## JSH: Math does not care

It amazes me that so many of you who seem to think you are mathematicians are really just people who like complicated stuff.

One of the most common criticisms of my work is that it's too simple.

Those of you who come across my postings who are outside the math field need to really think about that for a bit.

People in the math field criticise my research for being too simple.

These people LOVE results that few people in the world can comprehend as it proves to them that they are smarter than anyone else, so they hate simple results that are easily explained, as then it makes them feel less smart.

Most of my research leverages very simple ideas, and I like to use basic algebra as much as possible.

Simple means correct people.

Simple doesn't leave room for error, while complicated does.

I found that a lot of these complicated arguments that few people in the world understand—are wrong.

Rather than face the truth mathematicians mostly ignored my research, while some, especially on Usenet, turned to personal attacks, and a few would actually talk math, but refuse to concede to simple arguments explaining.

These people love useless complexity.

But the math does not care.

To mathematics there is no complexity in any argument. As far as the math is concerned there are no hard problems.

There is just what is correct.

Math people all over the world believe mathematics is their construct. They think they own it in some way so that it behaves according to their will.

But the math does not care.

When they are wrong, they are still wrong, even if few people in the world can understand why.

## JSH: Latest factoring idea, might work

I have been fascinated by this very simple yet very powerful quadratic residue result of mine, and not surprisingly, turned it against the factoring problem! (It looks like it can be used against Goldbach's, but that's not as sure a bet for me.)

What's weird here is that the freaking solution, is so freaking simple.

Because I found that the difference of factors of a composite are related to the quadratic residues of the numbers that add to give the composite, you can take any composite, find a couple of numbers that add to give it, and get info about its factors by these congruence relationships.

But I puzzled over that for a while not seeing a way to easily factor with that, until it occurred to me to force the difference of factors.

That is, if you have C, where C = p_1 p_2, then the difference of factors, p_1 - p_2, is, of course, enough information to factor C. But, of course, you don't have that difference.

But what if you multiply by ab, so you have ap_1 - bp_2 = 1?

Now you've forced the difference, but how do you find ab?

Well, my result lets you find ab mod n_1, where n_1 is some natural you get to pick!!!

It's so damn obvious that it just seems too simple, even now.

I am looking for someone to shoot down my exposition of the method in my other thread, to point out what's wrong with this idea.

If there is nothing wrong with it, then someone searching could have a very small search space with a large n_1 to factor even a large composite.

If this idea does work, it will be the second method that I've discovered that I think solves the factoring problem, as my previous hyperbolic factoring method, I think, should work, but it's complicated compared to this.

It is elegant in its own way though, and eventually I want to test it to see if it does work.

Guess I could easily test this latest idea as well, but I just can't bring myself to check factoring problem attempted solutions any more. They're just depressing in a way as they represent the need for force.

I mean, if things were the way they are supposed to be, I should have chosen going after Goldbach's Conjecture versus the factoring problem.

But things are messed up with current mathematicians fighting to keep the world from knowing about flawed mathematical ideas that I've proven don't work, so they have to be moved by force, as at this point, they show no signs of ever giving in to what's mathematically correct of their own free will.

## JSH: How can they care?

I'm sure you people want to keep the faith, but come on. How can any of these people you think are actually competent and excellent mathematicians keep so quiet if they really were?

I like to try and contact some of those big names every once in a while, as I try to find a way to break the impasse, which is why Mazur and Granville got early drafts of a key paper of mine.

Recently, I sent them some stuff about n^2 - r while I was on my way to figuring out my latest result, but got no reply THIS time.

They've learned.

If they reply, I talk about them on Usenet, when they sit quiet afterwards.

I fear that they do not give a damn about mathematics, and why should they?

It's screwed them over.

These people grew up being told mathematical ideas that I can shoot down with simple quadratic equations were gold.

They built their careers on research that my research shows is invalid.

What do they have left?

They just have the faith of the world, which keeps them in their positions, and keeps them getting paychecks.

What does Wiles have if the full story comes out?

Not only does he lose credit for proving FLT, but it's likely that ALL of his research over his entire career goes out, as not being valid mathematics.

These people get shot back to zero.

More and more I can understand why they would choose to sit quiet as in their position, would I do any different?

Maybe luckily for me I've been disillusioned so many times in life that it's hard for me to believe in anything any more, except what I can personally and simply prove down to basic axioms so that there is absolutely no room for error.

Then what happened to Wiles, Ribet, Taylor, Granville, Mazur and so many of you cannot happen.

If you all had gone through your lessons, proving everything back to basic axioms, you might possibly have found a flaw in ideal theory, and saved yourselves a lot of grief.

## JSH: So no, not heroes

So no, Wiles did not prove the Taniyama-Shimura conjecture, as his approach fails a simple logic test, failing by Cum Hoc, Ergo Propter Hoc.

The only reason he could step through an approach that might appear to prove the conjecture—if he didn't make any other mistakes—is that there is a problem with ideal theory.

It doesn't work.

I can show the problem with some simple quadratic equations, and explain the logic of the method that proves it, by way of the distributive property.

My ideas are formally peer reviewed and published, but by way of some social crap—an email campaign—some sci.math'ers broke the journal process and got my paper yanked by a gullible chief editor.

And later the journal died.

I contacted Mazur with an early draft of the paper before it got published, and he commented on it, and asked a question.

Andrew Granville got a draft in his role as editor of the New York Journal of Mathematics.

A math grad student from Cornell University, after noting the arguments on newsgroups contacted me out of the blue, offering his help in resolving the situation. I doubted his honesty, but he was persistent, so I sent him a simplified version of what went in my paper, and watched as he re-wrote it in his own words.

At the end he begged off.

## JSH: Power of myth, discoverer reality

I think I have mentioned this before that I am a big fan of the book THE POWER OF MYTH by Joseph Campbell, and I take his suggestion to heart to live my life like I am the hero of some mythological tale.

So there are quite a few postings in that vein.

With that said, hey, it is really starting to look like some kind of mythical tale where I do win out in the end, but not like how I thought, as, well, the simplest way to put it is, the discoveries just keep coming.

And thinking about it, that makes sense.

The major discoverers in mathematics are distinguished from the rest not only by how big their results are, but by them having more than one, or two, or even three.

And that is looking like what saves me, and confounds mathematicians who I think DO know about my research but suppose that they can sit on their hands, hope against hope the world never knows it, and have their lives work out ok.

I keep making discoveries.

And there is no protection against that, no way they could have realized, unless they read their history very carefully, that the major math discoverers tend to do that—keep making discoveries.

I think that is why the bad guys get to be the bad guys—and lose.

It is what they cannot imagine that undoes them.

If I had just one major result, or two—like I had—and they could watch those results not have any resonance, and people sit back while I was ridiculed, and get comfortable, it might make sense to think that they were safe.

But who could imagine I would just keep getting more?

And eventually, there would have to be a result that resonated?

If they could have known that then they would not have blocked for so many years, so sitting here, so many years after so much drama, including that destroyed math journal, and so much that has happened, the best explanation is that they did not conceive of me just continuing to find more major results.

And now Goldbach's Conjecture may be in reach.

I think there is a lot ot be said for the late Joseph Campbell and his ideas, and I think I will keep living my life as the hero of a great mythological tale, as increasingly, that is how the story actually looks, for real.

## JSH: Now you can see it happening

I'm reminding now with this quadratic residue result of when I came up with my prime counting function.

There was this stunned pause on the newsgroups for a while, as some posters realized I was right, and a few even admitted it was this neat thing.

Then the newsgroups recovered and posters came up with a couple of approaches:
1. Claim my prime counting function was Legendre's Method, or just claim it wasn't important.

2. Focus on speed, and emphasize that it was slow.
And YEARS passed, so now here we are again, with yet another result of mine after a bit of brainstorming and there's kind of the same pause, as certain posters like Magidin, and Ullrich, and the other usual suspects have to figure out how to convince people that this result isn't important.

Magidin has put up some stuff, where he just mentions old known things about quadratic residues, so he's already reacting a bit faster than he did with my prime counting function, where I don't remember him commenting much.

I haven't noticed much from Ullrich, but it's probably just a matter of time.

And that's how they do it.

MOST people suppose that important mathematical results wouldn't be attacked, so though they may wonder a bit, especially if they look at my research and compare it to what's out there, they TRUST that mathematicians as a group would not ignore something important, so I get stuck putting things on my blog, and whining about it on Usenet, where I get a lot of abuse.

So you can see it happening in real time, as, here we go again.

[A reply to someone who wrote that, since James was posting at a mathematical newsgroup, then he should post about Mathematics.]

Hey, I made a mistake as I may have started out wanting to talk of reminding now with the quadratic residue result and then shifted to saying reminded, but did not go back to change from "reminding" to "reminded".

As for math, why am I on freaking Usenet now anyway?

I am because the math establishment has succeeded at ignoring my results for years, so I have few ways to get the word out.

My point to you all is that they have to know what they are doing.

As you watch now with yet another result I want to emphasize up front that here we go again, so you can watch these people as I have watched them over the years with major result after major result where they just explain away, rationalize, and just plain lie about my research—and people believe them.

This is at least my fourth major result.

