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From: spudnik on 10 Mar 2010 17:07
no; n=4 is a very, very special case,
that required only "infinite descent," and
he did not follow that, one of hsi very few explicit proofs,
with a proviso about the general case. anyway,
the "theorem" seems to have been one of his earliest insights
into numbertheory; might it not?

> There is good circumstantial evidence that he did not; specifically,
> the fact that he produced a proof specific for n=4 at a later date but
> never mentioned the more general conjecture.

thus:
don't top-post, you God-am trollamatic!

> yep, JSH is pure Troll.- Hide quoted text -

--les OEuvres!
http://wlym.com

--Weber's electron, Moon's nucleus!
http://21stcenturysciencetech.com
From: Arturo Magidin on 10 Mar 2010 21:07
On Mar 10, 4:07 pm, spudnik <Space...(a)hotmail.com> wrote:

Fixing crossposting:

> > There is good circumstantial evidence that he did not; specifically,
> > the fact that he produced a proof specific for n=4 at a later date but
> > never mentioned the more general conjecture.

> no; n=4 is a very, very special case,
> that required only "infinite descent," and
> he did not follow that, one of hsi very few explicit proofs,
> with a proviso about the general case.

Somehow, this fails to seem like an argument for the proposition that
he did have a proof of the general case, despite you starting by
denying my statement to the contrary.

He made personal note that he had no reason to believe would ever
become public (it would not have become, but for his son publishing
them posthumously). He was continually challenging other
mathematicians with problems and theorems he thought were interesting
and had solved. Yet he never made any public statement about a general
proof, and his proof for n=4 is one of the few he actually presented,
rather than challenging people to prove it; and he did so at a date
later than his personal marginal note.

The circumstantial evidence is that he may have realized later that
his "marvelous proof" was not entirely correct, or not fully
justified; but since he had never made any public claim or challenge,
there was no need to comment about it publicly either.

> anyway,
> the "theorem" seems to have been one of his earliest insights
> into numbertheory; might it not?

"Might"? Yes. Possible. But there are few indications that he did have
a proof and lots of indications that he did not and realized it at
some point.

--
Arturo Magidin
From: Arturo Magidin on 10 Mar 2010 22:54
On Mar 10, 9:27 pm, spudnik <Space...(a)hotmail.com> wrote:
> perhaps, his initial proof was only for odd prime exponents,
> is what I am saying.  perhaps, he had an insight
> into what were later to be known as p-adics (which,
> of course, were part of the subjectum of the conference
> at which Wiles exposed his Secret Attic Proof .-)

So... you are willing to reject the idea that he had no proof, because
you think there is no evidence he did *not* have one; on the other
hand, you are perfectly willing to conjure up all sorts of ludicruous,
evidence-lacking, fanciful scenarios to justify your unfounded opinion
that he probably had one.

You know what? It was my mistake. I thought you were actually
interested in *knowing* something, not just in mouthing off.

--
Arturo Magidin
From: spudnik on 15 Mar 2010 20:58
I was just reading a nice, zero-level book
that came out of expositing the Wiles proof; basically,
the subjectum is Galois and reciprocity (and
I have a geometrical ideal for the latter, iff
it urns-out to apply .-)

the whole point of my digression into FLT is a)
that Fermat never revealed much of his method,
excepting his "reconstruction of Euclid's porisms,"
and b)
that the more important unsolved conjecture
of Fermat, remains (Next Theorem). but, yes,
there is certainly no conclusive evidence
that he had no proof of the so-called last theorem, and
it really does all hinge upon its relation to n=4!

