Monday, March 27, 2006


JSH: Wasting my time

The math newsgroups as far as I'm concerned have only two uses:
  1. As a place for me to talk out ideas as I brainstorm.

  2. As a place to get criticism that hopefully occasionally is freaking useful, so that I can weed out the errors, or learn something about why mathematicians believe something or other.
For years, you people have at least been of minimal use to me, but increasingly I'm finding I'm getting less and less useful feedback.

It's starting to bother me slightly.

I may have to figure out some way to clear out the losers and bring in more useful posters, and believe me, I know how to do it.

It might be time finally, again, to clean house on these newsgroups.

I've been a bit lazy about that but I'm starting to feel a little frustrated!!!

Yes, I'm pushing you past normal limits, like always, and my research is so far beyond what anyone has ever done that it's hard, but I need some useful feedback, and if I break all of you in the process of getting that feedback, so be it.

There are always more people being born, who grow up and do math, who will eventually come to one of these newsgroups, so I figure, hey, down the road, I'll just use someone else.

Monday, March 20, 2006


SF: Factoring and conic sections

When I first introduced my equations that follow from my non-polynomial factorization research I used equations that were hobbled in a special way:

k_1 y^2 = T

and y = n, which if you use that with

x^2 + xy + k_1 y^2 = k_2 z^2


(2(v^2 - k_2)z + vy)^2 = ((1-4k_1)y^2+4T)v^2 + 4k_2(k_1y^2 - T)


T = (x+y+vz)(vz-x)

you get equations provably—rather easily in fact—equivalent to what is commonly called Fermat's Factoring Method as you get rid of the hyperbola and instead have a quadratic.

Those of you who are experts on modern factoring techniques should know that all of those techniques inherit something from the Fermat factoring method, as quadratics in some way or another dominate current techniques, while the full equations I use rely on a hyperbola, unless you crush that out by using k_1 y^2 = T.

My research shows the potential of using any conic, not just parabolas, for factoring, but given the hundreds of years without that being shown, it's also clear that it's either extremely difficult to do, or impossible to do with previously known methods–what I call classical techniques.

You have to have that neat idea of using identities like

x+y+vz = x+y+vz

and then you have the world of conics opened up, and maybe there's some really snazzy way to use a circle or an ellipse, while I've shown how to use a hyperbola, where it's also neat that it's part of a hyperbloid.

That's how my research encompasses what came before and extends it.

And if you think that my ability to encompass previous factoring techniques, as provably I can, like my equations being able to reduce to the quadratic case, while extending to areas previously inaccessible is a hallmark of unimportant research, then you're just not being rational on the subject.

So why aren't people rational on the subject when it's my research?

I have two theories:
  1. My research is such a leap forward with such simple ideas that there's some kind of shock that researchers go into. It's almost like communications from another planet the leap is so huge.

  2. Looking around, researchers wait for someone else to move, and no one moves, so mostly there is quiet, while there are a few people who reply to me on Usenet, who if you read closely, don't actually make ANY sense at all.
I've seen some weird stuff from mathematicians trying to react to my research, and it just keeps adding up to the point that I feel somewhat guilty, but I keep wondering when will I find someone who can accept the facts without coming mentally unglued?

Here's one of my favorites from another research area–prime counting–as I sent my prime counting function to a mathematician at a college in Atlanta, and he rather forcefully proclaimed to me that it was impossible. Um, but, I'm sending him the equations that actually DO work, and he's saying that they're impossible?

You do the math.

Oh, and then there's that Cornell math grad student who worked through some of my research in his own words, until he got to the end and stated that the result seemed correct for INTEGERS when it followed more generally, and then he said he needed to research algebraic integers.

And yes, I've been in contact with him since then by email, when he's been somewhat upset at some things I've said, while seemingly comfortable with his own ignoring of a revolutionary proof, as I think he just figures that no one will ever believe me.

And, if mathematicians can just use cognitive dissonance, and simply quit being rational about my research, maybe no one will, for a while, unless someone develops that factoring research into something practical and puts you all out of jobs.

