Harristotelian Logic

One thing that gets lost in discussions about my research is the simple fact that identities do not add properties, as they are always true, so how can subtracting from an identity change the ring?

Like, with my now infamous paper posters seized on my starting the paper in the ring of algebraic integers when provably you get to this point where you are NOT in that ring, which is why I'd point out that they attacked my paper by seizing on its most crucial point.

So how can the ring change if all I'm doing is subtracting from an identity?

Remember an identity is something usually thought trivial, like x=x.

If I subtract x=x from x^2 + y^2 = z^2, can I change the ring?

No, I get

x^2 -x + y^2 = z^2 - x

and the ring will not care. And it cannot care.

And it CANNOT CHANGE as a result of subtracting from the identity!!!

Crucial to showing you have a mathematical intuition that is equal to the task presented by my research is understanding that I subtract from identities.

So how can the ring change?

If I start in the ring of algebraic integers, like saying that's what I'm doing in my paper, and use expressions derived by subtracting from identities, HOW CAN THE RING CHANGE?

But it does. And you know it does as that was the entire point posters who emailed the editors against my paper were making, and I myself have noted that yes, you end up outside of the ring of algebraic integers, when you start in it, and my research is about subtracting from identities.

So what gives?

Part of it is that I pulled out a piece from the full proof of Fermat's Last Theorem, so you don't see the beginning in a lot of what I posted and in what I put in my original paper, so you don't see the identities that start things, or what is subtracted from them, though posters who'd argued with me for years did see that beginning because remember, I first posted the proof of Fermat's Last Theorem, and later moved to concentrating on just one piece and that proof is all about subtracting the FLT equation from an identity, and analyzing the residue.

Those posters chose to ignore that I subtract from identities when they argued against my research.

But how can subtracting from an identity change the ring?

I'm going to leave you with that question. If you've kept up with the discussion you know that I had a paper published. If you've looked over objections to that paper you know that they center on the result not being true in the ring of algebraic integers, despite the paper starting in that ring.

But my methods involve subtracting from an identity, so how can you start in the ring of algebraic integers, only subtract from an identity, and find that you are no longer in the ring?

Any answers?

[A reply to someone who asked James whether he was talking about his paper “NonPolynomialFactorization.pdf”.]

No, I'm talking about my original paper, which readers can see at my Extreme Mathematics group.

See: http://groups.google.com/group/extrememathematics/web/non-polynomial-factorization-paper

The new paper they can also get there is the latest version of a simplified explanation where I've gone to quadratics as they are simpler, and I've now added in the identities that I call tautological spaces so that it is clear from beginning to end how it all works.

If you have read that paper then you cannot honestly continue to dispute my results.

What happened is that I was thinking to myself, why can't I reverse the process and get to the conditional from the expressions that I know are derived in a tautological space?

I do so in that paper and close the question of whether or not algebraic integer functions can exist with my original:

P(x) = 2(f(x) + 1)(g(x) + 1)

by showing they can only be algebraic integer functions with algebraic integer x, when Q(x) = -2x + 1 or Q(x) = -2x - 1.

If you are at all serious about mathematics and read that paper then all your objections have to fall away and you need to comprehend then that you have helped block the acceptance of a short proof of Fermat's Last Theorem from a young man who has been trying very, very, very hard.

Yes, I do rub people the wrong way a lot, but what does playing nice and kissing butt have to do with discovering great mathematics?

Real discovery is messy. Historians clean it all up for the history books, so don't think you know how this all should have happened.

This is how it happened.