email@example.com wrote in message news:<firstname.lastname@example.org>... > In article <email@example.com>, > James Harris <firstname.lastname@example.org> wrote: > >Wiles never finds a superset but instead tries to map two sets of > >objects, where one set contains objects called elliptic curves, while > >the other contains objects called modular forms. > > No, that's not what he tried to do. You were misinformed. He tried to > show that every elliptic curve is a Weil curve. The set of Weil curves > is the superset.
"In effect, the conjecture says that every rational elliptic curve is a modular form in disguise."
A little further down it's stated:
"Equivalently, for every elliptic curve, there is a modular form with the same Dirichlet L-series."
Note for readers: The Dirichlet L-series goes back to the 4 descriptors I've repeatedly mentioned.
Besides even if what you claim is correct, it'd mean that modular forms are Weil curves. Is that your assertion?
A good example for those who feel confused about the logical flaw I've highlighted in Wiles's work is to consider Hillary Clinton and Beyonce Knowles with the context of having children or capable of having children.
The superset in that context is the set of women, as women are the sex capable of having children.
Notice that with the superset identified I don't have to talk specifically about Hillary Clinton or Beyonce Knowles. I can simply talk about women and having children.
For Wiles to have a proof, he needs a superset, and if he had a superset, you wouldn't have to talk about elliptic curves or modular forms, as you could talk about the superset.
You could define the limitation on the superset, and it'd automatically apply to both.
> >Mathematicians noticed that for objects they checked 4 descriptors > >could be matched between objects that were members of these sets > > Does this sentence even make grammatical sense?
Possibly you need more punctuation.
Mathematicians noticed, that for objects they checked, 4 descriptors could be matched between objects that were members of these sets.
Technically (or maybe grammarians can correct me) the commas don't belong for a subordinate clause beginning with "that".
> >Wiles set out to map infinity against infinity and claimed proof that > >a limitation on modular forms was a limitation on elliptic curves. > > Nope, that's not what he set out to do. You were misinformed.
Well that goes back to your earlier claim, where you mention "Weil curve".
Continuing on, some readers may think that there's no way that mathematicians would go on for years making a claim that I can so easily show to be false as it is based on a logically flawed approach, but in my experience mathematicians live in a society that is very conforming as well as being strictly hierarchical.
The following is speculation, but I think it outlines what may have happened.
Wiles decided to prove Fermat's Last Theorem. Isolating himself he set out to find a way to show that the Taniyama-Shimura Conjecture was true. From published reports he spent at least seven years at this, while letting his colleagues believe he was working on something else. That's a deception that's important in context.
Assume that he really wanted to prove Fermat's Last Theorem, and consider that he was spending a lot of time by himself. Let's suppose that he had an approach and decided that he'd take it, and convinced himself that it'd work.
My understanding is that Wiles was a well established and respected mathematician: well within the ranks of the mathematical elite. When his fellow colleagues within his circle heard what he was working on, and that he felt that he'd succeeded, they probably felt elation.
Now let's suppose that slowly it sinks in that his path is logically flawed.
To tell him would mean forcing him to realize that he'd thrown away all those years, and would probably humiliate him. He'd be like some "crank", like so many others who'd thought they'd proven the great problem.
So instead they look carefully and find a "gap", which possibly would have let him out with some dignity. But Wiles gets a former student, and they work for a year to find a workaround.
It's easier after so much time for mathematicians to give in, as their society is so against confrontation on such matters, as their social order would not handle one of their elite being so humbled.
Now I have personal experience to add, as I contacted Ken Ribet a few years back when I had an unwise bet about one of my earlier flawed attempts at proving FLT (yeah, I lost the bet). He not only replied but offered to have one of his graduate students look over my work.
That should surprise you. He said he was intrigued by the idea of the bet.
I suggest to you that there may have been more to it.
I recently emailed Barry Mazur an early draft of my recent paper Advanced Polynomial Factorization and he replied back with encouragement and some pointed questions. I replied back of course including the final version, but haven't heard from him since.
What I've presented is speculation and circumstantial evidence based on limited contact that I've had with people most of you probably only read about, if you know about FLT, where you can read about Ken Ribet's paper, or Barry Mazur's role in the FLT saga.
But the people you just read about, I've contacted, and in some cases, as I've mentioned, they've answered back.
Who knows, maybe they *want* the truth to be known, but are trapped somewhat by circumstance and training. What might have began in a time of heavy emotion has continued now to a point where they may feel incapable of stopping it.
I suggest to you the possibility that they were trapped in the wiles of Wiles.
But that of course is speculation, and you may consider it wild speculation, which I understand. I'm merely trying to find some rational reason for a situation which is rather bizarre.
For what there is no doubt about is that without a superset, Wiles does not have a proof of the Taniyam-Shimura Conjecture, and therefore, has not proven Fermat's Last Theorem.