Then when people ask me about how all this happened, I'll remind them of that Cornell grad student—who will still be a grad student–and of Barry Mazur, and of that mathematician in Atlanta, and all the other mathematicians all over the world who managed to just not do what society should reasonably expect them to do, until a lot of other people paid the price.

Saturday, March 18, 2006


SF: A hyperbolic solution

It's worth mentioning to me that what I found is technically a four-dimensonal general factorization of a composite that traces a hyperbolic slice from a hyperbloid:

The factorization

T = (x+y+vz)(vz-x)

in four dimensions: x, y, z, v

where x, y and z are defined by

x^2 + xy + k_1 y^2 = k_2 z^2

so you have the hyperbloid, and next

(2(v^2 - k_2)z + vy)^2 = ((1-4k_1)y^2+4T)v^2 + 4k_2(k_1y^2 - T)

where and first step to using the equations to factor is to pick y, k_1 and k_2, and actually picking y gives you the slice.

That may sound like nothing you've ever heard of for factoring composites

Some may even think that's the point for why it should be ignored, as if something so bizarre as factoring using four dimensions must be a crackpot bit of work.

Or you may naively think that the equations don't work, or that someone has proven that they cannot be used to practically factor.

I haven't seen any proof that a research effort couldn't turn the initial research into a powerful factoring method, as instead I've seen some Usenet posters deriding me.

They like to make things personal on Usenet in the math and sciences newsgroups.

Some people make it their business to reply to my posts on almost any subject across Usenet, deriding my research and me.

Now then, if those equations—like nothing before seen—can be the start of a research effort that leads to a practical factoring, why should anyone assume that mainstream cryptologists or mathematicians would be the ones to do it?

I increasingly fear it more likely, as that culture is proud, that desperate people who don't care about the source, but are interested in ANY way to crack security systems would be the more likely ones to just try anything.

So—mainstream mathematicians care about the source and you know and I know they are capable of ignoring anything—versus—desperate people who may be willing to try anything, with a general composite factorization using a hyperbloid and four dimensions.

With all that said, it's also has not been proven that the equations can be made into a practical method, so they may just been some eosteric pure math oddity, but you can be sure that mathematicians will do their best to ignore them even in that area as that's what these people freaking do.

So how did I even get those equations?

I discovered my own technique for mathematical analysis where I subtract what I call conditionals, in this case the equation for the hyperbloid

x^2 + xy + k_1 y^2 = k_2 z^2

from what is commonly called an identity, which I found by manipulating

x+y+vz = x+y+vz

which is one of those clever ideas that you wonder was only discovered last century, by me.

I discovered the method back in the month of December 1999 and promptly posted about it on sci.math to much derision, as usual.

The full derivation demonstrating the technique is at my blog:

You can see that it is in my August 2005 archive and yes the equations have been around for that long, long enough that if they can be made practical there may be some person or persons out there as we speak who are cracking RSA easily, and not telling anyone.

If they can be made practical, and again, I don't know if they can, but even if they cannot be, if mathematicians were so "pure" as they claim, a solution of this type would be of some interest.

For those of you who do not understand how the real math world works, consider this is just one of my results, and I did get some research of mine published in a peer reviewed math journal, a somewhat small electronic one that had only been around for about a decade.

Well someone posted about it on sci.math and the newsgroup erupted in fury.

A group of them emailed the editors of the journal claiming my paper was wrong, and the chief editor yanked it THAT NIGHT in a clear knee-jerk reaction, giving in to the mob editorial decision, which he didn't know about—he clearly just thought he was getting emails from concerned mathematicians—not realizing he was dealing with sci.math people.

How do I know?

Because he emailed me claiming that publication was a mistake, and claimed to have a reviewers report showing the mistake, which was a faulty claim of error made by the Usenet poster W. Dale Hall, which I knew because he'd posted it the day before, when the sci.math people were planning the email assault—in posts!

That's the REAL math world.

That's real math society.

Not pretty, not a movie—a janitor with emotional problems (or without them) could not crack this world—not so brilliant or beautiful—but how things actually work in the real world of mathematics.

It is an academic world, with Ivory Tower people who can do things that most people would find incomprehensible, not because it's so brilliant, but because it's so damn stupid.

