If you're talking about your result with the rings that you discussed
with the notable professor, from what you have told us of your actions
with said professor, I get the inclination that he didn't have the heart
to tell you that the key points of your work were factually incorrect.
He didn't even offer to talk to me in person until I forwarded him an
email from Barry Mazur commenting on an early draft of the paper.
Remember, I'd sent him a paper to review for publication in a journal
for which he was an editor, and when I pressed him on acceptance, he
said he couldn't quite understand it.
After I forwarded him Mazur's email, he offered that I could visit and
explain it in person.
Besides it's trivial algebra:
If you have a polynomial P(x), where
P(x) = 1225x^2 - 15x + 14
I figured out a way to creatively factor it, AFTER you multiply by
some constant like 7, so you have
7*P(x) = (5a_1(x) + 7)(5a_2(x)+ 7)
where the a's are the two roots of
a^2 - (7x-1)a + (49x^2 - 14x) = 0.
The bored but curious can easily verify those equations work and easy
checks are at two points: x=0 and x=6.
And I got that wacky factorization by creative re-distribution after
multiplying by 7, as you have
7*P(x) = (49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2.
I say the distributive property doesn't care about the value of x, so
that you can find how it multiplied through using x=0 and generalize
from that to any value and can SEE that to be true at x=6.
But if that's true it blows up some widely held ideas in number theory
as mathematicians can prove that in something they call the ring of
algebraic integers, NEITHER of the a's can have 7 as a factor if the
functions give a non-rational number which you can see at x=1.
So the result is clever, simple, but revolutionary though easily
proven.
I, as well as numerous others, have looked at the algorithm and found it
wanting. The basic innovation seems... pointless, insufficient, but I'm
willing to accept that it might work. Yet it doesn't. Both algorithms,
and your extensions thereof, have been refuted by counterexamples.
Patricia gave you a program to test stuff with, and I extended it to be
easier to test (and am letting you use it).
Counter example claims have been made against my non-polynomial
factorization research as well.
I know that people can claim more than they can actually show, but
that refuting those claims is often useless, as it's a social issue,
not about what's true.
Extrapolating from your factoring work to elsewhere, you seem to
generate an algorithm, other people show you it doesn't work, you refine
it a little, it still doesn't work, and then people give up when it
becomes clear that you are not going to put any work into attacking it.
At that point you declare it to be correct and are then surprised to
discover that people don't accept this fact. Read the story of the
little boy who cried wolf again, it's very similar.
I have published research which was pulled by the editors after
publication and then the entire freaking mathematical journal died a
little later.
I have comments on my research from the TOP mathematicians in the
mathematical field who did nothing.
I talked about my prime counting function with Bruce Eckel who told me
he'd never seen anything like it and offered that he might put it in
one of his editions...that was years ago.
Once in frustration I contacted a U.S. Attorney's office and they
couldn't quite work themselves around the issue of mathematicians
lying about mathematical research.
I no longer believe at all in the system.
Your claims are meaningless to me because I know from years of
experience how people lie in this area.
And it's not isolated.
In cosmology there is Dr. Halton Arp, who was an assistant to Hubble
who can show with better evidence than those who argue with him that
cosmologists are saying that quasars are farther away than they are,
but they just call him a crackpot.
Besides, no matter what you may believe or not believe your assertions
against my optimal path algorithm have zero impact, so I have no
motivation to consider them relevant.
To get some sense of that just routinely do a search in Google on
"traveling salesman problem" to see where the algorithm you claim you
can show doesn't work, happens to be in the rankings.
It is moving up in those rankings.
The world is saying your are wrong. It's a wonderful reality test.
And what happens later?
Over time it's determined that the algorithm works just fine.
You are just some nobody who mouthed off against it on newsgroups to
no avail, who will probably not even be remembered for even that
error.
I've been in this saga for over a decade. I know who matters and who
does not.
Your comments have no impact.
James Harris