Monday, November 27, 2006


JSH: You people are stupid

Ok, let's just put it out there, you people as a group are stupid.

There is no way there can be nothing to my research when there is so much math behind it that says it has to be important.

No way.

It is complete bullshit that rules your world, which is how you people keep posturing despite your rank stupidity.

Only stupidity could explain the failure to even look into integrating that partial differential equation.

Only stupidity could explain the ability of posters to keep going on and on despite there being no other prime counting function that can even recursively call itself.

And that's just my research related to the prime count.

Only people stupid on a massive scale could ignore publication in a peer reviewed math journal, for an argument so damn trivial I can go over it in a couple of paragraphs using basic algebra.

You people are just damn stupid. Your community is stupid.

You are willfully stupid, stupid, stupid.

[A reply to someone who said that James is a “ranting tit”.]

At least I am right and have the mathematics to prove it.

I even got published.

You damn fools just said, duh, publication doesn't matter!

You are stupid.

I have the mathematics to prove my case.

I've had it for years.

Your society is just too damn stupid to go with the math.

You're just too damn stupid and full of yourselves.



JSH: Four years plus of failure

It has been over four years since I found what I call my prime counting function.

It is still an open question how closely the partial differential equation that follows it maps to the prime distribution because the current math world is broken, and rather than consider the answers to that question, most mathematicians have ignored me, while you can see the posters here who just work to dismiss the research.

The lack of answers is the fruit of their labors.

That's what such people are about, no answers, no solutions, ever.

Has it occurred to any of you that you could die, and a day later, some person or persons could finally look into that partial differential equation I found, and answer huge questions in mathematics, and the world go on and on about this amazing thing that research thought quack from some crackpot turned out to be important, but no one knew, because no one checked.

And mostly in looking over the history, they could see years of posturing from people who never did anything of value.

ANYONE can criticize.

You have four years plus to see the value of posters just calling me names and claiming my research is not new, as now you may know that yes, I did find a partial differential equation that follows from a prime counting function.

And it's an open question as to how closely integrating that partial differential equation gets you to the prime distribution.

STILL an open question, over four years later.

Still there are posters who seem to think this is just about posturing on some newsgroups as if no one cares if the question is EVER answered.


What kind of human beings does this make you to be, when you are so incurious, so incapable of wondering at the miniscule level necessary to get some answers?

Instead you sit by and either promote or are in complicit in just blanket do-nothingness.

A world of no answers, just talk.

Four plus years of total failure from your group and your community.

That's what the world has today.

Four plus years of total failure to find any kind of answer.

[A reply to someone who asked why is it that this is not a failure from James.]


You are the goddamn fools who refuse to check and then keep going on as if you are intelligent when you will NOT EVEN FUCKING CHECK!!!

Sunday, November 26, 2006


Functions with 2nd generation arguments

I like to separate mathematical development out into generations, where first generation approaches were covered by the traditional mathematics that most people think of when they think of "mathematics" or "math", followed by the 2nd generation of problems that can be covered by what I call extreme mathematics, followed by a 3rd generation of problems to be handled by generations of mathematicians yet unborn.

The first generation of mathematicians dealt with functions with simple arguments, like f(x) or f(x,y), etc. and only came close to more complex arguments with things like e^{-t^2}, while the 2nd generation comes out of the box with more complex arguments, like in my prime counting function in its various forms where you have functions with arguments like P(x,sqrt(y)) and P(y,sqrt(y)), which probably creates confusion for people brought up on the more primitive techniques, so this post is about understanding functions from 2nd generation math problems.

A function takes an argument and carries it to something else where that something else can be an explicit expression, for instance:

f(x,y) = x + y

carries arguments to the explicit expression x+y, where the first argument goes into x, and the second goes into y, so also

f(x,y^2) = x + y^2

as the more complex—2nd generation—argument has simply been carried to the explicit expression.

That's it. That's how more complicated arguments are handled in more advanced mathematics.

The argument itself is simply like an instruction to take this thing and place it inside of some other thing in a special way.

And you can still manipulate the functions using algebra like always as notice you can subtract the first from the second to get

f(x,y^2) - f(x,y) = y^2 - y

without any problem.


JSH: Minority view

A few days ago I asked that readers who use Google Groups use the ratings system that is provided through it where you can rate posts from 1 to 5 stars.

I have looked over threads that I created to talk about my research and found that along with my ratings, as I've started now routinely rating posts, I usually see 3 or 4 others and at times maybe 10 who have bothered to vote.

Giving the benefit of the doubt to opposition, let's say there are about 10 people out there then who disagree with me and are vocal in that disagreement.

Well I just checked Google Groups to see how many people it says subscribe to sci.math and it said 5,506, which is the number through Google Groups, so it's a lower number than the readership.

For instance, I don't subscribe to sci.math so I'm not part of that count. But, of course, I post on sci.math a lot.

But let's go with the low number to be fair and now go with the high number for the opposition based on ratings to get 10/5506 or about 0.18% of the sci.math readership clearly disagrees with me.

So I have one point of view and about 10 or so other people who don't seem to have any other support based on the ratings, argue with me, and that generates a lot of posts.

I like the ratings system as gives an overview of how many people on sci.math care to vote in one direction or another on these topics where if you just look at the volume of postings you might wrongly assume that the majority of sci.math is wrapped up in these discussions, when from the ratings, most don't care.

Actually, only about 0.18% clearly show that they do care.

I suggest you use the ratings if you use Google Groups. There is just no denying that much of the newsgroup doesn't care one way or the other when there is no voting for your point of view.

Friday, November 24, 2006


JSH: Under review

I wrote another paper and sent it to the Annals of Mathematics which verified receipt.

A version of the paper is at

and in keeping with the philosophy of extreme mathematics, I would appreciate comments.

The paper is under review as Princeton verified receipt. Uh, yeah that surprised even me.

This thread is for comments on the paper.

And yes, this paper could end it all. If Princeton does what it should then it doesn't matter what any of you say, as you know and I know that Princeton trumps every last one of you.

I especially welcome comments from posters who argue with me regularly.

I am curious though. Read the paper, and come back and post as confidently as you've done.

What gives you that faith?