> So... you are willing to reject the idea that he had no proof, because
> you think there is no evidence he did *not* have one; on the other
> hand, you are perfectly willing to conjure up all sorts of ludicruous,
> evidence-lacking, fanciful scenarios to justify your unfounded opinion
> that he probably had one.

thus:
your statements are somewhat mealy-mouthed. anyway, if
you would just dysabuse yourself of the concept
of an absolute vacuum, then that of a "rock o'light,"
you'd see that there is no need of aether. to wit, if
you examine the concepts of permeability & permitivity, a)
you might have to do some simple math, and b)
you'd see that nothing has neither quality -- or
you'd have to show how your aether does have it.
(I suppose that an experiment has been done,
to show the relative p&p of various degrees
of relative vacuum, but maybe not.)

the wave just goes though both of Young's pinholes, and
that is that -- or, see what Young said about it!

thus:
anyway, Einstein's biggest blunder was
with "homopolar generators," and getting in over his head
with Maxwell's wunnerful theory, which is also problematic;
or, so saith my school (and Schroedinger's cat,
in Meowse Code .-)

thus:
most of the interpretation of the EPR "paradox" results,
a la Alain Aspect et al, is due to the ideal of a photon,
in assinging all of the energy of the wave-front
as a "mass" (electron-voltage, say) of a particle, whence
the wave-energy was somehow collected by the photo-
eletrical device. here are two ways to get over this: a)
just consider the practice of audio quantization, the phonon; b)
show how the photoelectrical device is actually tuned
to absorb a particular frequency of light.
so, is the "phonon" just one cycle of the period
of the sound, and like-wise, is the photon just
one cycle of the frequency?

--Light: A History!
http://wlym.com

--Weber's electron, Moon's nucleus!
http://www.21stcenturysciencetech.com/

--Stop Cheeny, Rice, Waxman, Pendergast and
ICC's 3rd Brutish invasion of Sudan!
http://larouchepub.com
From: spudnik on 15 Mar 2010 21:17
also, I do have a strictly "computational" insight,
that anyone who proved it might have had to have had,
and that Fermat certainly did have -- so could
have Pascal, had he not been more into physics;
this relates to the p-adics, but I have very little
experience with them, per se -- other than,
"the archimedean valuation is oo-adic."

thus:
_There Are No Photons!_,
a new book on lighting for analog videographers
(Newton was *so* wrong (like,
he said that denser media made
for faster rocks o'light)).

thus:
the whole point of my digression into FLT is a)
that Fermat never revealed much of his method,
excepting his "reconstruction of Euclid's porisms,"
and b)
that there ia a more important unsolved conjecture
of Fermat (The Next Theorem). but, yes,
there is certainly no conclusive evidence
that he had no proof of the so-called last theorem, and
it really does all hinge upon its relation to n=4, and
the particualr order of these two insights.

> that he probably had one.

thus:
your statements are somewhat mealy-mouthed. anyway, if
you would just dysabuse yourself of the concept
of an absolute vacuum, then that of a "rock o'light,"
you'd see that there is no need of aether. to wit, if
you examine the concepts of permeability & permitivity, a)
you might have to do some simple math, and b)
you'd see that nothing has neither quality -- or
you'd have to show how your aether does have it.
(I suppose that an experiment has been done,
to show the relative p&p of various degrees
of relative vacuum, but maybe not.)

the wave just goes though both of Young's pinholes, and
that is that -- or, see what Young said about it!

thus:
anyway, Einstein's biggest blunder was
with "homopolar generators," and getting in over his head
with Maxwell's wunnerful theory, which is also problematic;
or, so saith my school (and Schroedinger's cat,
in Meowse Code .-)

thus:
most of the interpretation of the EPR "paradox" results,
a la Alain Aspect et al, is due to the ideal of a photon,
in assinging all of the energy of the wave-front
as a "mass" (electron-voltage, say) of a particle, whence
the wave-energy was somehow collected by the photo-
eletrical device. here are two ways to get over this: a)
just consider the practice of audio quantization, the phonon; b)
show how the photoelectrical device is actually tuned
to absorb a particular frequency of light.
so, is the "phonon" just one cycle of the period
of the sound, and like-wise, is the photon just
one cycle of the frequency?

--Light: A History!
http://wlym.com

--Weber's electron, Moon's nucleus!
http://www.21stcenturysciencetech.com/

--Stop Cheeny, Rice, Waxman, Pendergast and
ICC's 3rd Brutish invasion of Sudan!
http://larouchepub.com
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