[FOM] Proving FLT in PA

Timothy Y. Chow tchow at alum.mit.edu
Mon Feb 27 19:54:51 EST 2006

Harvey Friedman wrote:
> Maybe it is relatively easy for some appropriate scholar to attest that
> Failing this, what about the prospects for some appropriate scholar to
> attest that

What exactly do you mean here by "getting a scholar to attest"?  This 
could range from a casual remark at tea by a famous mathematician who may 
be notorious for confidently proclaiming statements that sometimes later 
turn out to be false, to a published paper with some real work in it.  
Attestations on the former end of the spectrum are probably easy to come 
by, but do we really gain much from them?

> It is somewhat surprising that algebraic geometers seem content to LEAVE
> things in this state.

Based on anecdotal evidence (discussions with friends who are in algebraic 
geometry), "content" is the wrong word.  There are plenty of algebraic 
geometers around who would like to understand the material in SGA 
(including SGA4 in particular) but are daunted by the amount of effort 
that would require and the time that it would take away from their own 
research.  Those who do understand the material will readily acknowledge 
that it would be good for a digestible version to be produced, but again 
have more pressing projects.

In other words, just because nobody is fixing the situation doesn't mean 
that everybody is "content" with it.  Was the mathematical community 
"content" with the status of the classification of finite simple groups 
prior to Aschbacher and Smith's recent work?  Some were, but a lot 
weren't; just because people weren't working on it doesn't mean they were 

And note that I'm talking just about rewriting SGA so that working 
algebraic geometers can understand it better and perhaps use it in their 
own research more substantially than by just quoting a few of the major 
theorems; this is something that mathematicians would be more motivated to 
do than simply "cleaning up the logical foundations."  If they can't even 
make time for the former, then they certainly won't make time for the 
latter, but this doesn't mean that they are "content" with the logical 


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