From vixen.cso.uiuc.edu!howland.reston.ans.net!gatech!ukma!rutgers!princeton!rugola.princeton.edu!wiles Mon Dec  6 10:29:31 CST 1993
Article: 46007 of sci.math
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From: wiles@rugola.Princeton.EDU (Andrew Wiles)
Newsgroups: sci.math
Subject: Fermat status
Message-ID: <1993Dec4.013650.12700@Princeton.EDU>
Date: 4 Dec 93 01:36:50 GMT
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	In view of the speculation on the status of my work on the  
Taniyama-Shimura conjecture and Fermat's Last Theorem I will give a  
brief account of the situation. During the review process a number of  
problems emerged, most of which have been resolved, but one in  
particular I have not yet settled. The key reduction of (most cases  
of ) the Taniyama-Shimura conjecture to the calculation of the Selmer  
group is correct. However the final calculation of a precise upper  
bound for the Selmer group in the semistable case (of the symmetric  
square representation associated to a modular form) is not yet  
complete as it stands. I believe that I will be able to finish this  
in the near future using the ideas explained in my Cambridge  
lectures.

	The fact that a lot of work remains to be done on the  
manuscript makes it still unsuitable for release as a preprint . In  
my course in Princeton beginning in February I will give a full  
account of this work.


Andrew Wiles.