Sunday, January 22, 2006


So why lie?

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:


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


as it has the exact same solutions.

With integer solutions you can solve and see but with irrationals, like


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:


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.

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