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Re: FLT Discussion: Simplifying
Posted:
Jan 20, 2001 4:46 PM
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In article <948l1f$n0g$1@nnrp1.deja.com>,
hale@mailhost.tcs.tulane.edu wrote:
> In article <947vks$5dt$1@nnrp1.deja.com>,
> jstevh@my-deja.com wrote:
> > You say, I'm forced to act like I'm outside of integers at the
start,
> > but what if there were an integer solution to FLT?
> >
> > Then wouldn't your objection fall away?
>
> No.
>
> One proof of Fermat's result that primes congruent to 1 modulo 4
> can be written as the sum of the squares of two integers uses
> complex numbers (in particular, Gaussian integers). You are
> proving a result about integers, there are integer solutions for
> the result, yet you go outside to complex numbers (and you have
> to specify that you are going out to complex numbers so that
> you can use their properties).
>
Nope. Turns out that it depends on what I call 'v' in the proof.
You've been arguing that I have to go to complex numbers for my proof
using x^2 + y^2 = 0. I think you're a bit confused by that, as you've
now gone to saying it also applies to my FLT proof.
It turns out that I can extend the ring I'm using in the FLT proof,
without going into complex numbers, and make all of your objections go
away.
But I prefer to discuss these details, and highlight problems with the
current mathematical understanding of these issues.
I don't know why you guys forget, when I've told you more than once,
that I have selfish interest in these discussions. One, I'm exploring
my own understanding of deep mathematical properties, and two, I'm
highlighting that many of you simply *believe* that you have a very
thorough understanding, when you don't.
After all, if it took the mathematical community 360 years to produce a
proof of several hundred pages of something that I proved in less than
five years with a couple of pages, then maybe you all don't know quite
as much as you think.
Again, as of now, I *could* if I wished produce something that covered
every base you folks can bring up, and that is in the standard form
that you're used to. But, from my perspective, it would be more
complicated than necessary (thought still much, much shorter than what
is currently accepted as a proof of FLT), and it would be continuing
perspectives that are too limited.
James Harris
Sent via Deja.com
http://www.deja.com/
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