Notice though you will not see headlines tomorrow about this major research find which could lead to a proof of one of the most famous still unsolved problems in mathematics.

But if Wiles, or Ribet or Taylor, or any of a number of other members of the in-crowd of mathematics had the same exact results, math people would be falling all over themselves getting excited and talking about the possibilities surrouding this extraordinary link between primes, their quadratic residues and factorization.

The point here is that I am not a crackpot.

I do make mistakes—using modern problem solving techniques, like brainstorming.

Despite my explanation of what I do, and the demonstrations, repeatedly, of how powerful modern problem solving techniques are, I get ridiculed for using them.

My results are usually huge, and still people ignore them.

The issues here are political.

Here we go again, but I hope that some of you will start acting like educated adults, and this time I will see less support for the people who make it their business to attack my research using any distraction, lie, or whatever they can think of, to convince you.

I still hope—wonder how that is possible giving what I have seen over the YEARS—that some of you, will maybe, this time, use critical thinking.

## JSH: Battles are fun, eh?

So now as things head towards the end, you can get some sense of why mythologies get built around these battles.

Sure not a lot that really is supernatural going on. I do not see anything that most people would call dramatic in the way of, oh, I guess, weirdness that would really give a sense of why these things are so potent.

But the fate of the world is being determined, and the future is being decided by who wins and who loses, just like each time before.

Some of you are now totally slaves to the dark side, unable to see the truth, committed all the way to the bitter end to battling it out, even though it is getting clearer to those that can be saved, what this is about, and what is at stake.

People like me pioneered the mathematics that built civilization.

And people like me fought these battles thousands of years before, and hundreds of years before, as most people forget, only learning something about them, from mythologies and legends.

Maybe the real thing is not so dramatic in some ways, but in a lot of others, it is so much grander.

## JSH: Working on the solution, still

So now there's yet another twist as I found yet another result, and yes, now you people can try to claim yet another result is wrong, or unimportant.

So you can fight this quadratic residue thing like you did all the other research.

And what else will you fight, eh?

What other major results will you work to convince the world are crap?

How long do you think you can do it?

Do any of you have the slightest hint of a clue of how much I can discover?

And with every discovery, I learn more, gain more, and realize just how important it is for me to win.

After all, the future is depending on me.

## SF: Hyperbolic factoring method

It turns out I DID fix the problem with my latest surrogate factoring equations:

T = (x+(k_3 -1)y - vz)(x + y + vz)

x^2 + k_3 xy + k_1 y^2 = k_2 z^2

(2(v^2 - k_2)z - (k_3 - 2)vy)^2 = (((k_3 - 2)^2 - 4(k_1 - k_3 + 1))y^2 - 4T)v^2 + 4k_2(k_1 - k_3 + 1)y^2 + 4Tk_2

where my earlier equations were the equivalent of k_3 = 1, which won't work. Also, k_3=2, won't work, but other values should be fine, like k_3 = 3.

I really wonder sometimes if you people are suicidal.

I am deliberately posting after my post on the sum of primes being related to quadratic residues—which relates to Goldbach's conjecture—as I want it to be absolutely clear if you people continue to push this that you are doing so with your eyes wide open.

Make no mistake. If math society wants to put itself in the position of answering to a lot of investors, in a world that is changed forever because you people sat on your hands and wished I'd go away, then don't be surprised if people all over the world fall all over themselves trying to figure out ways to punish you.

## JSH: Two mysteries, quadratic residues still

Looking over these nifty results I now have with quadratic residues I am amazed, yet again, with simple research results available in yet another high profile area.

It is amazing to me that I just kind of think about some area for a little while and out pops a remarkable simple answer, and then there is the question of why didn't anybody else think of it before?

With prime residues I have two mysteries, so you can see how I consider these kinds of questions as I work to understand how centuries could pass without people figuring out things I just get, often with little effort.

With quadratic residues, people have played with them a lot for years and n^2 - r is not this new thing. Neither is the reality that it has a masking effect for r not a square, where I'm only interested in natural numbers, of course.

So why wouldn't people have routinely used that masking effect of quadratic residues to find primes?

My quick answer is, they didn't have computers.

Gauss didn't want to just get big primes. He'd want to do things like get all primes up to some value, or count primes.

They did want to know about relations of quadratic residues to each other, and Euler did a lot of work in that area, but did any of them care about questions like, how many primes up to 1000 have 2 as a quadratic residue?

Today, computers make it easy to ask lots of simple questions about quadratic residues and write programs that just go look. Even if you don't know a lot about the subject, modern computers are powerful enough that brute force will get you a lot of answers.

In the past, they had pen and paper, patience, and the will to know.

That's one mystery, but the other is odder as my simple result relating quadratic residues to Goldbach's conjecture did not require computers.

Playing with it does not require computers as you can look at p_1 + p_2 and consider this relationship with the factorization of 2(p_1 + p_2) and it's just this neat thing.

I am reminded of how I've often wondered about my prime counting function, and why wouldn't past mathematicians have figured it out?

The derivation is straightforward, and to me rather easy, though, as I've pointed out, no other human being that I've seen has been able to step through from beginning to end a similar derivation, even after looking at mine.

In any event, the Goldbach relationship is what is probably going to force all of this into the public eye, and maybe math historians can help then on the questions about how much was known before by my predecessors, and how they could have missed things that I so easily catch.

Oh yeah, so now you have some sense of why it is so difficult to handle a major discoverer.

History books don't teach you these things, I guess.

The problem is that you can't know what I'll figure out next, and I just keep figuring things out.

That's how people like me create history. We are so prolific that others can work for centuries on doors we open.

People trying to block my work would probably prefer me to just keep talking about FLT, which, you'll notice, is all that's even mentioned on Crank.net when it attacks me.

Some of you may focus on my research about non-polynomial factorization, working to try and block it.

While others are dismissive of my factoring approaches and terminology like "surrogate factoring".

Oh, and of course, there are those of you who actively work to block interest in my prime counting function, and the partial differential equation that follows from it, which could lead to proving or disproving the Riemann Hypothesis.

But now I'm going into quadratic residues and the Goldbach conjecture, and possibly it's sinking in for some of you now, you cannot win.

People like you may have been after Euler or Gauss, but history doesn't record it, so you don't understand the lessons of history, but I do.

I think this time it should be fully documented that people like you exist, that Newton wasn't just this nasty person, but likely faced all kinds of things, from people like you, that history didn't record, and that part of the problem—why people like you go on for as long as you do—is that you don't have worries about consequences.

I think now is the time to change that so that the lesson is indelible in history.

Yes, we always beat you.

Hmmm…yes, we do always beat you. Maybe the best lesson from me here is that winning wasn't in doubt, but learning about who I am, and what I must do, were.

I needed the challenge, I guess. I had to fight through, not just in discovering what I did, but in learning about humanity, and why it all is important.

It couldn't be easy.

It never is, for one of us.

## JSH: Goldbach, quadratic residues, brainstorming

So the point of brainstorming is to throw out a LOT of ideas quickly, where you know many of them are likely to be crap, and see where that takes you.

Well I went from crappy assertions about the twin primes conjecture, to nifty work on quadratic residues, to figuring out a relation between quadratic residues and Goldbach's conjecture.

That's brainstorming, and that's extreme mathematics.

Now I am very hopeful that the impasse can be ended so I shouldn't need the newsgroups anymore and besides, it's getting to where it's nearly impossible for me to put anything out here without dealing with a tremendous ton of junk in reply, so you people have done a very good job at convincing me that these newsgroups are a waste of my time.

But I put it all on my blog.

I keep wondering how so many of you can be so naive about problem solving, and so willing to follow along with people who don't seem to know very much more than how to be obnoxious in reply to me, as if you weren't, some of you could have made your careers by following out from lines of my research.

But now, you're too far behind. The rest of the mathematical world knows ahead of you, and there's no way to catch up.

And it's your fault. I was hanging out here first.

## Prime rules and extreme mathematics

Relying on my prime counting function I have some interesting rules governing primes, where it took a couple of days to them right!!!

Given a prime p, if p+1 has 3 as a factor, then p+2 is either prime or equals a prime squared.

If instead p-1 has 3 as a factor, then either p-2 is prime, or it factors into exactly two primes, or at least one factor of p-2 must be less than p^{1/3}.

Those are the correct set of prime rules, and it took me a couple of days to figure them out, where with the p-1 case it was a major mess.

But that's the discovery process! It's messy.

And part of extreme mathematics as I practice it is letting people in on the full discovery process, including the mistakes and failed arguments, along with the mirages, where you think you're right, but you're wrong!

Test the rules. It is extreme mathematics so maybe I missed something, but as these iterations go through that gets less and less likely.

## JSH: Irreducible complexity

I know the term has a bad connotation for a lot of people, but the reason my prime counting function is impossible for most people to re-derive, even if they read the derivation of it, is that it is irreducibly complex.

So your brain has a hard time figuring out how to start, or step through the derivation, even if you've read how I did it.

I think it may be one of the few irreducibly complex mathematical results currently known, and the reason it's irreducibly complex is that you can't break it down to simpler steps to understand the derivation.

Most of my research is irreducibly complex.

It's like you kind of have to know how it all works together ahead of time, which makes me wonder how I figured it out.