[A reply to someone who wrote that, when the paper is rejected, James will blame the sinister cadre of sci.math again.]

No. I know and you know that Princeton doesn't give a damn what you think.

There is only one case where sci.math definitely interfered and killed a journal and that is with SWJPAM.

There is no way that Princeton would fall in the same way.

You people can't kill the Annals of Mathematics.

I dare you to try. Send your emails. Just try.

[A reply to someone who explained to James how uninteresting and dishonest his paper is.]

The replies in this thread reek of fear.

What I actually did was go from a prime counting sieve function, to a constrained summation of a partial difference equation that counts primes, to the partial differential equation that follows from it.

The three forms connect the dots from the discrete count of primes to a continuous function directly, for the first time in mathematical history, showing how the count of primes connects to continuous functions, and accomplishing what notables like Gauss and Riemann set out to do so long ago.

That is done in just two pages, and is an accomplishment at the pinnacle of human achievement in mathematics, but it's also an accomplishment members of the sci.math newsgroup have enviously and jealously fought to disparage.

It is one of the greatest accomplishments in the history of human thought.

It is more than a great enough accomplishment to merit publication in one of the world's top math journals.



A member of the sci.math newsgroup managed to get past my screening and join the group, revealing himself when he systematically down rated all of my posts.

I have banned that person from the group.

It shows you how these people operated.
Looks like people not members of the group can rate posts so I was wrong on that point.

As shown by a group of sci.math'ers who came in to downrate my posts.

Still, it shows how these people operate.

There was other evidence the banned person was a hostile sci.math'er so I'm comfortable with the decision to ban that person.

I do wish Google would allow you to only let group members rate posts, as I think their Beta still needs a bit more options for group owners, as this current ongoing sabotage by members of the sci.math newsgroup shows.

The juvenile behavior from members of the Usenet sci.math group reveals a clear weakness in Google's current setup.

Wednesday, November 22, 2006


JSH: Use ratings

People coming in with Google Groups can rate posts, and I'd like more people to start rating to help me pick which people to reply to.

If this experiment works, I'll start going more by group opinions on posts.

I'd like to try and see if more of the crap posters can be weeded out in this way, as they are down-rated to a level that I know I can completely ignore them from now on.

And no, down rating my posts will not matter to me.

I personally rate them highly.

This is just a way for those who wish to give me feedback as to which people they think I should answer.


JSH: Ever talk to a mathematician?

I wonder how many of you actually have sat down and had any kind of conversation with a mathematician at a university.

I have had a few such conversations, like maybe half a dozen or so over the years.

If you have not, then to you mathematicians may just be something out of a novel, or a movie, but I assure you they are just people.

And they are mostly safe from consequences in a very protected world.

This story would not have played out like it has if they were not so safe.

My research is so obviously important that the supporting evidence is overwhelming, but we all here know the rules, and the rules say that what the mathematicians at universities say is important about mathematics is what the world says is important.

So they know they can sit quietly, and they know the impact of sitting quietly.

I've TALKED to some of these people in person. They are protected in a way that most of you aren't.

Remember the story with Wiles? How he worked for over seven years with no one knowing exactly what he was doing? He spent a lot of that time at home with his family.

Can you do the same? Can you comprehend that world?

No one knows what you're really doing, but you have a good salary, respect and admiration, to go off and do what you want for over seven years.

To them this whole thing may be kind of a puzzle, and it might not feel real to them that by leaving me out here arguing with fringe people they are doing a bad thing.

In their world, you protect YOUR research. Academics work to further their OWN CAREERS.

Tellingly a leading math professor at my own alma mater Vanderbilt University told me when I sat down to explain my work on factoring polynomials into non-polynomial factors—worked it all out on the chalkboard in a discussion that covered all the major issues over a couple of hours—that I lacked "polish".

Well I have a B.Sc. in physics so I'm pondering why in the hell "polish" matters when the result is so dramatic, and you know, sitting here now I think that professor was just doing things by the rules of his society. My polish means so much in an academic world where polish is part of the rules, like the social rules that govern human behavior in many other areas.

But here and now with my research those rules are shown to be out-dated, but that society is safe. Those mathematicians do not have to acknowledge my research no matter how important it is easily shown to be because world society does not make them, and by the rules they know, there are no consequences.

Ever talk to a mathematician? Doing so might open your eyes to how their world works, so that you understand that this drama is not about arguments on Usenet, as Usenet has no real impact on their world.

It's about the society of mathematicians in universities around the world, and the rules they play by.


Attacking reformulations, prime contradictions

One thing that is clear at this point is the position by several posters arguing with me that my prime counting function is a useless reformulation of information already known about prime counting.

There is much to support that view:

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

That prime counting function in its sieve form clearly has elements that can be found in prior prime counting research, and, guess what?

It gives the same answer as the count of primes is the same.

So what good is a reformulation?

Well, posters in going to so much trouble to proclaim my research old have repeatedly pointed out links between my prime counting function and previously known algorithms for counting primes and functions like the sieve function phi(x,a) used in those algorithms.

Um, but that sounds like they're saying that with one function, I can do everything that mathematicians previously did with multiple functions like using pi(x) and phi(x,a), so where before you had two or more, with my ideas, you have one function, which posters repeatedly point out can be optimized in EXACTLY THE SAME WAYS as what was previously known.

So this reformulation captures everything you need and you can work from it alone to do prime counting, going over old ground, so saying the reformulation is worthless can have some merit, right?

After all, prime counting isn't advanced by it, as I've finally acknowledged though early on I had high hopes that you could find much faster prime counting algorithms with it, so the reformulation despite its scope and size is a waste of time?

Well, hold on a minute. Sure, my prime counting function can be used to do everything known before, so you can say that it is going over old ground, so that if history had been different there might never have been a phi(x,a) function or even a one variable pi(x) function as you can do everything with my multi-variable function. But history shows humanity didn't go that route, so that's it, right?

BUT, the function I give—look back if you need to refresh yourself—recursively calls itself and directly counts primes, so you can use something simple, where I'll go to the classical prime counting function to show it:

pi(x) - pi(x-1)

with a natural number x greater than 3 is only non-zero if x is prime.

