FOM: General intellectual interest/challenges
Lou van den Dries
vddries at math.uiuc.edu
Tue Dec 16 00:16:05 EST 1997
Concerning Harvey's "needle in the haystack comment". It was not
my intent to argue that position, and I am sorry my comment about
"who, 200 years ago, could have predicted ..." was a bit elliptic.
What i meant to say is that central ideas often emerge only with
great difficulty and passing of time, even while not at all difficult
by themselves. They just do not lie on the surface. Elliptic
curves y^2 = x^3 + ax + b are not wildly complicated things compared
to the objects considered typically in fom research, nor are
zeta functions. Zeta functions (of arithmetic objects) seem to
encode in an uncanny way an enormous amount of information about
the object, and often satisfy remarkable symmetries, functional
equations, etc. You can denounce it as "inbred" and "snooty",
it doesn't take away the facts. While I am far from being an expert,
I think it is very possible that the uses of such objects in
some complexity questions is not at all temporary or an accident.
In any case, I think the burden to show otherwise is on your side.
Also note that I am not a number theorist or complexity theorist
(while having some interest in those areas), and have no plans to
work on P=NP? (having other fish to fry) using elliptic curves
or whatever. Still, I don't think it's a treasonable offense to
know a little bit on elliptic curves or zeta functions. I am
amazed how these poor things seem to elicit so much abuse on
mathematicians.
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