I eventually sent a revised paper—cleaning up some details and putting it upfront how big the paper was as I didn't do that before—to the Annals of Mathematics "published bimonthly with the cooperation of Princeton University and the Institute for Advanced Study."


I was told that the paper was accepted for review, and months passed…

After six months I checked in and was told that a rejection had been sent a month after they got the paper, but I never got any email.

I asked for a reason for the rejection, and was told none was available, as my contact at Princeton University told me that someone else had just noted the database and there was no additional information.

They were stuck. Perfect paper with a dramatic conclusion which I now know leads to the conclusion that ideal theory is wrong, among other huge revolutionary things.

But how amateur!

Just claim an email was sent, when I have MSN and an email from Princeton through MSN is not going to just disappear without a trace all that freaking often, and then I have to contact someone nice enough on the inside to at least get the info out that someone had put that in their database, but, no more info available.

If these stories sound impossible to you, you do not know the real math world.

It is quite possible that I have put up one of the most important research finds in the history of factoring, and it is just being ignored by people you do not understand.

[A reply to someone who wrote that James' work can be ignored can be ignored because the author is a crackpot.]

I'm not a crackpot. And, hey, at least I understand the distributive property, unlike you.

The reality is that there is nothing else out there like pulling points from a hyperbloid plus one variable to generally factor a composite.

It's the kind of simple but brilliant idea that would generate a lot of excitement, if I weren't the person pointing out the obvious, as then it just sounds self-serving.

Like, just consider a sample headline:

Amateur Mathematician Finds Way to Factor in 4-d

The real story here is that most academics are not creative people and know nothing about what it really takes to make a major discovery.

They can read about people who made great discoveries in the past but have no clue about what it actually takes or how hard it is, and how frustrating the process is, or how long it is.

So I take years to figure things out with a lot of mistakes and messy stuff along the way, and you people push that as proof that I must just be some crackpot, and then you refuse to acknowledge even simple things about the correct results once I've finally refined them to the level of total rigor.

What, you think that it was easy for any of them in the past?

Have you any clue what it took?

At the end of the day, people re-write history and make it seem so nice and glamorous or like it's about eureka moments in the bathtub.

Or you just have some dream and suddenly you have it all figured out!

Many a morning I've awakened wishing I'd get that dream.

It's hard work on a level you cannot begin to comprehend. YEARS of effort, working hard to understand, to find some truth.

It's actually about years of hard, very hard work, lots of failure, and finally emerging battle-scarred and wiser with knowledge that has never before been known.

And people like me are supposed to get at least a nod of appreciation here or there as if we don't pay that cost and take all that pain and misery to figure out these things, they just never get found, as who else is going to do it?


Want to take years of pain and misery, knocking your head against the wall of a hard problem, fail again and again, have to get back up and keep trying just with the hope that some day you MAY figure it out?

You people think it's about being brilliant so it's easy. So stuff just comes to you.

No. It's about working damn hard, night and day for years until you finally figure things out.

It's not about brilliance but about HARD WORK.

And because you can't comprehend that, you keep up your nonsense in replies to me, as you have no comprehension of what I've been through.

Sunday, March 12, 2006


JSH: Freaky, eh?

So yeah, I figured out how to do some mathematical analysis in such a way that I can easily generate factoring equations the like of which have never been seen on this planet.

I think it interesting that some of you have such a contempt for the textbooks in the field so that you come here on Usenet and, say, insult me, or claim my research just doesn't work and isn't of value, when I can just go out there, do a little research, and see there has never been seen anything like it before.

So yeah, that's how it's easy for me to just ignore a lot of you.

I rely on the known research in the field.

You're just some mean people on Usenet, what do you know?

I discovered the techniques I use to get my current surrogate factoring equations back in December 1999 so I have years now of familiarity with them, and they still are like nothing in the mathematical field, but they are my discoveries.

I have my prime counting function research where I use a partial difference equation--specially constrained--to count prime numbers, where it is also unique, though in that case, its similarities to what was previously known is telling!

A partial difference equation in prime counting, and Usenet people jumped up and down claiming it was no value, when there are no others known.