Because of that my prime counting function can go from being a sieve function, so that instead of having P(x,n) where n is a count of primes, you can use P(x,y) where y is just a natural number like x, as the function can call itself to sieve out the primes on its own, without human aid.

Hmmm…that sounds like more than just a reformulation now.

And besides, remember reformulations aren't necessarily all bad. How about Laplace Transforms? Or Hamiltonians?

Why just hate reformulations? Posters here clearly do as they repeatedly attack my research.

Yes I've made grand claims at times and had to back-track, but I acknowledge being excited about my own ideas and discoveries and hoping that they are grander than they may be, and I can stand corrected.

But even the reformulation argument begins to fall apart when the P(x,y) function arrives, able to do what no other "prime counting function" has ever been known to do in mathematical history.

And posters attack that noting that algorithms counting primes are now slow.

Um, is all prime counting just about fast prime counting, as excuse me, but isn't there something called the Riemann Hypothesis which gives methods that are even slower?

If speed actually counting primes is all that matters, why in the hell does anyone care about the Riemann Hypothesis?

Of course, it's not just about speed counting primes, and here the objections of posters go into hysteria and denial as they bounce all over the map, to ignore a unique feature of my research, but hey, this is Usenet.

Usenet is known for having people who are at the extremes of human behavior, who can say just about anything, and it's not like the math world is ruled by Usenet.

Nope. My research is not blocked by strange people objecting in weird ways on Usenet and calling me nasty names.

It is blocked by mathematicians at universities allowing that to go on by refusing to acknowledge my research, no matter how much I try to get them to pay attention.

So no, it's not about the posters calling me nasty names, and not even Erik Max Francis calling me a crackpot on his website, but aboutprofessors at universities, sitting quietly.

And that is why I say that the academic world today is a dinosaur with medieval crap like tenure giving them too much leeway, so that they can sit without fear of reprisals if the truth is known.

Do you think ANY math professor on this planet is brave enough to quietly sit by while my research is wrongly reviled on Usenet and the web if they thought it could impact their own careers?

If they thought they would be tossed out of their universities and forced to get a real job in the outside world, where results actually matter?

I doubt it. They don't strike me as being brave people.

But they are smart enough to know that today's academic world makes them almost bullet-proof when it comes to consequences for ignoring my research and leaving it to fringe people on Usenet to wrongly go after it, while they sit quietly, knowing they are safe from consequences, while also knowing that they are the key to having important research like my prime counting function properly acknowledged.

If they sit quietly long enough, they can hope that it will all just go away and the knowledge will be lost, with their academic careers safely protected.


Real issues with prime counting

Repeatedly posters arguing with me shift the discussion back to the reality of relationships between my research and past research, where a lot of things have been worked out over the centuries that people have been looking at prime numbers, and it's not like my research changes all of that history.

What it does do is put certain things about the prime distribution in a new light.

Remember, past mathematicians were enthralled by the puzzling relationship between the discrete count of primes and functions like x/ln(x), as why? Why should there be this link between a discrete value and these other functions that are continuous?

Well, my research says the simple reason for the link is that the prime count is close to the output of the summation of a partial difference equation—close, but not exact to it.

And that's it.

Hundreds of years of history in trying to understand primes and it turns out that there is this almost trivial relationship that can explain everything that intrigued mathematicians over the years.

So, in a way, yes, posters are right about the simplicity of my ideas and that most of what is found in my prime counting function was previously known, but it's where it's new that things get interesting—and kind of boring.

A partial difference equation is not a sieve function. Sieves require people help them in special ways, like with phi(x,a), you need to have a list of primes.

My prime counting function has a sieve form, but it also has a partial difference equation form, where it doesn't need a list of primes and from that you can get to a partial differential equation, where of course, lists of primes are useless.

All of that spells simplicity.

The explanations for the prime distribution that come from my research could fit in a paper.

Now one paper does not a department of mathematicians support, let alone a world full of people who need to be able to write papers to survive in an academic world that is about, writing papers, as much as anything else.

So the why of a conspiracy to block my research—deny things like the partial difference equation being a first in prime counting—is that my work simplifies to a degree that I am the one person who gets most of the use out of it.

Same thing happens with my other research like non-polynomial factorization. There I find neat analysis tools that show that all those rings that mathematicians use are just extra stuff.

And with my research you just have one ring.

Again, simplicity does not support math departments.

My research shrivels up a lot of math areas so that you have a lot less extra stuff.

Now that should be a good thing!!!

Certainly building from the simplifications people can find lots of complexity again over time, and great strides in human knowledge, but that makes it a young person's game.

Do you think old mathematicians with established careers and a big body of work that has just been out-dated want to start all over?

There are two key things with my prime counting research:
  1. A prime counting function that recursively calls itself—never before seen in mathematical history.

  2. As a result of that ability to call itself, you have a partial difference equation, so that sieving is eliminated, as the prime counting function can find its own primes.
Yes, a lot of the basic mathematics is simple, and a lot of older mathematics looks like my equations, especially in certain form, and my equations in their sieve forms—note, not their difference equation or differential equation forms—can be related back to the old sieve functions—all of them, and not just phi(x,a) though that is a favorite.

Math people are people too. And a lot of them worked very hard thinking they were at the cutting edge of knowledge—and they were for their time.

I am the future, with advanced techniques that befuddle math people as you can see on these newsgroups as they belittle brainstorming.

My research takes away the easy road for them, starts them over with much more powerful tools for analysis that more simply answer some of the biggest questions they grew up with, and rather than embrace the work necessary in dealing with the new reality, they hold on to the old.

Monday, November 20, 2006


JSH: Questioning certainty

Mathematics is one of the few areas where truth can be determined and something known to be true as an absolute.

The reality of my research is not a moving target, but a solid body of research done over more than a decade, available at any time for review by those who want the truth.

>From publication and the dramatic collapse of the math journal, to the simple reality that to this day no other multi-variable prime counting function is known, no other known prime counting function can recursively call itself, and no other prime counting function leads to a partial difference and a partial differential equation, it's not a rational question to ask if my mathematical findings are of value.

No court of law has ever had more definitive proof, for anyone, who wishes to accept the truth.

But the secondary reality of my research is a math world that in choosing to escape reality and then call its research pure, lost its way, and today mathematical proof is not enough for people who call themselves mathematicians. As they simply rely on telling each other what truth is.

