[FOM] FLT and ZFC, again

[joeshipman@aol.com]

>-----Original Message-----
>From: Timothy Y. Chow <tchow at alum.mit.edu>
>
>Here are some further comments by the anonymous number theorist.
>
>> But I never *tell* people
>> that this is how I think:  because there are two kinds of people, 
right?
>> Those that don't care about the issue, and those that do care, and 
the
>> ones that do care have done the same as me: spent a day or two 
checking
>> that there is nothing remotely resembling a problem in formalising 
the
>> proof of FLT within ZFC. In fact I bet one can even jettison the 
axiom of
>> replacement and formalise the proof within V_{omega+omega} or some 
such
>> place, although I confess that I've never spent any time whatsoever
>> checking _that_ statement!

What your anonymous number theorist says is what I had basically 
supposed all along -- the infuriating thing is that he, or many other 
number theorists, COULD prove and publish a meta-theorem to the effect 
that all proofs satisfying certain restrictions on the type of 
constructions they do can dispense with the "Universes" axiom, but they 
prefer to annoy the logicians by leaving all this background knowledge 
unpublished (which I see as related to the fact that your number 
theorist wants to remain anonymous). There is a weird sociological 
phenomenon going on here involving a lack of respect for reasonable 
concerns raised by other mathematicians.

-- JS
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