Oh well. In any event, to see what an irreducibly complex mathematical result looks like, check out my Wikipedia article now in the history of the prime counting function:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&oldid=9142249

I know it's weird, and it's even weirder if you try to derive it, as your brain tells you that you can, but you just can't. Or at least, most of you can't.

If you can, then you're not normal.

And that means your brain is wired differently than just about every one else on the planet.

## Screwy little prime results

I have started looking at my prime counting function looking for some kind of prime result that will break the current impasse, but so far just have screwy little prime results, where I had some troubles with the details.

Like I'm currently using a minor tidbit result that given a prime x, if x-1 has 3 as a factor, then it must be true that if f is a factor of x-2, f<x^{1/3}, or f>sqrt(x), or it turns out, f may equal the largest prime less than sqrt(x).

That's what I call a screwy little prime result. It is true out to positive infinity.

That's the result I've been using.

The special case where f equals the largest prime less than sqrt(x) happens if p is the largest prime less than sqrt(x), and floor(x/p) is prime, while floor((x-3)/p) is not.

It is only then that x-2 wil have p as a factor.

So that's what I have so far. I'm looking to get something bigger, but in the meantime, the tidbit result is fun to play with, and you can wonder about how it's proven!

I do have the proof.

Oh yeah, it's possible to prove it with previously known prime counting functions! You can use Meissel's for instance, but I think it's a bit easier with mine.

Can anyone prove it? Or do you think maybe what I said is false, and someone wants to find a counterexample?

Just try. I have the proof, so knock yourselves out.
Oh goody, I figured out a way to simplify it!!!

If x mod p equals 2 then you have the special case, otherwise you do not.

So I can toss all that about floor(x/p) and floor((x-3)/p), which makes it less ugly!

It's almost not screwy and kind of a nifty result now.

Can anyone prove it?

I can.

[A reply to someone who found a counterexample, namely x = 67 and f = 5.]

Yuck. You're right.

Maybe I should give the argument—which clearly is not a proof as it doesn't work—and move from there.
Ok, here's the latest fix.

If x is prime and x-1 = 0 mod 3

then either x-2 has only two prime factors, is prime, or its factors are less than x1/3 or greater than sqrt(x).

I was still doing the silly mistake.

The problem is that the prime p can be any prime in the interval from x^{1/3} to sqrt(x), and not just the largest prime up to sqrt(x).

I don't know if it's worth mentioning now at this point, but hey, at least I think that's it.

## A twin primes conjecture

From my prime counting function I can easily derive the following rules for twin primes, which I'll call a conjecture, as, um, I might be wrong:

Given a prime x where x > 3, if x-1 is divisible by 3, and for every prime p less than x^{1/3} but greater than 3 it is true that

x > 2 mod p

then x-2 must be prime.

I think that should work. It may be known anyway, but the key thing here is that you have this condition on primes less than x^{1/3} which is one of those interesting things, I think.

Now if only I could prove that there must exist an infinite number of x's out to positive infinity where all those conditions are met.

Oh well. Here's an example of it in action.

Let x=139. 138 is divisible by 3, so that condition is met.

The only prime less than 138^{1/3} and greater than 3 is 5, and

139 = 4 mod 5

so the last condition is met, and yup, 137 is prime.

A single counterexample ends the conjecture, of course.

The conjecture follows from my prime counting function easily enough, with a little bit of work, but I did it all in my head, so hey, I might be wrong. I don't think so, but I just thought it up in an effort to give this thing a little boost.

Can any of you re-derive it?

[A reply to someone who noticed that x = 233 is a counterexample.]

Yeah. Thanks. You get a counterexample in the following situation.

If p is the largest prime less than sqrt(x), and floor(x/p) is prime, then you have a counterexample.

With 223, the largest prime less than sqrt(223) is 13 and

floor(223/13) = 17.

That's the only way. The explanation for why I missed that is simple enough.

Oh, the full rules then are, if x is prime and

x-1 = 0 mod 3

and now the new rule—and with p the largest prime less than sqrt(x), if floor(x/p) is not prime, if x-2 is coprime to all primes less than x^{1/3} then x-2 is prime.

That is the absolute set of conditions which I can prove, so it's not a conjecture.

I did one dumb thing in the derivation which is why I missed that other rule.

Besides, now I think it's uglier. I liked it simple!!!

## Reality check: Counting prime numbers

Some of you may be to used to going to a reference to appreciate how hard it is to do something like figure out a way to count prime numbers, so here is a simple check, a reality check, where you need to do your best to stay away from references, as I want you at some point to try and figure out your own way to count prime numbers.

If you already know of some of the basic methods, then try to improve on them—without looking at a reference. See if you really know them then.

If you are an expert in the area then the super test which no one in the world to my knowledge has ever been able to succeed at, making it the hardest intelligence question known, re-derive my prime counting function.

To see it the best place is at the Wikipedia in an article I wrote that is now in the history:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&oldid=9142249

See if you can derive the function shown there.

The point of this reality check is to remind you all that finding something new, without help, and without references is not easy. It's not the kind of accomplishment that deserves ridicule, or calm dismissal.

If any of you manage to re-derive my prime counting function, without having seen my derivation, then please tell me, as I'm keeping up with the results of what may be the hardest intelligence test question ever.

To my knowledge in all of human history I am the only person to figure out that partial difference equation and how to count primes with it.

I'd like to know if any other human being is even capable of coming close, having at least seen the equations, which is more than I had when I figured them out from scratch.

I am sure that some nincompoops may reply in this thread with nonsense, but they will be ignored.

The reality check requires that you do something, and try.

Talk is not of interest to me.

## Meissel's Formula, who knew?

It's one of those funny things that years ago I was confronted with the reality that clearly Meissel was using a variant of my prime counting function:

http://mathworld.wolfram.com/MeisselsFormula.html

And, one mathematician to whom I sent it, years ago, said, something like, oh that's just a variant of Meissel's Formula.

He was wrong, but I'll get back to that.

So when posters kept going on and on claiming what I had was Legendre's Method, I could look to see if anyone corrected them to say, no, it's just Meissel's.

No one did.

My prime counting research more than any other research of mine has helped me to see how often posters lied, how routinely other people let them, and how easily people on the newsgroup could be fooled about basic things in the area of prime numbers.

Ok, so there is my prime counting function in its sieve form with y>=sqrt(x) plainly visible in part of Meissel's Formula, so did I copy from there?

Nope. Can't be as I derived my prime counting function from scratch, as a pure thinking exercise.

I just went at it for a couple of weeks thinking about how to count primes, and figured it out, completely off the top of my head.

But more importantly, I emphasize that it is the SIEVE form of my prime counting function with y>=sqrt(x) because that's a child variant, from which you cannot get the parent expression!

The parent expression is a partial difference equation and not a sieve.

But here is where things get really interesting, as there is just no way in hell that short and succinct formula I found is not important, and even if it were somehow not new, there's no reason not to show a short variant of Meissel's Formula, if it were that, which takes up only four lines to display.

But you see, the trouble for mathematicians is that it's not a variant, it's a parent expression, so it blows the lid off the entire problem, so they ignore it, and posters lie about it, screwing up details.

Why is it so important that I keep emphasizing "partial difference equation"?

Because a partial difference equation is just the discrete form of a partial differential equation!!!

So to get the prime count with my prime counting function, I'm doing a discrete integration.

The parallel is an integration of a partial differential equation.

However, I don't do a straight summation, but force the partial difference equation to count slightly off from what it would on its own with the rule that if y>=sqrt(x)

p(x,y) = p(x,sqrt(x))

which explains why the prime distribution is off from the continuous functions.

You see, it's off from the discrete summation as well!

So you have the answer for the why of the prime number theorem, plus the potential to directly calculate the error term, and check the Riemann Hypothesis.

All with one succinct expression of the prime counting function.

So for years now mathematicians have had the capacity to rigorously check the Riemann Hypothesis, and simply chosen not to do it.

They don't really care what the answer is, I think, as I think the answer is that it's false, so if anyone is checking, they aren't talking about what they found.

And I think they aren't checking.

Toss your books on the subject. Math society doesn't really give a damn.

[A reply to someone who asked James what did he mean by “sqrt”.]

Yeah, and I noted that part of the definition is the use of natural numbers.

You people look stupid.

On every point I refute you and you just come back and reply, reply, reply knowing that eventually I'll get tired of it and move on, but you still look stupid.

Trouble is, that your repetitive behavior does work.

People believe you. They trust you. So when I finally wander off, and you people start claiming total victory, they think I've been refuted, when every time I crush your claims, show your objections to be specious, and often show that you don't know much of the subject at hand.

So that happens with Peters and natural numbers, and with this Santos guy and partial difference equations.

The reason none of this matters though is that people naturally expect top mathematicians to step in for a major result and acknowledge its value.

While the people considered to be tops in the field sit back, and hold their breath, hoping that you people ignore the mathematical truth, this charade goes on.

So why do they sit back?

Think it through. ALL of my research kills sacred cows—pet ideas and methods of mathematicians all over the world.

Do you think they want a simple way to check the Riemann Hypothesis?

How do you get grants with that?

How do you pull in millions of dollars for your department with a simple answer?

