Re: Prime numbers, counting tells it all

jstevh@xxxxxxx wrote:
marcus_b wrote:
jstevh@xxxxxxx wrote:
William Hughes wrote:
jst...@xxxxxxx wrote:
marcus_b wrote:
jstevh@xxxxxxx wrote:
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.


This is not based on a reading of Wiles' papers, which is why
Harris doesn't cite anything specific in those papers or provide a
direct quote. This is based solely on Harris' willfully unquestioning
acceptance of an extremely stupid secondary source: Wikipedia.
Below is the relevant quote from the following site:

http://en.wikipedia.org/wiki/Fermat's_last_theorem

"The main problem that Wiles had to overcome was to establish
a correspondence between semistable elliptic curves over the
rational field, and the modular semistable elliptic curves over
the rationals, which he did by explicitly showing that there were
equal numbers of each."

If in fact this is literally all Wiles did, Harris would be right.
You
cannot prove that a given correspondence between two infinite
sets is one-to-one by just showing that the two sets have the same
cardinality. But of course this isn't an adequate description of
what Wiles did. What Harris has discovered here is that Wikipedia
is not a reliable font of all knowledge. Surprise, surprise.

Marcus.


Actually it was a MathWorld page

And now you are going to explain that the MathWorld
page said something different.

in a previous discussion on this issue
and some poster came back to make the SAME TYPE CLAIM asserting that
MathWorld had the problem:

Here's the messageid:

1111254785.818349.100280@xxxxxxxxxxxxxxxxxxxxxxxxxxxx

Like I said, you can point out flaws in Wiles' work but it doesn't
matter, as you can see posters shifting all over the map and it doesn't
matter.

The math field in "pure math" areas is completely corrupted.


Or not. I guess it must have said the same thing.

- William Hughes

My point is that you people make the same excuses no matter what, so
before when I talked about what MathWorld said about Wiles' work the
SAME type assertion was used to try and hide the obvious flaw in what
Wiles did, as was just used by a poster attacking what is on the
Wikipedia, but he didn't know that I actually talked about MathWorld
before or he forgot, so it's a great example to show people how empty
you people are of substantive objections.


The "SAME type assertion was used" because evidently the earlier
poster and I reached the same conclusion: you have never read
Wiles' paper, only secondary sources. It's pretty clear that
Wikipedia copied MathWorld (which is older), so the fact that the
earlier poster found one source and I found another is immaterial.
The fact is, that quotation is your only basis for your claim. Other-
wise you would do what several people here have asked: cite a
direct quote from one or more of Wiles' papers. But you are very
conspicuously not doing that.

It is just a reality that what Wiles tried to do is logically stupid.
Sorry but that's just the logical reality.


Sorry, but all you can really claim here is that the quote from
Wikipedia/MathWorld is logically stupid. And you are logically
stupid and dishonest to boot for claiming that the error was due
to Wiles.


But that goes to the delusions of grandeur that you and other Usenet
posters continually show.

So you attack an electronic math journal reviewed by Mathematical
Reviews as a crap journal.

And now you assault MathWorld and the Wikipedia.


Not really. Everyone knows, or should, that Wikipedia is
unreliable, and MathWorld is not like a refereed journal.
Did you ever notice that they are both almost exclusively
descriptive, leaving out proofs for virtually everthing they
describe? That's not real math. That's Spectator Math for
the masses. The problem is not Wikipedia anyway. It's you,
claiming on the basis of an obviously false statement there
or in MathWorld that you have found an error in Wiles' work
- without ever having read Wiles' work. Again, if you really
could prove what you claim, you would be quoting an exact
passage from Wiles' papers. I note that in this reply you have yet
again passed up the opportunity to do that. Wonder why.


To you people that all makes sense!!!


You think MathWorld and Wikipedia should be accepted
as infallible Authorities???


But to most people it shows you are in your own little world and that
maybe they've given people like you way to much credit when they listen
to you about my research.

Quite simply, you people act like there is no authority higher than
you, so to you it's a casual thing to claim that MathWorld is stupid as
well as say the same thing about the Wikipedia.


There's no Authority higher than brute logic and correct
mathematics. It's astonishing to hear you suggest that fluff like
Wiki and MathWorld are Authorities, when you very blithely
claim to refute 150 years of hard, proven and tested mathematics
from the likes of Dedekind, Kummer, and Hilbert. Whoyougonna
believe? Dedekind or Wikipedia ? Hilbert or Harris?


But, um, who in the hell are you? Last I noticed you were just some
Usenet posters.

Who appear to shift your identities as well as the latest questions
about Greg aka "Tim Peters" reveal.


Your leg has been pulled. Delusional paranoia caused you
to fall for it. Wake up and smell the fish.


I guess you feel that you can say anything on Usenet without ever being
accountable for it, and don't care what people might be disappointed to
learn they have been quite boldly lied to by people who have callously
manipulated them.


Everyone's accountable here. You have to prove what you
say. If you don't, no one believes you. It's that simple. That's
why Tim Peters keeps whipping your ass. In this case you can
prove me wrong and tromp me in the dust by quoting the appropriate
passage from Wiles. You've had every chance. But you haven't
done it. Why not?

Marcus.


___JSH

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