[RC5] Beal's Problem A DN challenge?

jmv16 at cornell.edu jmv16 at cornell.edu
Tue Jul 6 00:13:47 EDT 1999

On Sun, 4 Jul 1999, Robert L. Barry wrote:

> Even though Fermat's Last Theorem is probably one of the most widely 
> known and talked about mathematical riddles, it is also admitted by those
> mathematicians who understand it to have no known practical applications. 
> It did wonders for the advancement of pure mathematics, but that's about
> it. 

Well, it depends exactly what qualifies as practical applications. 
Certainly it's not the key to some everyday problem, but it's not just the
trivial puzzle that it may initially seem.  Wiles' proof is essentially
the direct application[1] of a conjecture, the name of which escapes me at
the moment[2], and that conjecture revolutionized a couple fields of

[1] And I'm not kidding.  If I remember correctly, the paper in which he
proves the conjecture is something like 150-200 pages long, and the paper
that applies it to the Last Theorem is shorter by an order of magnitude. 

[2] I can look it up if anybody's interested, however, I strongly 
recommend Simon Singh's _Fermat's_Enigma_.  It's very well written, etc, 
and the mathematics is kept to a reasonable level (the complicated stuff 
is all in apendicies so that it can be ignored by the uninterested 
without disrupting the text).  And the tale is quite good--like a 
mystery, almost...

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