NetNews Usenet Archive 1993 #1/NN_1993_1.iso/spool/sci/math/17820

Internet Message Format | 1993-01-08 | 3.4 KB

Xref: sparky sci.math:17820 alt.flame:17742
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Path: sparky!uunet!pipex!pavo.csi.cam.ac.uk!gjm11
From: [e-mail] (G.J. McCaughan)
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
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Date: Fri, 8 Jan 1993 04:22:11 GMT
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In article <[e-mail]> [e-mail] (brett mcinnes) writes:
>[e-mail] (G.J. McCaughan) writes:
...
>: A few comments:
>:
>:  * It's pretty. If the only reason for being interested in any mathematical
>:    result is because it helps you prove other mathematical results, there's
>:    a bit of an infinite regress there. In my opinion, one of the main reasons
>:    for doing mathematics at all is its aesthetic appeal; and FLT *does* have
>:    aesthetic appeal.
>I disagree. :)  My point is that if the proof were easy, nobody would have
>heard of this result or care about it.:

On what grounds do you say this? Just saying that you don't happen to find it
exciting isn't enough, of course.

>:  * It does connect with the rest of mathematics, anyway. Not just the algebraic
>:    geometry you say you've heard all the propaganda for, but other areas of
>:    number theory, to do with modular forms and the like.
>: I did not say that I had heard propaganda for algebraic geometry, only
>for FLT. Algebraic geometry does not need propaganda; it really is
>significant.

I beg your pardon; I should have said "about" rather than "for".

>:  * "frankly, who cares? It's recreational mathematics, right?" Does the fact
>:    that something is "recreational" -- that people other than professional
>:    mathematicians are interested in it, in other words -- make it boring?
>: Usually. Look at this newsgroup.

Oh, rubbish. You're arguing backwards. Yes, most problems about which ignorant
people produce crap are simple to state, like FLT; that's because the really
complicated things are beyond them. It doesn't follow that most simple-to-state
problems are bad ones.

>:  * Work on FLT was one of the big motivators for the theory of ideals. I don't
>:    call that trivial, boring, or even "recreational".
>: Neither did I. Only FLT itself.

You haven't answered either of my main points: namely, that FLT is interesting
on its own account, and that it is connected quite intimately with other areas
of mathematics, and has given rise to work which is clearly important.

Actually, you have sort of answered my first point, simply by disagreeing with
me. So -- do you agree that the aesthetic element is a very important one in
mathematics? If so, what sort of thing do you consider aesthetically pleasing
enough? Is incomprehensibility to all who don't have at least a good degree in
mathematics a necessary condition?

Perhaps I'll understand better if you tell me what you think of some other
famous conjectures. What do you think of:
 * the twin prime conjecture?
 * the Goldbach conjecture?
 * the four-colour problem?
 * the Poincare conjecture?
 * the Riemann hypothesis?

--
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
[e-mail]  Cambridge University, England.    [Research student]