How do you put your grads through? How do you hand out perks and approval for some while putting out others?

How do you maintain your status if some guy puts out simple answers to big questions?

These people don't think it's that important.

If it were a cure for cancer or appeared to be about life and death, then maybe they would step up, but they can tell themselves that it's JUST about prime numbers.

Get it yet?

Prime numbers aren't important enough to them to tell the truth.

Not when their careers are involved, which is why I get to argue with senseless and often stupid people on newsgroups despite having huge accomplishments.

And yes, if you had made those accomplishments instead of me, they would do it to you as well.

### Saturday, April 15, 2006

Can the continual arguments over trivial mathematics have a lot to do with bad mathematical educations where many of you don't know what a sieve is, or what a partial difference equation is, or properly understand the concept of proof?

Is it really that simple?

Could I simply be arguing with a badly educated crowd of people?

That could explain a lot.

What amazes me is how often I can talk about these things, people reply with nonsense and it not matter as there is a already a reply by some guy named Santos where he just claims that my research is on the current Wikipedia prime counting function page, but if you look, it's not.

But some stupid reader will look at that reply, and go, oh, yeah, someone is claiming that his research is not new, so it must not be!

Why is it that easy for them?

Direct evidence. On the history page where you can see the prime counting function article I wrote you can see it takes about four lines total to present my prime counting function.

Hey that's because it uses a partial difference equation.

Get a clue! Show some intelligence people!

It's succinct. It's succinct because it's THE ANSWER which explains the why of the prime distribution. There is no other research like it in the world.

But still some person just replies claiming something else is the same, and I've seen this happen again and again and again over the years, you people believe them.

On my side the issue here is, what's wrong with you people?

I am curious. I am frustrated because I keep defining human beings as people who can be convinced by facts, and finding my definitions fail.

So that's part of it, for those who wonder why I keep posting, as I'm trying to find the dumbness limit. I'm researching how stupid human beings can be in ignoring the obvious.

I actually do see people as closer to other apes after going through this experience, as more and more I see that facts are less important to most of you than, I'm at a loss.

It's like I'm trying to understand the minds of creatures at a level so much lower that it is difficult.

Like trying to read the mind of a cat. Why is the cat really doing that?

Not sure.

Why are you people really doing this?

I'm not sure.

## JSH: Denial is so remarkable

I read posts where some arrogant person will confidently proclaim that I don't know any mathematics and go on and on with this or that negative, as people repeat what they hear.

Ok, so that works with most people. So?

But I see other posters who will claim that no one believes me, and why do I continue if no one believes me?

You people are trapped by your social needs and befuddled that I'm not.

Are any of you real mathematicians?

I don't think so.

I find it so amazing that I can put up a concise prime counting formula, which actually explains the prime distributiion quickly, and succinctly because it uses a partial difference equation—and I know some of you must know why that's significant—but for those who don't it's why the equations don't require a sieve to count prime numbers, and find primes on their own up to the square root of the input number.

That is an explanation that Gauss looked for, and Riemann looked for, and unlike you people who are caught up in some kind of weird math glitz and glamor world, they actually cared about what the answer was.

But you read that the Riemann Hypothesis is the greatest thing in mathematics and is THE route to understanding the prime distribution as you people are no better than people who are caught up in celebrity news, and that's all that matters to you.

Screw the actual answer. You have pop culture math telling you what's important.

Oh, wow!!! Wonderful!!!

You just believe celebrity math.

You're such children!!!

Gauss actually cared about the truth. Euler actually wanted to know what was mathematically correct. Dedekind wanted to know what was mathematically true.

You people don't give a damn.

You play social games. You look for answers that suit people's careers.

And direct demonstration has no impact on you, but I promise you this, you will be as ephemeral as the rest of the style over substance world.

But you don't care just like "celebrity" people today don't care as this world no longer values knowledge.

It values claims. That's why George W. Bush can claim this or that, say Rumsfeld is the best person for the job, no matter what the facts say, or how many generals under him talk about his incompetence.

This world is about style over substance. Claims over facts.

People who think all that matters is if you have the crowd on your side.

Screw the crowd, what's true?

I want to know what's true. I don't care what millions of Americans believe is true.

I don't give a damn about what the "American people" have decided is the answer.

I want to know what is the actual answer. Not what the latest poll says is convincing.

You people don't give a damn about mathematics.

You are just so low, so base, yet you think you are part of the same society that Gauss and Riemann were part of?

## Prime research, how can people so easily lie?

I am just caught up on this question of how is it possible for me to show something in the area of prime numbers like my prime counting function:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&oldid=9142249

People can look at it, compare it with what's known, and nothing else uses a partial difference equation.

But some stupid people can just lie in posts and it's believed.

If they are not lying, let one of them, any one of them, put up a link here, to where people can see that my research is not new.

It's that easy. I'm giving a link to what I have. Someone needs to put up a link to some other research where a partial difference equation is being summed to get a count of prime numbers.

Lying about mathematis is SUPPOSED to be a stupid and worthless thing, as in mathematics you can just put up the facts, show the result and that IS SUPPOSED TO WORK!!!

But here you let people get away with making claims that cannot be supported by the facts, so you break the system.

## JSH: Things never before done

It amazes me how I can put up discoveries showing mathematics never before seen that explains big questions and you people can decide that the appropriate response is to lie about the mathematics and call me names.

There has never before been a direct link between a straight mathematical equation and the prime distribution.

No one figured out how to do it before. And no, sieve methods don't count, and brute force methods don't count, and Riemann's idea is just a hypothesis.

Don't you know he was looking for what I found?

And you stupidly lie and people believe the stupid lies when they don't even make sense!

For years a bunch of sci.math'ers were claiming that what I found was just Legendre's Method.

But Legendre's work doesn't have a partial difference equation!!!

When I'd push about the partial difference equation, people would start talking about it being slow!

You people are stupid. You tell stupid lies. And you just amaze me for acting so, so stupid!

So you push me to work on factoring. So I go ahead and figure out a new way to factor, trying my best to make it harmless, hoping some sense of self-preservation will step in, but no, you people are stupid. You are STUPID!!!

So I can put up a hyperblic factoring method and you just act like it doesn't matter that IT HAS NEVER BEEN DONE BEFORE just like you act like it doesn't matter that NO ONE IN HISTORY EVER FOUND A PARTIAL DIFFERENCE EQUATION THAT COUNTS PRIMES and I just keep realizing that you people are STUPID!!!

You people are just freaking stupid. You're stupid. You are stupid. YOU ARE STUPID!!

## Prime research, emphasis on the obvious

Now, once I again, I remind of an experiment where I wrote the first prime counting function on the Wikipedia, now available in the history:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&oldid=9142249

I wrote the entire article, while there are a couple of minor edits by others.

There you can see a p(x,y) function defined, where you see a summation.

That summation is different from any other summation you see in any other prime counting research (except maybe brute force techniques) as it is NOT a summation over primes.

That's because within the summation is a partial difference equation, so it's not a sieve method.

Because of that it directly links the prime distribution to a straight mathematical function, for the first time ever.

Not with a hypothesis, but with a direct equation, which is a difference equation.

Ok, so it's a difference equation, but it's still the first time the prime distribution has been linked to any equations directly, where in this case, importantly, there is this constraint that

p(x,y) = p(x,sqrt(x))

if y>sqrt(x)

where it is important as without it the COUNT IS NOT EXACT so you have this difference that steps in, which is the BEST EXPLANATION for why there is an error range given by the prime number theorem.

These are facts.

So why won't mathematicians acknowledge my research?

Because modern supposedly top mathematicians are assholes who care about themselves first and foremost and have been spoiled by a system that lets them get away with giving in to their silly little freaking egos.

And yes I am bitter.

These idiots have turned the system upside down, where a unique discovery is a means for the discoverer to face ridicule!

I want them publicly flogged. Yes, so yes, I am bitter.

It's so damn easy to see the truth here but while you little sycophants forget about mathematical proof and forget about giving a damn about the truth, these dumbass academic shits can get away with it!!!

So I blame YOU and I blame them.

If only any of you gave a damn about mathematics.

## JSH: Can I destroy history?

I have had my share of challenges and solved problems, but the greatest challenge to me is the question of history, and control of it.

Reading stories about discoverers where historians would say this or that person had this opinion or discovered this or that thing on this date, I wondered, how did they know, really?

For those of you who think I'm just some deluded person, it just sounds like more in that vein, but for those of you who may know otherwise, consider what I am doing.

I am going to make the history here.

My creation. Not what actually happened or how it happened, but my creative will to see if I can make another story, one that I know isn't the truth, and see if that becomes the historical record.

And no, I never plan on correcting it, if I succeed.

The full experiment is to change history--or what people believe is history.

To succeed, necessarily, once I destroy what actually happened, and remake it, I can never go over the details of what was done.

Already more has been lost than any of you realize.

And I have enough discoveries that I can pick and choose what the world will know, keeping some things already, to myself for all time.

It's the kind of game that only someone at my level can play.

How much information can I totally and absolutely control?

I will know, but you won't.

## Rings and valid expressions

There have been these discussions about my non-polynomial factorization research where the replies go on and on, when it can be about dumb things like square roots having two values (others arguing against, me arguing for), and considering the big picture, I think quite a few of them may be clipped by talking some about rings and expressions valid within them.

