I've been a JSH-addict for a while now, and I think I for once should give a reply to one of his posts, that I thought was really outrageous (well, they aren't that rare). I know it isn't my bussiness, but I get really annoyed by his arrogant tone and lack of understanding (Denial isn't just a river in Egypt) of the objections raised about his "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.
You prefer to discuss the examples. As several posters have pointed out, you consider your own examples to consitute proofs (or at least that they obviously leads to a proof), and that others counterexamples aren't counterproofs (since you can't disprove a proof!) Also, what exactly is the current mathematical understanding of these issues you are talking about?
> 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.
There are several introductory texts on algebraic structures that you should have peek at:
"Topic in Algebra" Herstein
or any book with the title
"A first introduction to Abstract Algebra"
and later perhaps something like "Algebra" by Lang. I think you'll be able to work up your intuition with rings and fields and suchalike by studying those.
> 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.
How do you know that you've proved it? As far as I know, you are the only one that believes you've proved the theorem. That should be a hint.
> 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. >
It would suffice if you gave a -proof-, using the properties of the ring you are working within. I don't recommend that you take a peek at -all- rings and give a contradiction by studying them all.