So you people question certainty, and in doing so, you go after the very great things that make us human--not only our need to know, but our ability to accept the truth.

You people are the diminishment of a world.

To the extent that you can fight mathematical certainty, and dramatic facts to live a lie, you prove the power of denial against any truth, and bring into question the future of the entire human race.

If not here, where truth is an absolute, then where?

Or will humanity never escape the ability of some people to choose what they want over what is, for their own needs at the expense of the greater good of us all.

Sunday, November 19, 2006


JSH: Scary, eh?

Thousands of people around the world I'm sure have the expertise to trace through Wiles's paper—with the assumption that it is wrong—to see if that assumption leads to a contradiction.

That simple test shows that it does not.

Supposedly, showing an error in a major paper at that level would make a person famous, and gain them prestige and even could lead to money.

Wiles turned down millions in endorsements, while receiving quite a bit of money from math prizes alone.

But no one will do it because the math world is not what most people think.

No one will do it because they know that mathematicians who control things would close ranks around Wiles, deny any assertions of error, and block them, so they'd get nothing, but pain and misery.

Maybe they could post about the problems on Usenet and get called
stupid and insane.

I like the test I outlined above which is called the null test as the thing to do is reply back with the line in Wiles's paper where assuming the opposite of what he claims to prove leads to a contradiction.

One poster—Arturo Magidin—already made a false claim, where he re-worked some of the lines of a crucial point in Wiles's work, and claimed an error with the conclusion of what Wiles calls "Theorem 5.2".

But that can only happen if the proof is by contradiction, so Magidin tried to claim he'd turned Wiles's work into that, but sorry, creativity at protecting your hero does not math make.

To pass the null test a contradiction has to be shown with Wiles's actual paper, not with something creatively re-worded, and a contradiction would not show at the conclusion of an argument, as the logical break has to occur before then.

Remember, mathematical proofs are logical chains. An actual proof will show a break in the chain BEFORE the conclusion if you assume something that goes against its logic.


JSH: Willful ignorance

I will admit I'm at a loss on what to do with this situation as it is so far outside of the boundaries of what I thought was possible, as I've managed to communicate with quite a few mathematicians over the years about my research.

Only on the newsgroups is it this nasty and vicious kind of thing—as Usenet is a place where some people behave in ways they can't get away with in the regular world.

Most communications have been cordial. I've even more than once received encouragement.

But the typical scenario will be after a little bit of explaining, I will be told that what I have is kind of interesting and maybe that I should try to get it published, and that will be it.

After that they just walk away.

If I push a bit, then they just shut off and won't talk to me any more as usually communication is by email.

I've enlisted the help of family and friends of the family and one story is a telling one, as a professor at a school in California thought he could just go to a colleague with my research on prime counting, and that colleague said he'd get back to him—and went on sabbatical for six months.

When he got back he claimed to not remember ever saying he'd do anything, and didn't offer any further help.

And, of course, there is the reality that I did get some of my research published—only to have the journal crumble with some sci.math'ers managing censorship with a few emails to those editors.

So what to do?

I can prove that what I say is true, and have done so repeatedly. I can simply explain and even demonstrate.

I can show uniqueness and relate to some of the hottest topics out there with primes and possibly giving alternate approaches to the Riemann Hypothesis, and mathematicians can willfully just avoid.

One of my favorite examples to show the complexity of the situation is that of a math grad at Cornell University, who decided to email me and see if he could be more convincing by email than posters had been on the newsgroups.

I asked what was in it for me to work with him, and he claimed that if I could convince him, then he could go to his department and I'd have the backing of Cornell University.

But I found out he promised big because he thought I was wrong, as I just simply sent him one of my simpler arguments on non-polynomial factorization, something like what is currently the lead post on my math blog, and let him work his own way through it.

He started fast, re-writing the first pieces in his own words, and then his emails came at longer intervals, and I just went about my business as I have all kinds of things I do anyway, and I've learned not to expect a lot from any particular source.

Well after over three months, he finally go to the end, having re-worked the entire argument in his own words, and then begged off, claiming he needed to go do research on algebraic integers.

And that was that.

I've emailed him a few times since then and most he's done is to express some displeasure with me bringing him up all the time as an example, and somehow he seems to have forgotten the offer of help if I could convince him, or even his own excuse about needing to read up on algebraic integers.

Yet supposedly if he'd followed through and helped champion the clearly correct mathematics—he'd verified it himself—he could have been one of the most famous people in math history.

So why wouldn't he do it?

I think the simplest answer goes back to the triviality of the disproof of Wiles' approach to the Taniyama-Shimura Conjecture, as I can find problems with it all kinds of ways, and can explain to a non-mathematician why it can't work because it has just this trivial logical fallacy that takes it apart.

Or I can suggest that a mathematician just trace through his paper—as it's not even hard if you know a bit of number theory and you don't have to get into the really complicated stuff to find this—and just assume that the conclusion of his paper is false and try to find a contradiction with that assumption at any point in his paper.

I call that the null test and Wiles's paper fails it.

So you have supposedly one of the great achievements of humanity, this research by Wiles which is easily shown to be crap by multiple ways, contrasted with my ability not only to simply prove very important things, but demonstrate and explain to math people—and have them do nothing.

I think that grad student walked away because he knew what his society would do if he did try to go with the math. After all, Wiles's mistake is rather obvious and dumb, yet mathematicians have put him forward as this great researcher with this important research that solves Fermat's Last Theorem.

So the grad student knows that his society will not go with the truth, so it's pointless, even if he can work it all through himself and figure out that I'm right, as modern math people are not about what is right.

The other side of it, of course, is that one of my simpler approaches and techniques easily explained does it turns out lead to a rather short proof of Fermat's Last Theorem, which is why there has been so much controversy and why so much energy is directed against my paper on non-polynomial factorization.

You see, I decided I'd try to get my research across in stages, so I pulled out the most important techniques in my proof of FLT, and wrote a paper covering them, sent that paper to various journals and it was published:

There you see just this blurb that it was withdrawn—yeah, by the editors and not by me.


for more information about the now defunct journal as I'm linking to a site mirror.