There seems to be confusion about the distributive property when you have an expression not valid in a particular ring, like consider the simple example:

In the ring of algebraic integers let

7*(f(x) + 1) = x + 7

—and you have a contradiction as the expression is NOT valid in that ring, as it requires

f(x) = x/7

so notice that SAYING you're in the ring of algebraic integers, doesn't mean you actually are.

Here you're pushed out of the ring.

Notice though that the distributive property still works so you have

7*f(x) + 7 = x + 7

and it's just that f(x) = x/7, so the value you get from a function does not impact the distributive property.

So 7 still multiplied through.

With more complex factorizations you can get more complex behavior so that when you move to

7*C(x) = (f(x) + 7)(g(x) + 1)

where f(0) = g(0) and C(x) is a polynomial

you can start in the ring of algebraic integers, have the equations valid in the ring of algebraic integers, but still get a result not valid in that ring.

That's where things get subtle and where it's possible for malicious people to confuse the issue.

Now the argument that shows that you're forced out of a particular ring, like the ring of algebraic integers, for certain expressions isn't complicated, and relies on the distributive property still.

Just like with

7*(f(x) + 1) = x + 7

where you can SAY you're in the ring of algebraic integers, and find something that may look to a naive person like you defied the distributive property, it's still true that 7 multiplied through, as the distributive property simply says that if you multiply a group, you multiply each of the elements within that group, so f(x) and 1 get multiplied by 7.

But you don't see 7 times x on the right side.

So? It doesn't change the distributive property.

With more complicated expressions you get more complicated behavior, so that with

7*C(x) = (f(x) + 7)(g(x) + 1)

where f(0)=g(0) = 0

you can find C(x), f(x) and g(x) such that you are pushed out of the ring if you follow logically where the 7 must have multiplied through.

What makes this situation frustrating is that the mathematics is simple to the point of triviality, and I think most of you can comprehend that a function can be outside of a ring, so that someone arguing against the distributive property who jumped up and down about

7*(f(x) + 1) = x + 7

because you can't SEE the 7 multiplied times x, would not be very convincing.

But with slightly more complicated expressions where the proof is simple, people seem willing to try and SEE the 7, and when they don't see it, they are convinced by posters like Rick Decker or W. Dale Hall, who make it their business to be confusing on this issue.

The value of the functions does not change the distributive property.

That is just immutable.

If you are mathematicians, given a proof, you will follow the proof.

When posters claim examples that contradict a proof, you will look to find what's wrong with their claims versus simply tossing out the proof as if mathematical proof meant nothing to you.

Doubt is a good thing. It should lead you to depend on what is absolute, and in mathematics that is mathematical proof.

The proof is simple with

7*C(x) = (f(x) + 7)(g(x) + 1)

on the complex plane, where f(0) = g(0) and C(x) is a polynomial

if you accept that the distributive property does not care about the value of what is being multiplied, then the value of the function does not change the distributive property.

That's the main point. Accept it or challenge.

If you accept it, then it must be true that if the value of the function does not matter then ANY VALUE can be used, and therefore, it follows logically that x=0 is valid as a useful value.

Accept that logical step, or challenge.

Now then, if it does not matter what value is used, so x=0 is valid, then it is just a matter of noting that at x=0 you have

7*C(0) = (0 + 7)(0 + 1)

showing that 7 multiplied through only one, and the proof is done.

Examples equivalent to

7*(f(x) + 1) = x + 1

do NOT REFUTE A MATHEMATICAL PROOF!!!

I think part of the problem here is that many of you do not comprehend what a mathematical proof actually is, so you think that proofs can be broken, or created, or they are fragile things that can shake with arguing.

But what proofs are, are points of truth that do not require faith.

You don't have to believe in some person or entity. You don't have to trust or worry about what education level one person has versus another.

All those are points irrelevant to a proof, so when people question my not having a degree in mathematics as my degree is in physics, you do not have to worry about that if you know what mathematics is about, as what you really need is the proof.

With the proof social crap is irrelevant. It doesn't matter how many people argue with me. It doesn't matter what your gut feeling tells you.

Trace the logical steps from a truth, and the conclusion that follows MUST BE TRUE.

See my definition of mathematical proof:

http://mymath.blogspot.com/2005/07/definition-of-mathematical-proof.html

The arguing would have been over years ago if mathematicians followed proofs as I have the proofs, people just lie about them.

Given a proof, argument is just a waste of time, because a proof cannot be refuted.

You may have heard of proofs being refuted. You may have heard of proofs failing, but then, they were not proofs!!!

If someone has proof that you are dead, but it turns out you are not dead (as none of you are) then did they really have proof?

Was it failed proof? Did their proof collapse? Can someone create a proof that you are dead and then someone else refute it?

NO!!! They just didn't have proof.

## JSH: Prime counting should be easier

I don't need the non-polynomial factorization result.

I think that the reason I can't get anywhere with my prime counting research is that mathematicians are worried about letting all my research in, so if I didn't have that find, then maybe I'd be making progress.

I think it's kind of a sickening result.

Over a hundred years of effort, all those people who thought they had it right, and all that effort, just lost.

I look for proof that I am wrong. I assume often enough that I am wrong, and then find that the mathematics goes one way.

Look at what's happening here.

You people went after a mathematical journal. It died.

Look at Decker, an otherwise seemingly thoughtful person, down to attacking the square root having two solutions.

You people are tearing apart your own world.

I don't like the result. It scares me about how wrong people can be on a huge scale, which really scares me given the challenges the world is facing as I have to realize that humanity can screw it all up, and then what?

What makes any of you think that extinction isn't around the corner?

The issues playing out here are about the future of the human race.

To the extent that the truth can be faced I believe that problems can be solved.

You have it all in front of you, and examples in other areas, like with America and Iraq.

Denial of the truth leads to pain and destruction.

If humanity cannot face its problems, it's doomed to be killed by them.

What? You think something or someone OUT THERE is going to save us?

Why? If we can't solve our problems, then, who will?

God?

## JSH: Negative politics

It's all politics now.

Posters can't match me mathematically, and now can't even claim counterexamples to my research as I've simplified, and removed room for the specious objections.

That leaves them nothing else to do but just SAY negative things, and notice the negative campaign has not stopped.

It's a political world.

Politics have always been important in modern mathematics as mathematicians who gained renown and developed a reputation could get more as a result, but a mathematical proof is a proof is a proof is a proof without regard to who discovers it.

You people made it political so that you say that mathematicians create proofs, and ascribe discovery to personality.

Not a surprise as you're not different from the rest of the world, but here instead of Julia Roberts it's Mazur or instead of Tom Cruise, you have Taylor.

Human beings have a NEED for politics and for celebrities and for special rules for people thought special.

So my research gets suppressed because you look at me as not being the kind of person you are willing to allow to have research at that level.

And the political campaign continues.

History shows that in situations like this, your group has to lose members and the people who are dedicated to the old system have to leave first before there is progress, which indicates this could take some decades, but I'm hoping.

As time goes on and people now children who grow up and read about my work and come to understand it move into the colleges and universities around the world, the politics will change, the heroes will change, and the story will move forward.

My hope, still, is that I don't have to wait for the slow process, but it may be necessary.

Your group may lie about mathematics for decades yet, generate so much worthless work in areas where I've shown the mathematical ideas you have don't work, and be proud of it, until the day when it's all known to have been wasted effort, and it's tossed out, as the new blood arrives.

I like to think that some of you would care about wasting your time, working hard for nothing except future repudiation in a world where people will know you had the opportunity to know the truth, but chose instead, to ignore it.

## Prime counting research, most telling

I like to talk about much of my research and push the reality of how simple it is, while mathematicians who supposedly care about important mathematics keep ignoring my results, but it's always with my prime counting research that people outside the field can check, and I am most puzzled by the behavior of the mathematical community.

I like to point out now that I wrote an article on the Wikipedia a while back which now is in the history:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&oldid=9142249

Sure it's a bit rough despite a few edits but not bad for a quick effort, and hey, how often do you write an entire encyclopedia article? It's a non-trivial task, even for me.

But, the way people go on and on about me and my research you'd think anyone could do it.

I have an explanation for questions about the prime distribution.

It's a simple explanation. Maybe it's not sexy enough for many of you, who love the complexity of the Riemann Hypothesis, but it's an answer.

I know you don't want the answer. I know because it's been years since I found it and mathematicians are still acting as if the answer isn't out there.

But it's the answer, so it won't change. You can go your entire lives, with lies, convince yourselves that you care about mathematics when you don't. Hold on to information that is not what is true, and it doesn't change.

The Pythagorean Theorem didn't actually belong to Pythagoras. Knowledge has value beyond your feelings about that knowledge.

Yes, I'm sure some of you would just as soon slit your wrists as live in a world where I'm known for what I actually accomplished, but it's not really my math.

You're robbing yourselves, robbing the world, and your feelings on this issue are just childish.

Hiding information from the world to attack the discoverer is not brilliant, and it's so obvious that you must have realized I could figure it out.

You people want to hurt me. And to you the simplest way is to deny my research.

So? People like to hurt each other. What does that have to do with mathematics?

