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Re: Tautologies, math, and Wiles's work
Posted:
Jul 9, 2003 12:42 PM
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In article <3c65f87.0307090658.74196bbc@posting.google.com>,
James Harris <jstevh@msn.com> wrote:
><Quote>
>As of the early 1990s, most mathematicians believed that the
>Taniyama-Shimura conjecture was not accessible to proof. However, A.
>Wiles was not one of these. He attempted to establish the
>correspondence between the set of elliptic curves and the set of
>modular elliptic curves by showing that the number of each was the
>same. Wiles accomplished this by "counting" Galois representations and
>comparing them with the number of modular forms.
></Quote>
[...]
>My assessment is that Wiles commits the logical fallacy of "Cum hoc
>ergo propter hoc".
Popular, secondhand sources inevitably oversimplify technical statements.
Here they even cue you to the fact by putting "counting" in scare quotes.
What you're doing is to take an informal statement in a secondary source
literally, noticing that it is not perfectly accurate mathematically, and
then concluding that the formal mathematics in the primary sources must
be logically flawed.
It's illegitimate to fault Wiles's argument on the basis of secondary
sources. If you think there is something wrong with Wiles's argument,
tell us specifically which claims in his paper, or in his joint paper
with Richard Taylor, are wrong. I assume you *have*, of course, read
and understood both papers? That you are not simply relying on secondary
sources because the primary sources are too advanced for you?
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
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