You can find the copy they deleted at my Extreme Mathematics group:

That's the original pdf file that was on the web at that point.

So neat trick, eh? I'd pull out the key part of my proof of FLT and get it published, and then come back to show the whole thing with the heart of it anchored by this published result.

And those sci.math people busted that plan up, and busted up a math journal along the way.

To get a full sense of how far gone modern math society is, I suggest you read:

There you can also get a link to the revision I made to that original paper and sent to the Annals of Mathematics at Princeton, and also see what they did.

Think of that grad student at Cornell. Probably a very smart kid at one of the premiere institutions in the United States, having proven to himself that some of the most dramatic claims in mathematical history were true, and all he had to do was help that research get known, and he could have gone down in math history.

His name in textbooks and people talking about him as an example of how the system should work.

But now I keep him anonymous, and use him as an example of a system so broken that a person would walk away from accolades and important mathematics rather than dare test his superiors who have gone so far away from mathematical truth that their own students don't even dare to try.


Highly stylized, very formal, completely wrong

The research of Andrew Wiles is a demonstration of why Middle Ages techniques which have dominated the mathematical world and to a large extent the academic world in general, do not work.

His paper is highly stylized in a special format that takes years to learn. And I can show how he fails with some simple examples like talking about objects with 4 wheels, to compare to his research relating mathematical objects with 4 numbers.

People go on and on as if proper respect and a great deal of prestige must be used when considering these people some society claims are brilliant, when their work is crap, because there is a process where you do certain things, then you too can be a math Ph.D, get published and build stature—based on the medieval rules versus actually accomplishing anything of value.

In contrast you hear about the modern world and the speed of business, which I'm sure many of you hate—that speed.

Innovation is continual which is how I can get on the web so easily and type up these posts—advancements with computers and worldwide communications have been dramatic.

Businesses have to be nimble and open to new ideas or they get beat soundly by the businesses that are.

But math people can ignore whatever they want. Sit quietly while dumb research is touted as brilliant.

And just not change because the medieval rules of their society protects them with things like tenure, lots of formality and hurdles for innovators to jump, and lots of ways that mediocre minds can protect themselves while doing nothing of value to society.

Brainstorming should be a crucial and well used part of modern problem solving in mathematics, but if it were then my using it on newsgroups would not be a reason for howling and accusations of insanity.

Good ideas should be grabbed up and prized, not lied about and denigrated as has been done with my prime counting research.

And lies should not be so easy.

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

I keep posting that all over the place to show you what real mathematical research can have done to it by your medieval society.

There isn't even another three dimensional prime counting function known.

Anyone who can web search can go now on the web and see for themselves that it is new, but posters have gone on literally for years claiming it's not.

Viable industries cannot behave that way.

You can't casually lie about hot new ideas and get away with it in the real world that is moving forward, versus your math world which is a dead zone, a dead pool where ideas are crushed, and people fight political battles and produce highly styled, very formal papers—that are completely wrong.

Like Andrew Wiles did.

My hope is that some of you will want to join the rest of us in the modern world.

Saturday, November 18, 2006


Calculus and my prime counting function

I've repeatedly emphasized the simple sieve form of my prime counting function to make a point that it is new, and unique in ways clearly seen to what was known before as you can just do a web search on "prime counting function" and easily see what math people already knew and find nothing close to the following.

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

I don't think you can find another multi-variable prime counting function in the math literature at all. I know I haven't found one, and it's another crucial point to make against people posting against this research.

But now things get a bit more complicated and I worry about making a more complicated post, but I need to address more directly just how important this research must be, and for that, there will need to be some calculus.

Because my prime counting function recursively call itself you can go from the sieve form to a fully mathematicized form with the following.

With natural numbers x and y, if y<sqrt(x) then

P(x,y) = floor(x) - 1 - sum for k=2 to y of (P(x/k,k-1) - P(k-1,sqrt(k-1)))( P(k,sqrt(k) - P(k-1,sqrt(k-1))))

else P(x,y) = P(x,sqrt(x)).

That may look a lot more complicated but the main difference here is that because

P(k,sqrt(k) - P(k-1,sqrt(k-1))

will equal 0 if k is not prime, I can use the prime counting function itself as a switch which will zero out everything if k is not prime, so you only get non-zero values when k is prime, just like before.

And now you have something never before seen at all with a prime counting function, which is a difference equation as part of it, and more specifically, what is being summed is a partial difference equation.

Not surprisingly, you can go from that to a partial differential equation:

P'y(x,y) = -(P(x/y,y) - P(y, sqrt(y))) P'(y, sqrt(y))

and again find something never before seen with a prime counting function.

So now to believe that my research is actually old you have to believe that no one bothered to go to a partial differential equation from the earlier form.

In its sieve form my prime counting function can be related directly to other sieve prime counting functions and elements within them.

Numerical integration of the partial differential equation can reveal if it is close to the prime count, and if it is, then it stands to reason also that it would be related to continuous functions that are close to that count as well, and more specifically if it is very close, to any functions that follow from the Riemann Hypothesis.

The other possibility is that despite following directly from the prime counting function, the numerical integration of the partial differential equation is completely unrelated to the prime count.

However, my own attempts at doing that integration show it to be closer than Li(x) but a bit further from the prime count than R(x), the Riemann function.

If Legendres had my prime counting function but failed to figure out the fully mathematicized form and failed to figure out the partial differential equation, then he missed some obvious things, and not only him but mathematicians that followed him did as well, including Riemann himself.

Proper follow through on this research alone should make headlines around the world.

It is just some of my number theory research.

For instance, I have also proven Fermat's Last Theorem.


JSH: They'd shred most of you

Reality is that the current math world has its own made up rules for who it allows to have major mathematical discoveries, and if you do not fit into that box of a Ph.D from a major university with a history of publications in popular math journals then they will not accept your results.

That applies to you as well as me.

So no, whatever your fantasy is about your own ability to one day figure out some neat math thing and get accolades for it, you cannot with the current math world unless you fit into the box above.

If you push, they will shred you.

At least I have a degree from a major American university in physics and a history of being labeled gifted to allow me to dismiss continual insults where I am called stupid, and insane but what about you?

