From: rhs@world.std.com (Richard H Schwartz)
Subject: Re: Fermat's flunkeys (was Re: A Real Challenge)
Organization: The World Public Access UNIX, Brookline, MA
Date: Fri, 10 Apr 1992 17:18:11 GMT

cjdcosta@eos.ncsu.edu (CHRISTOPHER J DCOSTA) writes:

>I *did* make an error in my original posting, and I apologize for it.
>WHat eats me, though, is some of the scornful, smug, and self righteous 
>postings that followed it up.

They were uncalled for.  One thing I love about the kind of conversations
I can have in Mensa and in r.o.m. is that lots of people know little bits
of information about lots of subjects, and are usually interested in 
learning a little more just for the fun of it.  It is rude to "talk shop"
at a Mensa gathering (though I'm afraid many of computer types do this
all to often); but if you can talk about a in interesting subject in a 
way that non-experts in the field can understand, that's great!

Here's how I would have answered the orignal post if I hadn't been 750
messages behind when it came up:

Fermat's "Last Theorem" is one of the great unsolved puzzles of math.
Some people think that, although the assertion is almost certainly true,
that it is unprovable and that Fermat's margin note was an error or
a cruel joke played on the thousands of mathematicians have tried and failed
to prove the assertion that for N greater than 2, there exist no integers
A, B, and C such that A^N + B^N = C^N.  Notwithstanding the lack of a 
general proof, modern mathematicians have succeeded in showing that the
assertion holds true for every N up to a very large number.  The reference
librarian at any good science and math library should be able to point you
to sources that cover the subject matter at in-depth or beginners levels.

>I do not, for a second, accept the argument that Fermat's theorem is
>something as commonplace as the wind, as some have made it out to be.

Well, it is very commonplace for people who have read about the history
of mathematics.  And as one of the great un-solved problems of number
theory, it should be included in any introductory course on the subject,
but only as background material to the specific problem of N = 3, since the 
general problem itself probably offers relatively little to students who 
are trying to work on introductory level problems.  Then again, I don't
remember gaining much from any number theory proof that I've read, so I'm
not a good judge of what's of value and what isn't :-)

>suspect is that it has recently been introduced into the undergraduate
>math curriculum of some Universities, which is why so many prunes around
>here are so keen to show off their newly acquired knowledge.

Sadistic Profs who want their students to waste countless hours duplicating
centuries of failure probably assign it as extra credit :-)

>And if you expect postings to be Gospel - Truth, then it's YOU who are
>the fool. ROM is NOT some kind of SPEAKER's FORUM where you're invited to
>hold forth on topics of technical expertise!! It's a forum for *CONVERSATION*,
>a two - way street, where besides speaking, you also listen and (hopefully)
>learn!

Bravo!  Mathematicians have failed for ages to prove the general assertion, 
but many useful results have undoubtedly come from their efforts.  There's
every reason to believe that anyone who reads this, mathematician or not,
can gain something.  For example: I'll bet there are people reading this
thread who are thinking to themselves, "Wow... there are math problems
that maybe can't be solved.  My checkbook must be one of them.  Yeah, that's
the ticket." :-)

No one in this group should be flamed for lack of rigorous preparation in 
their posts.  This isn't a classroom, and it isn't a technically-oriented 
newsgroup.  A polite correction is all that it takes.  Nor should anyone
be flamed for being just a *little* curious about a subject -- curious
enough to ask a question and hope for an understandable answer, but not 
curious enough to want to delve into the real nitty gritty.  Curiosity at
*any* level needs to be encouraged, and berating people for being curious
about the wrong thing or in the wrong place or to an insufficient degree
is just plain anti-intellectual.

BTW -- I'm wondering about failed attempts to solve the problem.  I'm sure
there have been published proofs that have been refuted.  I wonder how many 
people have done *thought* they had a proof, but then found an error on
their own.  I think that it might be fun to know a little bit about the 
methods that have been tried on this and other great problems, but since
only proofs that are thought to be correct would likely be published, it
seems to me that anyone who starts out fresh on the problem is going to end
up duplicating lots of dead-ends.  Maybe there should be a repository of 
wrong proofs and methods that someone else has shown to be a dead-end.  That 
could eventually lead to a new method of proof:  proof by exhaustively
avoiding anything that anyone else has ever tried.  

-rich
-- 
             Richard H. Schwartz, Scheduling Systems Inc.,
            1000 Massachusetts Avenue, Cambridge, MA  02138
                  (617) 864 8330; FAX (617) 864 8377
                          rhs@world.std.com