## Square roots, two values

One of the more bizarre aspects of continuing resistance to my research are arguments that I keep seeing where people rely on the convention that square roots return a single value, to claim counterexamples.

But, um, people, if you have sqrt(4), sure, convention can be that the answer is 2, but reality is that -2 works as well.

There are TWO solutions. The square root of 4 is not just 2, but is 2 and -2 as EITHER WORKS.

Convention may be one thing, but the mathematics says that the function has two answers.

Some people a while back didn't like two answers for functions so they proclaimed that functions should have only one value. So?

It's a convention, a human thing, just something people decided to do, to claim that the square root function has only one value. The other value is usually just ignored.

But with my research both values have impact, so you can get wrong results by just throwing away the other value, and sometimes it takes me a while to notice when some poster does that, but whether or not I catch you it doesn't change what's mathematically correct.
1. The square root function by convention is said to return only one value, where people take the positive, by convention, but that doesn't destroy the other solution! So -2 is still an answer to sqrt(4) no matter what people say.

2. My research pushes mathematical ideas to their limits in this area, and the error of throwing away the other solution for the square root has an impact.

3. Posters who rely on the error which I am pointing out to claim counterexamples are just being deliberately obtuse.
I have brought this issue up before. There have been strange arguments where posters go on and on about definitions being important in mathematics and other weird stuff, but the reality is that the negative
value still exists!!!

I find it to be one of the more surprising aspects of all of this that so many of you act as if it is beyond your comprehension that despire the decision of some people over a hundred years ago that functions should only have one value that the square root of a number will STILL be two answers.

Can this issue die yet? Or am I going to keep seeing people claiming to refute my work by relying on taking only a single value for the square root?

[A reply to someone who asked for an example of someone formally trained in mathematics who would deny that there are two numbers that can be the square root of a number.]

Rick Decker and W. Dale Hall are in a thread on sci.math where they are pushing what they claim is a counterexample to my simple analysis of

7*C(x) = (f(x) + 7)(g(x) + 1)

where C(x) is a polynomial and where a given requirement is that f(0) = g(0) = 0.

Their functions f(x) and g(x) are two-valued at x=0 by clever use of a square root.

So you have f(0) = 0 or -6.

That's the kind of behavior that I've learned to expect from people fighting my results.

You don't give a damn about what is actually correct.

For those who wonder what the fuss is about, if you do cheat, and ignore the rule that f(0) = g(0) = 0, you can appear to break a proof.

The proof is that since the distributive property doesn't care about the value of what it's multiplying, since it's just the statement that a multiplication distributes within a group

e.g. a*(f(x) + b) = a*f(x) + a*b

is true regardless of the value of f(x), you can, when there is some question about how a factor, like 7 in

7*C(x) = (f(x) + 7)(g(x) + 1)

distributes, you can take a convenience value—because the distributive property doesn't care about the value of what's being multiplied—and check there.

When f(x) and g(x) are both 0 you have a convenience value, but they have to just be 0, and not multi-valued at that point.

That shows that you have this general result when factoring a polynomial in this odd way that 7 will distribute to only one factor giving you

(f(x) + 7)

which is why the 7 is actually visible there.

But you can find examples in the ring of algebraic integers where that conclusion shows a problem with the ring, which is what people like Decker and Hall are trying to deny.

But the result is mathematically correct, so they have to cheat.

In this case, they cheat by using the square root as single-valued.

To me the reality that people cheat over and over again to hide from correct mathematical results is a community problem. Your community does not hold its members accountable.

You people get upset about a result, and there's nothing anyone can do to force you to follow what's mathematically correct, as you're like a gaggle of children with no rule by authority, or deference to what is mathematically correct.

You care only about how you FEEL about a solution, not what is proven.

[A reply to someone who said that the use of the absolute value of the square root eliminates every ambiguity.]

Sorry, but if what you are trying could work, I'd go right along with it.

It just does not work.

If somehow, someway you could use the absolute value to force the square root to return a single value in a mathematical sense that mattered then that would be one thing.

But it is just the same as saying—take the positive root only.

Consider this, aliens on planet Contrary say that the absolute value is the negative!!!

Can you say they're wrong?

Does the mathematics on planet Contrary really differ from that on planet Earth?

Or is mathematics an absolute?

## JSH: What was the experiment?

So I talk about doing social experiments and it's a good time to talk about the one big experiment that has been on-going from the beginning of my posting, which is the question of how groups and individuals respond to the truth.

I have long been curious about whether or not correct information can be presented to people where that information is of great importance, and people just ignore it, or even reject it.

In the past I would even talk about taking down my own credibility as I sought to see if it were possible for the information in and of itself to get picked up by people without needing a personality thought to be correct presenting it.

Moving forward I can do things differently, and quite deliberately point out to you that it's a political campaign. I will just run the campaign differently and get a different result.

But what's remarkable to me is how crucial it is for someone you trust to present information to you!!!

Even in mathematics, none of you displayed in any significant degree an ability to simply consider the mathematics itself, where you could determine truth without concern about personalities, and many of you made decisions against your own self-interest proving that the problem is a critical one.

Such an experiment could not have been done without modern networks, and probably can't be done again, once people are aware of this one.

As for the ethics of it, I have no problem with those as I've more than once noted what I was doing, and more than once talked about truth itself as a higher ideal.

Reality though is that most of you believe what you are told and rely on the source of the information, meaning you are vulnerable to people who lie to you that you trust, and you will act against your own self-interest to a great degree to hold on to false information.

Even when presented with very simple mathematical arguments you held on to the false information, and posters often displayed a great deal of anger when their beliefs were challenged.

You dismissed extraordinary information, like publication in a mathematical journal, and even explained away the destruction of that journal.

I saw no limits to your ability to hold on to false information, reject correct information no matter how presented as long as the presenter was not credible to you, and continue with a great deal of confidence in your flawed knowledge.

I have at times injected information into the mainstream by other means to see it flow around the world and even get repeated by some of you relying on trusted sources.

My take on the situation is that there are few limits to the ability to control information and what people believe.

Trusted sources hold the power of life and death as this experiment reveals that people are willing to suffer harm to themselves to hold on to information easily proven to be false.

I think the study can now be concluded.

## JSH: Valuing knowledge

The lesson I've given many of you is that you don't actually value knowledge, but instead value your feelings about what you think you know.

So I can give mathematical proof, but the proof doesn't make you feel the way you like, and you ignore it.

I still think it fascinating back when "Nora Baron" was posting, when I stepped through a reply to that poster where I'd carefully refuted each point, and simply, so I knew there was nowhere for that person to go in objecting with me, so you know what happened?

For once I was curious to see a reply and anxiously waited unti it came, and then I noticed that everything I had put in was deleted out.

I was surprised when my paper was published by the now defunct Southwest Journal of Pure and Applied Mathematics, and then surprised again, when the paper was yanked.

The knowledge isn't mine, not really. It's no more mine than the Pythagorean Theorem belonged to Pythagoras.

It's just knowledge.

For many of you, knowledge in and of itself isn't of value, so you can look at my prime counting function and disparage it, as your brain says, that's his.

And you don't like that feeling.

Did it never occur to any of you that I know that?

I understand your feelings. But my point is that you don't value knowledge.

What will it take for you to value knowledge more than your feelings?

I'm not sure, but I think it's important enough for me to keep making the effort, as I've done for these long years.

I want you to value what you can determine is actually correct, not what you feel is correct.

[A reply to someone who wrote that James hasn't exhausted all the possibilities of quadratic equations.]

I use simple ideas which means I get to rely on a lot of basic algebra, and you people ignore the results anyway.

I just had to do a thread reminding people that the square root has two values.

The hatred of unwanted knowledge here is just so huge as to be inescapable.

You people will not accept mathematical information you don't like, not because it's wrong, but because you don't like it.

So I have to catch some of you on silly things, like trying to hold on to the square root giving one answer when it gives two but by convention people just look at the single answer, usually.

Why is this important?

Because with a factorization like

7*C(x) = (f(x) + 7)(g(x) + 1)

and f(0) = g(0) = 0

it's not just for kicks, or for fun and games that the requirement is there that f(x) and g(x) equal 0 at x=0.

But some human convention is that functions have single values so some of you get some examples where using square roots you have two values, but you throw the other one away—by the human convention—and claim I'm wrong.

That's like, so childish. It is so intellectually specious as to be, incredible!

It's increasingly like I'm dealing with small children, and not mathematically sophisticated people!!!

## JSH: So now it's easy

As people have argued with me I've continued to simplify and abstract, and now it has come down to a rather simple statement—though odd in particular ways—about factoring a polynomial:

7*C(x) = (f(x) + 7)*(g(x) + 1) where f(0) = g(0) = 0

in the complex plane where C(x) is a polynomial, and you have its factorization on the right, with functions that are 0 at x=0.

Add in the obvious logical point that the distributive property is uncaring about the value of the internals of the group being multiplied and you have the result that can be used to show that the theory of ideals doesn't work.

And that's why people keep arguing with me about it.

The distributive property is simply a statement that if you multiply a group, you multiply the elements within that group, so when 7 is multiplied times the polynomial C(x), it multiplies times the internal elements of C(x).