If you make a math discovery, and do not fit in the box above, the current math community will tear you apart if you do not just quietly, shut down on your own.

If you push, they will shut you down.

You will be berated as stupid, an idiot, or a fool, and repeatedly called insane.

And most of you thinking that you should get applause from people you admire, when you face that you WOULD SHUT DOWN which is the point.

The point is your silence, shutting you up about your discovery.

So that's why it's relevant for me to talk about things like going to Duke University as a kid, as hey, if you do not have something like that in your background, what chance do you have?

When people rip on what you know is right, and call you names, what will you do if you do not have a degree from a top twenty university?

When you have person after person after person repeatedly calling you insane, how will you keep talking unless you have all that and your own open source Java program used around the world by—Java programmers?

You will not.

I can say do a search in a major search engine on the words class viewer and you will get a real world example of what I can do, and how big on the world stage I am.

I dominate these newsgroups, but repeatedly you're told that it's because I have nothing.

They would do the same to you—if you did not meekly shut up if you had your own research and did not fit into the box I described above and had dared to talk about it.

Consider just how far they can go.

I figured out a short way to count prime numbers:

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

To this day as easily verified by checking math websites, like go to MathWorld, you cannot find anything like it, as in a prime counting function that recursively and succinctly calls itself.

These people will NOT put that information up there. They will NOT record it properly for posterity.

They will NOT give acknowledgment or accolades to the discovery and you should thank God that you were not the person who figured that out, as it's simple enough that maybe you could have.

As the current math world would have given you hell.

If you dared talk about it, you would have been shredded.

Make no mistake. IN this day and age, you make any discovery in the math field at your own risk, as for most of you, it'd be better to keep quiet about it than risk the ire of the math community.

As they will come after you if you do not meekly follow their rules.


JSH: So what's your school?

Given all the hostile arguing here it is worth getting information about educations.

So here is mine and I hope posters who argue with me will give information about their educations.

I have a B.Sc. in physics from Vanderbilt University. Previous to that I was part of Duke University's Talent Identification Program (TIP) as a teenager, where I took geometry and briefly abstract algebra in their summer program one year, and structured C, taught by an IBM researcher from the IBM Research Triangle, the next.

I have been diagnosed as gifted much of my life. It is just a word.

Other posters would please give their education and math relevant backgrounds.

Thursday, November 16, 2006


Concise prime counting functions, where?

One intriguing line that has come up recently with my prime counting research is the assertion that it is well-known.

However, I JUST did a survey of math websites doing a search on "prime counting" and saw nothing like the following concise prime counting function, which is mine.

My prime counting function in its sieve form is as follows.

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

That is very concise, and it is in one line where you have the summation with my prime counting function in sieve form recursively calling itself.

It has been noted that it can be directly related to the phi function which usually is discussed with Legendre's Method.

But, um, I can see nothing out there on the web that gives anything like my prime counting function, so, what if?

What if there isn't anything on the web because no one figured it out before?

I figured it out along with posters on the newsgroups years ago because of all those arguments about my research, where it was worked out that it could be directly related to the phi function.

But what if the math world itself never knew until recently?

Questions that can be answered by links or references.

I am asking posters who claim that a concise way to represent the phi function was known previous to my research to give some links or references of some sort.

I am actually curious at this point. I doubt that MathWorld and websites like it would ignore a very succinct way to write the prime counting function if they knew about it before me, or that they would ignore simple optimizations that make counting primes faster, if they knew about them before me.

Yeah, maybe math people hate short and simple which is why you can STILL at this time as I just checked not find anything like what I have on MathWorld.

Is that satisfying for you? Believe they know this information but just hate short and simple?

I don't think so.

But I am quite confident that they would ignore anything and everything if it followed from my research.


JSH: Where is Christian Bau?

Kind of wondering where that nasty person went? He was obnoxious as hell but had to be at least somewhat brilliant as he coded an implementation of some of the fastest prime counting algorithms, using the research of Odlyzko and Lagarias et. al.

If he wasn't lying I think he even sped things up a bit from what they did.

So where is the little shit?

I'm surprised he isn't around to say something nasty about me.

I think he'd be more useful in these re-hashing's over old stuff with prime counting than the current sci.math crew I'm stuck with.

You people are dumb as rocks.

Wednesday, November 15, 2006


JSH: More fun this way?

So it turns out that Tim Peters is doing something dumb, and it occurs to me that maybe I could explain more or even code the proper way to iterate with primes above x^{1/3} when calculating pi(x) with my prime counting function in its sieve form, but hey I already did all of that!

It's all old stuff.

That Christian Bau knew all of this and was STILL an obnoxious little turd.

So better to just leave it like it is, as the truth doesn't matter to you people.

My prime counting function can only be forced to look like Legendre's with stupid implementation.

For iterations above x^{1/3} it is equivalent to Meissel, which anyone with a modicum of mathematical knowledge and understanding about prime counting can easily verify.

Even David Ullrich was never stupid enough to say my prime counting function was exactly Legendre's, as he'd always say "essentially" the same.

So the later sci.math'ers coming into the argument are just dumber than earlier ones, and did not read the history of the debates in this area, or didn't read them carefully enough.

In its sieve form—properly implemented—my prime counting function blows Legendre's away.

And I have properly implemented it in my program, where for primes over the transition point (even in the code it talks about the transition point), the program pulls out the count of primes directly from memory.

All of which just prove my point—the math world is about group processes.

You people do not care what is mathematically true, but only about playing follow the leader along paths laid out for you by someone else.

So even stupid math makes great sense to you! And you believe even blatantly wrong things—which other posters got right years ago—when the right person for the job comes along and tells it to you.

And Tim Peters was the right person for the job.


JSH: Naive coding

Oh, I just thought of something.

My prime counting function in its sieve form is what I've given quite a few times before.

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

Notice that qualification that if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

But if n is the count of primes up to and including sqrt(x), then P(x,n) = pi(x).

So for fast coding since you have a cache of primes anyway, you just directly grab the value of pi(x) if you have it, and yes, then, my prime counting function in its sieve form—even without the additional optimizations I talked about—is MUCH faster than Legendre's.

So I was right before noting it's faster—unless someone codes it dumb and iterates back through when you can use pi(x) and the primes already in memory, as you need the primes up to sqrt(x).

