Date: Tue, 20 Jan 2004 01:56:29 -0500 (EST)
From: "Keith F. Lynch" <kfl at keithlynch.net>
To: WSFA members <WSFAlist at keithlynch.net>
Subject: [WSFA] Re: a 100-year old math problem
Reply-To: WSFA members <WSFAlist at keithlynch.net>

Ron Kean wrote:

> ... how could the Conjecture have any practical value, considering
> that the real world seems to be one of only 3 dimensional space?

Math doesn't have to have any practical value to be of interest to
mathematicians, or to math fans like me.

> Might the Conjecture have some application in cosmology?

It's not impossible, but is unlikely, since the universe appears to be
flat on the large scale.  It doesn't look like it curves around and
closes on itself, at least not in the obvious way.  Which raises the
question of how it can be finite but unbounded.  Maybe it's infinite?
Or maybe it does curve back on itself, but only on a far vaster scale
than we can hope to measure?

One very practical application of that proof is winning a million
dollars.  That's one of the seven Clay Math Millenium Prize Problems.
There's a one million dollar reward for a proof or disproof of each
one.  See http://www.claymath.org/millennium

Some of them do have practical value.  Most don't, except in other
branches of math.  A really *interesting* math problem is one that's
not only difficult to prove, but whose proof has consequences in
many seemingly unrelated fields of math.

One that Eric and I have been discussing is the Riemann Conjecture.
It's difficult to even understand what the claim is, never mind
what might constitute a proof of it.  It involves the Riemann Zeta
function.  I independantly discovered this function when I was a
teenager.  I played with it briefly, but couldn't make heads or
tails of it, so I soon lost interest.

I regained interest when the million dollar prize was announced.  I
gained even more when this function turned out to be unexpectedly
involved in the solution to a cute geometry problem someone gave me
at this year's Capclave.

So I bought a book on the function last month.  So far, I've made it
halfway down page two.

That function is like an alien artifact.  Nobody knows quite what it
is, or does.  We poke and prod it in various ways, see what happens,
and look for patterns.
--
Keith F. Lynch - kfl at keithlynch.net - http://keithlynch.net/
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