So why lie?
- From: jstevh@xxxxxxx
- Date: 22 Jan 2006 12:48:21 -0800
For many of you none of this will seem possible until I explain why
mathematicians would think they could ignore or lie about a result
proving the theory of ideals is flawed, and get away with it.
If you look at all into this story you see a Who's Who of names like
Barry Mazur, Andrew Granville, and Ralph McKenzie at my alma mater
Vanderbilit University. Or Ioannis Argyros the chief editor who gave
in to the sci.math'ers and even mention of a math grad student at
Cornell University who so far I've kept anonymous.
How could all those people along with so many others on the sci.math
newsgroup work to hide a huge result, and think they could get away
with it?
The answer to that question is important and the relevance to this
group is, I think, that mathematics is important to the field of
cryptology and you are, I think, a more practical group, with a lot of
powerful math software you're quite adept with, and less reason to
fight to hold on to something like the theory of ideals.
But I know you need to know why and how.
The best explanation I have is that they didn't think it possible for
me to prove that I'm right in such a way that I couldn't be ignored by
reasonable people, not number theorists.
And why has a lot to do with the ambiguity in expressing irrational
solutions to polynomials.
The easiest way to explain that is with a simple example:
1+sqrt(4)
Since -2 or 2 is a solution to sqrt(4), it is true that there are two
solution to that expression and they are 3 and -1.
And, of course, I could just as easily use
1-sqrt(4)
as it has the exact same solutions.
With integer solutions you can solve and see but with irrationals, like
1+sqrt(2)
there is no such resolution.
My result covers irrational solutions where it's impossible to resolve
radicals to actually see the answer directly, so mathematicians who
know this could suppose that as long as the proofs were ignored, I
couldn't provide any other evidence to prove my case.
They would be safe because no one could SEE my results directly,
because with irrationals, it's usually impossible to directly see
factors, unless it's something trivial like sqrt(6), because you can't
resolve the radicals, like with the square root function because it has
two solutions.
But, if that was their reasoning--I am speculating--they didn't pay
enough attention to the full theory I have as it covers rational
solutions as well, so someone can directly show the result, using
integers.
Why didn't it occur to them?
I don't know. They focus on irrationals. The failure in the theory
they have is with irrationals and not rationals. The cross-over from
my more powerful theory didn't jump out at them, or something else.
I'm speculating. I found their behavior peculiar.
For a long time I actually believed that I could just present the proof
and SOME mathematician somewhere would just go with mathematical proof,
but years have gone by, a math journal is dead, and so far there has
still been this refusal to follow the rules.
So I'm on sci.crypt because I have a sense that here things are a bit
different than sci.math and I'm stuck. I have gone to journals. I
have gone directly to mathematicians.
I had freaking Barry Mazur and Andrew Granville looking over this
research.
One huge surprise for me was when the editors at the Southwest Journal
of Pure and Applied Mathematics published my paper and I naively
thought it was finally over.
I figured, the journal followed the rules and published the paper, so
maybe now there can be some movement on this, and then some
sci.math'ers got it yanked by an email campaign--something that's not
supposed to be possible.
It is an extraordinary situation because it is so huge. Over a hundred
years of number theory are affected by my result, where the wrong ideas
could flower because they covered irrationals.
So mathematicians could make claims about numbers where the claims were
false, but how do you check?
What's so freaking brilliant about my mathematical tools? How are they
so goddamn powerful?
Back to my simple example:
1+sqrt(4)
It has two solutions where one has 3 as a factor and one is coprime to
3, as the solutions are 3 and -1.
What if someone figured out analytical tools that allowed you to prove
that without having to resolve the square root?
Then without even bothering with sqrt(4) = +/- 2 you could prove that
one root had 3 as a factor while one is coprime to 3.
My research is a way to ask questions about factors of irrational roots
without having to resolve things like the square root, and for that
reason it has cross-over, as it applies when you CAN resolve solutions
as well.
That's a crucial point: the theory applies to BOTH rational and
irrational solutions without caring about such things.
So what it says CAN be checked, and that's why I'm pushing that now.
Some people, if they reasoned as I think they did, miscalculated by not
taking that into account.
So with
a^3 + 3(-1+xf^2)a^2 - f^2(x^3 f^4 - 3x^2 f^2 + 3x) = 0
you can find integer solutions where f is a non-zero non-unit algebraic
integer coprime to x which is a non-zero algebraic integer, and SEE
directly that my theory works!
Note, I have the mathematical proof. The problem here is that the
mathematics I've found uproots over a hundred years of number theory
showing it to be invalid, which is an impact on the mathematical field
like no other in its entire history.
Easy to dismiss such a claim and lots of social reasons to try and hide
it.
One immediate impact of this result is to take away some rather
dramatic claims of proof, like, well, like that Andrew Wiles proved
Fermat's Last Theorem, as the tools he used are shown to be, useless.
My understanding is that Barry Mazur is a friend of Andrew Wiles.
Human nature is human nature. People can do the damndest things when
they don't think it all the way through, and here, notice how hard it
is for me to push this result, despite mathematical proof.
The sad reality is that if those people made that calculation, if Barry
Mazur or Andrew Granville or any number of others thought about the
odds of my getting it across that the theory of ideals is flawed, and
concluded that the truth was unlikely to be known, then so far the
reality has shown the odds are indeed long.
But in situations like these it is often about time. But once you make
one bad decision, you can feel trapped by it, and keep playing the
odds.
I have gone to the journals. Hell, one died. I have talked to
mathematicians directly.
I can talk and talk and talk but if people trust the wrong people, or
just can't accept that there could be a hundred year plus problem that
escaped everyone, then yeah, the odds are long.
But such odds have been beaten before. History shows that the truth
comes out, so my best guess is that they're playing for time.
If it takes decades then they could be retired and well away before the
real fallout begins.
Just speculation, but I'm dealing with an extraordinary situation where
I managed to contact the right people and put the information in front
of them, and they didn't do what they were supposed to do.
You people have the tools to put up the evidence to end this, and force
the situation.
Sometimes I wonder if it isn't better to just let the flawed
mathematics stay in place.
Humanity got by for over a hundred years with number theory over
irrationals that was wrong, so maybe that field is just not important
enough for all the drama.
Maybe not. Maybe what's the real story here is that certain fields in
mathematics are NOT actually all that important, so it really doesn't
matter to the world what people in those particular fields believe,
wrong or right.
Maybe so.
James Harris
.
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