My takes that a step further and actually uses a bigger sieving than necessary so it stores more primes than there are up to and including sqrt(x).

It also has a nifty implementation of a search algorithm to go find those primes quickly.

So Tim Peters could match my prime counting function against Legendre's and get the same speed ONLY by stupidly coding the top iterations.


Simpler code challenge with prime counting

Well, wouldn't you know that Tim Peters and his supporters whined all over the place in the thread with my previous code challenge, and it seems like it is just not a fair test—according to them—for him to have to code in Python an equal speed or faster prime counting algorithm against my code already done in Java.


So I have a new test.

See, I am a fair person and I want to help Tim Peters out.

His claim is that optimizations to my prime counting function are equivalent to optimizations to Legendre's Method.

My prime counting function in its sieve form is as follows.

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

It can be immediately sped up by using the following.

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - floor(x/2) - 1 - sum for i=2 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

That may not seem like much to many of you and I noticed a post where Peters claims that you can just speed up Legendre's Method the same way, so the challenge is simple:

He is to code an implementation in Python of the speed-up of my prime counting function, do the same with Legendre's in the way he thinks it is to be done, and post a timing test comparing the two.


I've lightened the load of Peters, and notice I'm even being a lot nicer in the post itself, and didn't even say anything about the Python losing its bite or talk about its cool but slimy scales.

Ok, on to the mathematics, as, why is this challenge significant?

Well, it turns out that as you optimize my prime counting function it approaches Meissel's Formula.

Now I know that, and have told Peters more than once that at the top end of the iterations it IS the equivalent of Meissel's Formula, but he just keeps babbling like he doesn't get it.

So a simple test is in order.

Let's see what Tim Peters—the supposed Python code guru—and his people say to this one.

Will they whine their way out, again?

Tuesday, November 14, 2006


JSH: Not a Mensa fan

I know at least one of you doesn't seem to like Mensa. Yes, I was a member a while back, but I found that group didn't help me much. The people seemed to mostly be interested in, puzzles—man-made puzzles.

I'm thinking, hey, the real world gives HARD puzzles, so why bother with some crap some person comes up with?

In any event, I couldn't get off the IQ kick immediately as society says all this junk about people with high IQ's so I ended up hanging with "ultra high iq" people.

That ended up being more frustrating, though at least one group published my paper in their book of mostly, um, puzzles.

I've already given notice to the high IQ community that I am not exactly appreciative of them not championing my research.

I think many of them are people who are less about real accomplishment than about what they can score on some man-made test.

Don't bother worrying about how high I score on those tests. It's high, but you people don't respect that anyway.

And lately, I don't either.

The high IQ people had their chance. Now I owe them nothing.


JSH: You are completely out-classed

As I build a multi-media empire connecting my various web and usenet activities, it occurs to me that many of you, despite the world wide impact I already have on the math world, still think this is just some little minor adventure on usenet.

And some of you seem to think sci.math is a small newsgroup of a few hundred readers and a few dozen regular posters plus kids coming with their homework.

But it is free access to the world, where I can put the math out there, engage in vigorous debate, and slowly but surely build momentum.

The latest Code Challenge is yet again a bit of sheer brilliance forcing a concrete result—code to match against mine and time against mine counting primes—or yet another failure by people who argue with me to actually deliver.

You people are completely out-classed.

You engage in playground tactics, with insults being all you have, as if that will always work, when the real issue is about the time it takes to slowly work new ideas into the public consciousness.

Meanwhile as I challenge people to think, they are also being asked to consider ideas they would previously probably never thought about at all—like what if mathematicians aren't actually doing anything of value at all, how would we know?

Well it'd be nice if computers could check and at least see if they are right, but wait!!!

Math people claim computers are too stupid to check them on their "pure math" research!!!

Seemed plausible years ago, but less plausible as each year goes by, and you people find more excuses for obvious failures.

Meanwhile you get to just convince a committee of fellow mathematicians, rip on people who dare to enter your domain and try to make their own discoveries, often claiming they must be mentally ill, as if you all had medical degrees.

If my aims weren't so big, I could attempt to sweep in and finish this early, but I think that math academics are just the tip of a bigger problem across academia.

I think the entire academic world across the entire planet needs changing and I need enough momentum for that revolution.

I need mathematicians to build up the energy needed not only to handle them, but also archaeologists, art historians, linguists, MBA's, and every other academic all the way to English professors or language professors in countries that are not predominately English.

So yes, you people keep thinking you are winning as you get time, but time gives me momentum to use what you are doing here to change how English professors live.

First thing, of course, at the arrival of the revolution will be to get rid of tenure.

The Dark Ages died a long time ago, and tenure should have died with them.

Ok, enough chatter about the big picture, back to the grind. As I build momentum and move forward with the task of changing the entire world—of academia.


Prime counting: code challenge!!!

The poster Tim Peters makes several claims in his bid to convince the newsgroups that MY prime counting function is old math, old hat and not worth your interest, AND he claims to be a code guru himself with the Python scripting language.

But is he really? Or is he full of hot air?

Time for a code challenge!!!

Rather than have all these dumb arguments with an increasing number of threads I say, let the computers tell the truth here:

At my new Google Groups "ExtremeMathematics" you can get MY CODE, a Java applet, and you do NOT have to be a programmer to run it, test it, and see it scream through prime counts as you can download un-zip it and just open the html file to safely run the applet.

Java rules.

(If a tar-ball would be appreciated I could put one on the site.)

In the other corner the loudmouth Tim Peters can show if Python has what it takes with optimizations he claims can be easily done to Legendre's Formula to prove that my research is not valuable.

I CHALLENGE him to put up Python code against my prime counting applet code, where JAVA RULES!!!

Python is not up to the challenge with him as a programmer. He is too weak. His math skills and coding skills are not strong enough.


Since the easy way for Peters to cheat is to go to other algorithms done by other people versus doing his own, I will add that he is to put up the prime counting function that his code uses.

The key expression in my code is

N/2 -(N-4)/6 - (N-16)/10 + (N-16)/30 - (N-8)/14 + (N-22)/42 + (N-106)/70 - (N-106)/210 +2 - S

where then the prime counting function sieve form algorithm being used is as follows.