No one else in history from what I've been able to find has ever figured out a way to use a partial difference equation, constrained or otherwise, to count prime numbers, and because it is a partial difference equation with a partial differential equation analog, it may hold the key to answering the Riemann Hypothesis.

That information is easily found out by checking the literature.

Usenet people claim it's junk.

Usenet people seem to think that no one checks them on things they say.

Usenet people are wrong on that score.

So I think a lot of you are not very bright. I see many of you as simply territorial animals who see Usenet as your space when it's a public space, merely enforcing the point that you are not very bright.

So, short story is that I discount most of what most of you say immediately as, I don't see you as being all that intelligent, while you make points that I can just check the literature on—which I DO—and see that you're full of it.

Freaky, eh?

Some of you seem to think you're so brilliant and it's bizarre reading your posts, checking the literature, seeing you're clueless and then noticing that you are really excited over trying to protect your little corner of Usenet when it's a public space.

I have results never before seen, discoveries that provably advance the frontiers of human knowledge, and the knowledge that history shows this sort of interim period is quite normal and expected given those facts.

Fun stuff, yeah!

Saturday, March 11, 2006


JSH: You have nothing

Think back, those of you who have been on the newsgroup long enough, to my pointing out that mathematicians would fight the truth.

Now I have you on the record fighting the distributive property.

You people have nothing.

You cannot have mathematical proof, when you do not follow mathematical proof.

You're now less than religious zealots.

ANY statement you make can be challenged from now on, based on your proven ability to lie about what people might have thought before was of most value to you.

I told you years ago what you would do.

You people do not care about mathematics.

You care about your egos, you care about your salaries as professors if you are one, you care about your potential career as a mathematician.

And I can take all of that away from you, so you care about lying about, the distributive property.

You have nothing left for me to take.

You sold your souls. Congratulations.

Thursday, March 09, 2006


JSH: Putting it all together

What continually impresses me about the mathematics which proves my case is that it is so simple, and the proof relies on such basic logical principles—yet people can argue about them, and most mathematicians can ignore the results!

The mathematical story starts with the distributive property, commonly expressed as

a*(b+c) = a*b + a*c

where my brilliant and clever idea (if I do say so myself) means that you have the distributive property with functions, so you need to consider something like

a*(f(x) + b) = a*f(x) + a*b

and my dramatic, awe inspiring, and controversial position, over which mathematicians on this newsgroup have argued for years, and a paper got published and retracted by a journal which later keeled over and died, is that the value of f(x) <gasp> is irrelevant to the operation of the distributive property.

Yup, that's it. Sorry if you're disappointed given the build-up, but my position which is so controversial, over which so much discussion has gone on for years is that the value of f(x) has no meaning on

a*(f(x) + b) = a*f(x) + a*b

as if you accept that as true then when f(x)=0 is not a special case where you can have behavior one way, and then when x doesn't equal 0, have it go another.

If you think that can't be it that people couldn't argue against that position for years, I'm going to quickly make it more complicated for you by giving you the result valid over the complex plane that given

7(A'(x) + 1)(B'(x) + 1) = (A(x) + 7)(B(x) + 1)

where all the functions go to 0 at x=0, it must be true then, by the distributive property that

A(x) = 7A'(x) and B'(x) = B(x)

where I use the convention that A is the first function and B the second, though if you hate ordering conventions, you might argue that possibly

B(x) = 7A'(x).

And if you think that doesn't follow from the distributive property, think again.

After all, you can just check—get this—at x=0, as all the functions go to 0, and find that 7 must have multiplied through the first as you just have

7(0 + 1)(0 + 1) = (0 + 7)(0 + 1)

and if the value of the functions is irrelevant to the distributive property, then you know that 7 multiplied through the first for ALL x.

You see, the distributive property doesn't care what value x is…which is the crucial point that sci.math'ers have argued against for years, claiming that x=0 is a "special case".

What can you do in the face of irrational beliefs?

If some person says that 2+2=5, and you hold up two fingers, and then hold up two more and they say, yup, five fingers, what can you do?

You may think you can do something, but I'm here to tell you that if people wish to just argue away something and deny, they will just deny, just like posters deny that they're arguing against the distributive property when they do just that repeatedly.

