Re: Prime numbers, counting tells it all

Jesse F. Hughes wrote:
jstevh@xxxxxxx writes:

Frank J. Lhota wrote:
<jstevh@xxxxxxx> wrote in message
news:1163131549.861525.241370@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
...
So no Andrew Wiles did not prove Fermat's Last Theorem. But he can
rely on supporters around the world claiming he did no matter how many
ways you prove he failed. Their word against the mathematics.

So you've read and understood Andrew Wiles' proof of FLT? If so, and you can
prove that Wiles' proof is in error, you could legitimately earn a place in
Math history. So please, please, *PLEASE* tell us which step in the FLT
proof did Andrew Wiles trip up!


His approach fails by the logical fallacy Cum Hoc, Ergo Propter Hoc.

You did not answer his question.

In deductive proofs (like Wiles's and every other mathematical
argument), every step must either be an axiom, an assumption (later
discharged) or follow from previous steps. If a mathematical argument
is fallacious, then there must be some step which satisfies none of
these conditions. Most probably, this would be a conclusion which
does not follow from the premises.

So, what is it? Which step?


Actually that's a good thing to make an issue out of, and the proper
answer is a surprising one, which is, if you follow through Wiles'
entire paper, and assume that you already have a modular form that is
not an elliptic curve, you can't find a contradiction with that
assumption!

It's the null test.

I've talked about the null test before and posters dodge it, run away
from it and otherwise ignore the remarkable reality that if you just
assume the opposition of what Wiles claims he proves and go through his
entire paper, you can't find a single thing that contradicts with it.

Instead of giving a clear answer, you have always stated that the
problem was an informal fallacy about causality. This just is not
possible. Mathematics is a deductive science. Mathematical arguments
do not involve causal or other inductive reasoning[1].


Actually, no and I've explained how the logical fallacy, which is
USUALLY about causality does apply for his highly particular approach
to a highly particular problem.

It's not even hard. Like I can talk about someone finding objects with
four wheels, and trying to come to a conclusion about objects with four
wheels, like they have four doors, and then coming upon a child's
wagon.

Mathematicians found this thing that seemed to connect elliptic curves
and modular forms that is about four numbers--the four wheels of my
analogy--and Wiles just does a dumb thing of trying to compare infinite
sets.

It's illogical.

Your answer is rather like my complaint that the Chicago Bears should
have lost last week's game because of the infield fly rule.

It just don't apply.


I've explained and explained and explained.

People like you think that all you have to do is disagree.

And you know that has worked for years on sci.math so I guess that's
why you keep doing it, as I connect the dots.

Readers can note that I relate my specific objection to the use of the
4 numbers that are used to relate modular forms to elliptic curves and
if you do that and really go back and consider what Wiles was doing, it
just jumps out at you that it is just so dumb.

He tries to COMPARE infinite sets, and it turns out there are technical
reasons for why he can maybe have thought he succeeded--that go back to
quirks of the ring of algebraic integers which I've shown using
non-polynomial factorization--but you don't have to know much math at
all to know that logically his approach must fail.

And if you do know enough math to try it, doing the null test will just
give you that sinking feeling in your gut, so try it!!!

Go back through Wiles' work assuming the opposite of what was
supposedly proven to be true and try to find a point where that
assumption contradicts with ANYTHING in his paper.

But just keep wishing.

And in the meantime, figure out which step doesn't follow from the
previous ones.

Footnotes:
[1] Mathematical induction is not "inductive" in the sense I mean.

--
Jesse F. Hughes

I've looked over Wiles' work. That's why I like to tell people to do
the null test.

Try it. Go look at his paper, assume the opposite of what he
supposedly proves and try to find a point where that gives a
contradiction.

Or just keep talking, like you've done for years. It works with these
people.

So if that is what you think of as an accomplishment, fine. You can
fool people too dumb to check you on the mathematical facts. Big deal.

So they're too damn stupid to know you're wrong and trust you, so what?


James Harris

.

Relevant Pages

  • Re: Andrew Wiles page on Wikipedia
    ... Andrew Wiles is an international expert on the [[Birch and ... He still writes papers on elliptic curves. ... Wiles' loves mathematics and his love of mathematics dates from his ... The conjecture is now a theorem and was ...
    (sci.math)
  • Re: Prime numbers, counting tells it all
    ... Their word against the mathematics. ... So you've read and understood Andrew Wiles' proof of FLT? ... Mathematicians found this thing that seemed to connect elliptic curves ...
    (sci.math)
  • Re: Prime numbers, counting tells it all
    ... Their word against the mathematics. ... So you've read and understood Andrew Wiles' proof of FLT? ... matter, as you can see posters shifting all over the map and it doesn't ...
    (sci.math)
  • Re: PBZ: Short Proof of Fermats Last Theorem
    ... and a steady flux of attacks against Wiles. ... > “The mathematics of the new physics,” ... there are trillions upon trillions ... > between Escultura and several mathematicians around the World. ...
    (sci.math)
  • Re: Prime numbers, counting tells it all
    ... Their word against the mathematics. ... So you've read and understood Andrew Wiles' proof of FLT? ... matter, as you can see posters shifting all over the map and it doesn't ...
    (sci.math)
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