. BEFORE the work of Abraham Robinson, there 
was no metatheorem, and journal editors would have insisted on the 
proof being reworked using limits.

I consider it an insult to the mathematical community that Wiles et al 
don't even pay lip service to normal standards of rigor by at least 
REMARKING that there is a logical issue here and that IN THE PARTICULAR 
THEOREM BEING PROVED the extra assumptions can be eliminated. They 
don't have to give the details of how they are eliminated in the 
published proof, as long as they are officially prepared to supply more 
details to those who ask for more details.

-- Joe Shipman