So why would they? What's so important that people would argue about it for YEARS anyway?

Well, if you accept the distributive property and accept that it works for functions too without caring about what value they have then with a few simple ideas I call non-polynomial factorization you can prove that with the quadratic generator:

a^2 -(1+fx)a + (f^2 x^2 + 2fx) = 0

given algebraic integers f and x, it must be true that f is a factor of only one of the roots, but then you can also prove that in the ring of algebraic integers, if the roots are non-rational then f cannot be a factor of EITHER of the roots, so you have this nifty apparent contradiction.

Posters arguing with me say that I'm wrong, but remember, my results rely on the distributive property, so the way mathematics works, they are attacking the distributive property as that's the linchpin of the result—the keystone.

If you think, hey, maybe the distributive property DOES fail, then, um, you're in that 2+2=5 crowd, and you may as well move along, nothing for you here.

For the rest of you, the resolution to the apparent contradiction is that the ring of algebraic integers is missing some numbers—those numbers that would allow 7 to be a factor of one of the roots—and is doing it in a special way.

My favorite analogy when trying to introduce people to the problem with the ring of algebraic integers is to consider evens as a ring, as notice 2 and 6 are then coprime—because 3 is NOT even.

But now we're getting into heavy duty territory, as I'm challenging standard usage of Galois Theory, and it turns out, also the ideal theory, as the position that the ring of algebraic integers IS complete and cannot have the problem I describe, relies on, guess what, ideal theory!!!

Didn't know that?

Yup. The position that the ring of algebraic integers cannot have the problem I claim it does, relies on ideal theory. And ideal theory is THE basis for that position, so that it is just, well, it's just ideal theory!

But I can explain to you why I think ideal theory doesn't work very quickly, as, you see, it dosn't take into consideration convergent infinite series.

You see, if you append ½ to the ring of integers, you get the field of reals. If you append ½ and i to the ring of integers, you get the field of complex numbers.

It's like a switch. If you break the rules that give you meaningful coprimeness, then you break them completely. You can't break them halfway!!!

So what are those rules? Not to worry, I figured them out:
  1. 1 and -1 are the only rationals that are units in the ring.

  2. Given a member m of the ring there must exist a non-zero member n such that mn is an integer, and if mn is not a factor of m, then n cannot be a unit in the ring.

Those are THE RULES that are necessary for coprimeness to meaningfully hold in a ring, so that you can talk about factors and say things like 2 is coprime to 3.

If you break those rules, then you lose out on integer-like behavior.

If you append ½ to the ring of integers, you break those rules, so ideal theory fails and specifically, convergent infinite series step in, and you get the field of reals.

Denial is a potent thing. Mathematicians get taught things are a certain way, and I see a lot of posters talking about definitions. They seem to think these definitions are what mathematics is.

But mathematics is about what follows logically from the basic axioms.

Human beings can define away but if the definitions aren't in line with the basic axioms and what follows logically, then the definitions DO NOT HOLD mathematically.

It's like, define 2+2=5, so?

So there, you can see why mathematicians would argue against the distributive property for years as my ideas are revolutionary.

I can go from the distributive property to overthrowing ideal theory, and do it in a couple of pages using mostly quadratics and basic algebra.

No other achievement is like it in human history, resistance to it is unlike any other in human history.

Mathematicians do not want to admit being wrong, so I get to argue with people fighting the distributive property!

Remember the logical chain and how quickly it got hard for some of you, how I went from

a*(b+c) = a*b + a*c


a*(f(x) + b) = a*f(x) + a*b

with the DRAMATIC CLAIM that the value of f(x) doesn't matter to the distributive property, to pushing on you that given

7(A'(x) + 1)(B'(x) + 1) = (A(x) + 7)(B(x) + 1)

where all the functions go to 0 at x=0, it must be true—by the distributive property—that

A(x) = 7A'(x) and B'(x) = B(x)

and next thing you know I'm talking about the failure of ideal theory!!!

That's mathematics.

The logic flows from axioms by logical steps to a conclusion which then must be true.

Human beings though, well, they're quirky. When they get wrapped up in some idea, they can be very ornery about letting it go, even when it's been mathematically proven to be false.

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