Being a clever person, I split up C(x) internally into two main factors, and ask the question, how does 7 or its factors distribute?

Using the logic that the value of elements within a group can't affect the distributive property, it's trivial to prove that 7 can only have multiplied through one of those two main factors of C(x).

Why is it a big deal?

Because you can take the general result—true on the complex plane—go to the ring of algebraic integers and get a contradiction!!!

So the ring of algebraic integers contradicts with a result valid over the complex plane, oh, and also valid in the ring of integers.

That proves the ring of algebraic integers has special properties previously unknown, which is why the result is generally invalid in that ring.

Considering the issues carefully that leads to the conclusion that ideal theory must not work.

It's such a trivial argument at the start that it is hard to believe that it leads to showing such complicated mathematical ideas as those used in ideal theory to be flawed, but that's how the wrong ideas stay in place.

Remember, I am the one here arguing who has a peer reviewed and published result in this area, though yes, sci.math'ers emailed the editors of the journal and managed to get my paper yanked, but it still went through formal peer review, and it still was published.

The mathematics is trivial to the point of disbelief that people could argue about it, or that it could shoot down such massive and long-held ideas.

And yes, mathematicians are just people too so they can sit on important information, hold on to ideas that have been shown wrong, just as easily as people held on to the idea that the earth was the center of the universe for so long.

You might say that ideal theory is the center of these people's universe and they refuse to let it go, even though it is so easily, and trivially, proven to be false.

## Polynomials, general factorization, distributive property

Here I will give an explanation with some basic examples, where I make the effort in the hope that it will clear the air about how I use the distributive property with certain factorizations of a polynomial.

Consider a polynomial C(x) with a constant term that is 1 on the complex plane.

Multiply it by 7 and factor it as

7*C(x) = (f(x) + 7)*(g(x) + 1)

where f(0) = g(0) = 0.

The reason the polynomial is multiplied by a constant is that in some of my research you get expressions similar to the above, where I'm abstracting for simplicity.

Now if f(x) and g(x) are simple linear functions, it's easy enough to see how 7 distributes through, for instance, if C(x) = x^2 + 2x + 1 and g(x) = x, then it must be true that

f(x) = 7x

where it doesn't mean anything in the complex plane to say that f(x) has 7 as a factor as so does g(x), though it equals x.

The mathematical terminology hasn't been developed for these types of arguments, so I usually just say that 7 multiplied through one factor of C(x), in this case, 7x+7.

I doubt many would argue that for any polynomial C(x) on the complex plane, where f(x) and g(x) are linear functions of x that 7 would have to have multiplied through the factor where 7 is visible, with the requirement that f(0) = g(0) = 0.

Well, let C(x) = x^2 + x - 1, and

g(x) = sqrt(x^2 + x) + 1

and notice that though it's not a polynomial it still must be true that 7 multiplied through the first factor, and again, as these results are valid in the complex plane it's meaningless to say that 7 is a factor of f(x).

But, of course, for this example

f(x) = 7*sqrt(x^2 + x)

and the question is how to describe the general case with

7*C(x) = (f(x) + 7)*(g(x) + 1)

where f(0) = g(0) = 0.

Now I can give specific cases repeatedly, but it's better to try and abstract out what's happening—why is it true that 7 multiplies through the one factor?

Can anyone give a counterexample where it does not?

I like these examples because I not only show the simple polynomial case—which should be very familiar—but I also give an explicit non-polynomial factorization where again you can actually see the result.

The question then for those who disagree with me is, can you have an explicit solution where the seemingly simple result that 7 multiplied through f(x) + 7 is violated?

Can you break my toy examples?

If so, give the counterexample.

If not, why not?

## JSH: Power of suggestion

Ok, time for a break, but hey, isn't this fun!!! Don't worry, posts like this one won't change the effect as it is long-lasting. It has to do with how information travels within the human brain.

You depend on those cycles—I call them—to maintain your personality and concept of reality as firm.

What I can do is, you could say, loosen the brain's sense of reality as being this solid thing, and cause you to have a more relaxed point of view.

Some of it's suggestion and part of it is using contradiction in special ways.

What's odd about it is that you can tell people what you're doing and it's not a protection.

The only protection is NOT to read my posts!

Even I have to be careful with some of them now, as you have to concentrate to keep your grip on reality.

As we move forward for some of you it will be an invigorating experience. Ideas will come to you, and your perspective will shift.

The world will look different.

But for some of you, it will terrify you. Things will happen that you can't believe and some of them, unfortunately, will not be real, but your mind may have some problems of which you are not aware which will be revealed by these techniques.

Look for them—contradictions, odd phrasing—things that seem just slightly odd, and understand the power of suggestion in all of it, as you know, it's how magicians do it!!

Reality is firm, but your view of it is not. Your view of reality is what can be shifted.

Ok, enough fun, as I'm thinking that maybe for some of you it's time to sleep. You know, there's all that work done, and now it's time to do something else.

And besides, I need to talk about math, like some primes or something.

Sleep isn't bad for thinking about math, as sometimes, ideas come to you early in the morning, if you wake up early.

## JSH: Should we talk?

The guy who runs Crank.net claims on his website to be in San Jose, which is not far from here.

Maybe I could just drive down there and TALK to him and we could work things out?

What do you think?

Do you think he's a reasonable person?

Can't two men just get together and discuss some math and work out all this negativity and namecalling versus allowing distance to matter?

It seems that in the past things were simpler, people could just talk to each other. Maybe all this high tech just distances us all too much. You know?

Do any of you recommend that I try to visit Erik Max Francis in San Jose?

He's not far from here. It shouldn't be difficult to go.

I think your advice on this matter is of importance. I want you to reply and help me figure this out.

## JSH: Wonder why?

The real story here is that I stumbled across simple results that disprove the value of ideas thought brilliant, which is why they are "pure"—they don't work.

You see, it's not that they might someday have practical application.

It's that they are wrong, so they can never be practical.

The key result was peer reviewed AND published, but notice how sci.math'ers reacted to that publication!

You people cannot handle the truth.

## JSH: Experiments beginning

I have used the newsgroups primarily for brainstorming purposes where I come up with ideas and find that I can more easily judge them and find flaws when I talk about them, and at times posters DO give cogent criticisms which I can use. Also I get information on mathematical topics.

However, given that the mathematical community has shut the door on journals, it seems to me that I need to expand how I use the newsgroups and look to using them as a backdoor into the mathematical community, so that I can break through the current impasse.

That will require that I do some research, which some might consider dubious ethically, so I'm giving fair warning upfront.

In the past I didn't care much about responses and would play at things here and there, but not seriously.

Now that changes.

Some posts will be purely for an effect, where I can do things like see how Google search results shift as people change their search patterns to see what happens.

Some experiments may be in some ways detrimental to a sense of well-being of some of you, while, there is a small chance that for some of you some of the postings may have a dramatic impact.

I will rely on modern psychology, sociology and theories about group dynamics as well as the latest research I may find on neurophysiology and, here and there other things I might throw into the mix.

There will be no further warning, and you will, hardly know exactly what's happening, as it's happening, understand sometimes bizarre changes you will see in the newsgroup, or comprehend some of the behaviors you will see.

This post is, of course, itself the beginning. The information I've given you is partly to introduce the IDEA of the experiment, so that the concept itself will begin the changes I need.

Knowing that is no protection, and in fact, thinking on this subject will only deepen the effect.

Reading this post more than once, may not be good for your mental health, so I recommend that you only read it once. Sometimes the actual postioning of words, pattersn that are hidden to the naked eye, and special phrasings are simply meant to induce certain effects in your brain.

This post should only be read once for many reasons.

## JSH: Consistency check, Riemann Hypothesis

Being a real researcher with wide interests I can talk about my other mathematical research, which should foil posters who like it when I can focus on one thing, like notice at the Crank.net page that rips on me, that guy only talks about my attempts at proving Fermat's Last Theorem, and lists for supposed refutations of my work, only links talking about older arguments.

That focus on one area is keeping it simple: convince the people with something simple as that's the easy way.

That's part of the consistency check: posters trying to convince you that my work is of no interest need to focus on just one piece, while I have multiple results.

So what does that have to do with the Riemann Hypothesis?

Well, supposedly mathematicians are enthralled by this hypothesis and the question of whether or not it is correct, but I'll give you evidence in this post that actually they aren't that interested in the answer, but instead wish to just hold on to it as being correct.

I can say that because one of my other research results is a find of a special prime counting function, where it's special in that I found a partial difference equation that is SPECIALLY CONSTRAINED so that it counts primes. I put those words in bold because that's very important, and I'll come back to it later.

Reference:
http://mymath.blogspot.com/2005/06/partial-differential-prime-counting.html

Ok, so I found a way to count prime numbers with a specially constrained partial difference equation, so, like to count primes up to 100, it finds, on its own—without any sieve—that 2, 3, 5 and 7 are primes, and it spits out the answer 25.

So because it uses a partial difference equation it finds primes as it counts.

Nothing else in known mathematics does that, and that's not a debatable point—it's an ignored point.

But that ability makes the pure math version slow.

The pure math is slow, but you can get algorithms that DO use sieves to speed it up.

And in fact, I did so and made a fast Java program that for its size may the fastest possible, and the fastest currently known—for its size and complexity—in the world, despite being a Java program.

