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*To*: Alexander Zenkin <alexzen@com2com.ru>, fom@math.psu.edu*Subject*: Re: FOM: FLT, 4CT, CFSG: Depth, length, and width of proofs*From*: Joe Shipman <shipman@savera.com>*Date*: Tue, 08 Dec 1998 09:41:55 -0500*Organization*: Savera systems*References*: <366C1FC2.C1F82153@savera.com> <366C6C4A.C03C3784@com2com.ru>*Sender*: owner-fom@math.psu.edu

Alexander Zenkin wrote: > Dear Joe, > > first of all thanks very much for your brilliant analysis of the > outstanding solutions of the three great Theorems: FLT, 4CT and CFSG as to > their "long, deep, and wide". But if it is possible, could you tell your > opinion on the theorems, and especially on the theorems solutions as to > their influence upon the mathematics as a whole or, maybe, upon any specific > directions of mathematics? > > Thank you in advance, > Alexander FLT: The theorem itself has no direct impact but the proof has a lot of influence in Number Theory because Wiles developed a number of new techniques. 4CT: The theorem itself has no direct impact but the proof had a great deal of philosophical and foundational importance (though no particular importance in its field of graph theory). CFSG: The theorem had a big impact in group theory because many open questions could now be resolved (the classification of all finite groups with a property P could for many P be reduced to questions about simple groups). The proof was such a hodgepodge that it is hard to assess its impact -- I am sure some of the pieces involved important new techniques in group theory, but I think almost all its influence outside of group theory is sociological/philosophical. Thanks for the kind words! -- JS

**References**:**Joe Shipman**- FOM: FLT, 4CT, CFSG: Depth, length, and width of proofs

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