But posters don't talk about that, they compare it against the fastest known period.

That's another consistency check.

So what does this have to do with the Riemann Hypothesis?

Well, remember I emphasized that the partial difference equation is specially constrained, as you have to force it to behave and give a count of prime numbers, but if you don't constrain it, get this, it's slightly off.

It's just slightly different from the prime count.

It has a partial differential equation analog which is close to the partial difference equation, unconstrained.

Any of you getting it yet?

My find indicates the reason for why the prime distribution is close to continuous functions, but also tells why it's not exact: there's this special constraint to the partial difference equation that forces an exact count.

So, it indicates that the Riemann Hyothesis is probably false.

However, standard mainstream mathematical belief is that the Riemann Hypothesis is true.

Now going from the indication that I have that it's false to proof could take who knows what effort, but mathematicians will not make the effort.

In case you hadn't noticed, my results are overturning results.

Every one of my research finds kills a sacred cow of mathematicians.

So far they have been able to hide that fact, go on with what they have, and convince the world that they are serious about mathematics.

The dirty little secret though is that mathematicians don't care about the correct answers, but care about holding on to the answers they believed were right before I came along.

My research takes away ideal theory, standard interpretations of Galois Theory, and in so doing takes away much of a hundred years of mathematical ideas and papers, and that's just one side of it.

My research with prime numbers may take away the Riemann Hypothesis.

So the inner side of the motivation for mathematicians all over the world to avoid my research is that I take away too many cherished beliefs.

The dirty little secret is that acknowledging my research means that most of what many mathematicians have thought was true, goes away, and what is actually the truth is not what they want.

Consistency checks are a good thing.

## JSH: Political realities

Let's face facts, the arguments are not really that substantive in terms of the mathematics.

So I can give

7*P(x) = (f(x) + 7)*(g(x) + 1)

where f(x) and g(x) go to 0 and explain the logic of it all indefinitely without it mattering what's mathematically true because of the politics of the situation, and the reality that my results overturn the idea that mathematics is immune from overturning results.

So mathematicians will be damned before they ever admit there's a problem with the definition of algebraic integers, and they will refuse to admit that something as hallowed as ideal theory could be simply flawed.

Proof is irrelevant to the politics of the situation.

What is fully revealed here is what's not new: human beings can say something, like mathematical proof, is what's important but reality is that what they think they can get away with, is what's important.

If mathematicians thought for a second that the world might take me seriously, look into my research and realize that it's correct, top mathematicians all over the world would be falling over themselves to talk about my research and its importance, as the proofs are the easy part.

But you know and I know that the arguments can go on indefinitely and the world can be fooled indefinitely so they keep quiet, not even caring about therefore dooming their place in history.

Mathematical proof is great as a concept, but human nature has evolved over quite some time, far longer than that concept and human nature is winning here where I can show over and over again that people are arguing against the distributive property to fight my research and itnot matter as at the end of the day, human beings are apes slightly more evolved than their cousins, and often the least important thing is what people say is important to them, when the impact of the truth isn't what they would like.
One of the things I find MOST fascinating in discussions on this newsgroup is the importance some of you seem to attribute to SAYING my results are wrong, and I guess getting that feedback from others in agreement with you, or at least not disagreeing with you.

But wait, I have mathematical proofs and research results that are HUGE in terms of impact, such that Gauss himself would be proud to have any one of them. I figure, hey, resistance is likely, and not surprising, especially since my research steps on so many toes, and eventually these things get worked out in favor of the truth.

So I can relax and try to have fun.

You know, like, I'm a major discoverer, probably one of the most important in human history.

I might be better off not having to deal with many people knowing that for a while, as then it's like having a vacation, and it's fun arguing about my results.

So, it's not really a big deal from one perspective, though I do find myself endlessly fascinated with the ability of some people to delude themselves, and feel important while they're putting on a show.

These threads are partly my statement as a discoverer against social orders that can create messes like what is happening now in Iraq.

They are MY way of showing people that it is important to fight always for what is true, as otherwise you may find yourself in a conversation with a person who is, well, not someone you should be arguing with, and have yourself a part of history in a negative way.

So yes, I've let some of you make yourselves infamous to prove what I think are important points, and no, even now, you may still not know it, which is part of the endlessly fascinating piece!!!

Meanwhile, I get to stay on vacation, in a world that needs people like me to inspire and to help solve pressing problems, and I get to blame you people for it.

Vacation is nice. I have a world of people to mix and mingle with who have no idea of just how powerful I really am, which is a good thing, I think.

I can come here and argue when I feel like it, or wander about in the world at large, anonymous, with abilities far beyond what any people around me dream are possible, thanks to many of you.

April Fools!!!
That was kind of fun, just replying to people no matter what, and to show something as you can see what good it does.

Some of you seem to be fascinated by the issue of me abandoning threads.

I do so because inane posters will reply, reply, reply no matter what to clog them up!

There is a process going on which requires that members of the mathematical community act together as a group to try to contain the information.

So they have their tactics, and I have mine.

The mathematical community is like a creature fighting for its survival using its members to try and hide the truth. I am the hero fighting the many-headed monster ya da ya da ya da blah blah blah as the mythologies predicted, and being who I am, I can't give up, and what I'm fighting can't give up so you see this drama.

Hey that's why the stories are so fascinating.

You get this interminable battle that just goes on and on, and one of my people gets born, fights for a while, crushes the bad guys, and then there's another gap, and then the battle gets fought again, and in the meantime people tell and write stories, come up with mythologies, and we become so much bigger!

It's kind of cool, but I can think of other things I'd rather be doing, but hey, got to fight till I win.

That's what my people do.

And later some will write stories and legends and try to imagine what could it possibly be like to be any of us, and imagine that they would have been on the winning side.

I make history. That's what my people do. Others get to watch, get crushed, or read about it all later.

## Mathematical logic & distributive property

There have been some long going and somewhat strange arguments on the newsgroups which boil down to misunderstandings from some about the distributive property when functions are involved, so here is a short discourse that explains the mathematical logic in simple but exhaustive detail.

The distributive property embodies the concept that when you multiply a group you multiply the elements within that group in turn as well, so

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

is just a simple way of mathematically saying that, and notice that if you have functions, so that you have

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

you have a situation where the value of the function is irrelevant to that operation, which is to say that even if a function is the member of a group being multiplied it still gets multiplied with the rest of the group regardless of its value.

You see, the function kind of gets dragged along with everything else. Being a function gives it no special powers in that situation!

So, if at some value of x you have that the function equals 0, that doesn't change the distributive property, asf or example at that point with what I have above you just have

a*(0 + b) = a*0 + a*b

which is just a*b = a*b which is, of course, still true, as the VALUE of the function is irrelevant, as the key fact is that it is a member of a group that is being multiplied.

Now to the type of example that has sparked SO MUCH ARGUING and debate from primarily the sci.math newsgroup:

On the complex plane given the polynomial P(x), and functions f(x) and g(x)

where f(0)=0 and g(0) = 0

let

7*P(x) = (f(x) + 7)*(g(x) + 1)

which I'll emphasize is true for all x, it must be true by the distributive property that 7 has multiplied through only the factor

f(x) + 7

where by "multiplied through" I mean 7 has multiplied times only one of the two factors of P(x), where the product is f(x)+7.

Now given that there MUST be two factors it can seem reasonable to suppose that 7 split between those factors, except that if it did, like say sqrt(7) multiplies times each, then by the distributive property, what must happen?

Obviously then sqrt(7) would show in the factors so you would have something like

7*P(x) = (f(x) + sqrt(7))*(g(x) + sqrt(7))

where the logical principle is easy—the value of the functions inside the factors of P(x) is irrelevant to the operation of the distributive property, so you can check at x=0, to see how that occurred, just like with

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

when I could consider a value where f(x) is 0.

Some posters have proclaimed that the 7 itself must be the product of two functions, so that how it multiplies through varies as x varies, but, um, how do you even know about x with those expressions?

So their claim is that the functions are somehow reaching outside of their groups to control how their group is being multiplied in direct contradiction to the logical principle that with

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

the value of the function has no impact on the how the distributive property operates.

And remember the distributive property is just telling you that if you multiply a group, you end up multiplying the elements within the group as the multiplication distributes through.

One way to look at the arguments of posters claiming the functions can force how 7 multiplies with

7*P(x) = (f(x) + 7)*(g(x) + 1)

is to use the expression "tail wagging the dog" to emphasize the point that the functions just don't have the capacity to affect the simple principle that when you multiply a group you multiply the elements within that group.

So if it's that easy, why would people argue against what I just said?

Well, consider what I've called the Decker example—in the ring of algebraic integers

7 Q(x) = 7((x^2 + x)(5^2) + (-1 + x)(5) + 7) = 7(25 x^2 + 30 x + 2)

and

7 Q(x) = (5a_1(x) + 7)(5a_2(x) + 7)

where the a's are defined by

a^2 - (x - 1)a + 7(x^2 + x) = 0.

NOW we have some complexity!!!

But is it really all that complicated?

I'll leave it as an exercise to see if posters think that with this simple example the rules have changed.

Think of it as a test. Given what you have above, what must be true with the Decker example?