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - x/2 +(x-4)/6 + (x-16)/10 - (x-16)/30 + (x-8)/14 - (x-22)/42 - (x-106)/70 + (x-106)/210 - 2 - sum for i=4 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

(Hint: Do timing tests of my applet against Mathematica or other math software.)

The program I use relies on extra use of memory as well some other smart coding ideas for speed enhancement, so Peters can use whatever else he can figure out--as a supposed Python guru—around the core mathematics.

My program can also be seen at the ExtremeMathematics group, or you can simply open the jar file to see what it is using to confirm important details.

The point of this challenge is the sad reality that there are people that lie to you about mathematics, and they lie quite boldly, or Peters can deliver the code.

I delivered.

Can he?

Keep up with the challenge HERE on these newsgroups and nowhere else as the blow-by-blow of Java against Python in the math software challenge of the year commences!!!

Read to see whether or not Peters is all talk or can actually code!!!

Read to see if the bizarre and annoying tactic of empty postings to obscure the mathematical truth by him and his dark cabal continue to work!

READ to find out the truth about prime counting.

And oh yeah, nothing against scripting languages like Python, but Java is the dominant programming language on the planet.

And don't you forget it.

Monday, November 13, 2006


JSH: Every read Riemann's own words?

A poster claiming to be a "real mathematician" challenged me slightly about Riemann, when it turns out that yes, a while back I got a direct translation of his notes where he came up with his famous hypothesis, and I wonder, how many of you have read them?

They're kind of depressing given all the hype surrounding them, and you have to get a sense that Riemann himself would have been surprised at all of that hype.

He speculates a bit. Does a few sketchy things. And that's it.

I think a recent math person named Goldstone actually got shot down in his claims of having a proof of the Twin Primes Conjecture doing the same sketchy things that Riemann did to give you just some comprehension of the real math world.

Of course, I could be wrong on that one.

Anyone remember the criticism of Goldstone's work? Or did I get the name wrong?

How is what he did similar to what Riemann did? Or, do you claim they are completely unrelated?

If so, how did I come to my conclusion then? Just reaching?


JSH: Learning mathematics

People lie.

That is actually a good reason for someone who just gets sick of the lies to come to mathematics.

I don't try to get people to like me. Notice posters acting like that's a big deal?

Who cares? People lie all the time about all kinds of things. And then they go off and kill other people for lies, or rape, or steal, or just do whatever they can to make some other person miserable, and for what?

For lies.

In mathematics, if you start with a truth and proceed by logical steps then the conclusion you find then MUST BE TRUE.

It is not a surprise to me that some people came into mathematics and learned to lie with it.

People lie.

But if you want to learn mathematics you need to step outside of the group and learn to do something that most human beings are incapable of doing: accepting the truth because it is logically proven.

And not because your are told something is true.

Most human beings, no matter what they say, are incapable of truly believing something just because it is logically proven to be true.

They believe things because their parents taught them a certain way or thing. Or they look around and notice a lot of other people nodding their heads and they agree for that reason.

Mathematicians—true mathematicians—are a breed apart.

You have been given a test of a generation. I came into a situation requiring special handling, as most important to me is excluding out people who rely on group processes to believe.

I want those people who prove.

This process continues which is why now is a good time to send this message.

The group will fight the truth and if anyone out there is one of those special people then I want you to watch them, to understand how most human beings see the world and come to conclusions.

And understand that mathematicians—real mathematicians—must hold to a higher ideal.

Only then can you learn the true mathematics and begin to understand your world, the reality that underpins it, and comprehend the future that awaits us all.

If I find one other person then this has been worth it. If not, then, well, you'll see.


JSH: Protecting the Riemann Hypothesis

So yes, I think it quite likely that mathematicians are protecting the Riemann Hypothesis, which is the deep reason to ignore my prime counting function.

I think they are quite capable of doing it, even if deep down they know that the Riemann Hypothesis is probably wrong because it's more CONVENIENT for them.


JSH: Prime counting is the crusher

It turns out that my prime counting research is a crusher, which is why posters have to lie differently about it, as for instance, they can't claim it's wrong!

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

Here rather than give LaTex I've copied a bit from a sci.math poster.

That is just a neat and tidy prime counting function which differs from Legendre's in a key way, as with Legendre's you use exclusion-inclusion where you get counts of composites using the primes.

So to count the primes up to and including x you start with floor(x/2) which gives you the count of evens, and next you use floor(x/3) as you go up by prime, BUT now you have a problem!!!

Some of the composites that have 3 as a factors are even, so you have over-counted and Legendre's corrects by now adding back in floor(x/6).

WHAT I did in contrast was say, hey, find out all the evens, but now when you look at numbers that have 3 as a factor, don't bother counting those that are even! So my prime counting function is different in a simple way: it counts composites by prime excluding the counts of composites already found with a lesser prime.

May not seem like a big deal but that leads to a short prime counting function in its sieve form as I showed above.

But you can easily speed it up as well!!!

With natural numbers x and n, where p_i is the i_th prime:

P(x,n) = x - floor(x/2) - 1 - sum for i=2 to n of {(P(x/p_i,i-1) - (i-1))}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

Now it's over TWICE as fast! Just like that.

That cannot be done with Legendre's method. It just can't be written that succinctly or sped up as easily and YES you can keep going!!!

You can keep speeding it up!

Now notice, I just quickly gave you key facts that make my prime counting function different in crucial ways, and it is neater and more concise as well.

Posters have special problems in counter-acting the truth of my research here, so usually they simply go to making things up!!!

My suggestion to those of you who care even a little bit about primes it to just code what I have above, and speed it up a bit. Then go and look at the clunky stuff that mathematicians continue to obstinately use, as if they don't have a working neuron in their heads.

Remember, my prime counting function differs in that I went to the common-sense idea of counting at each prime ONLY those composites that have that prime as a factor but NO LESSER PRIMES as a factor.

Here's a tidbit to play with as floor((x-3)/6) gives the count of composites that have 3 as a factor but do NOT have 2 as a factor, for instance with x=12, floor((12-3)/6) = 1.

So what is that one?

It's 9 of course. Um, but what about 3?

Well 3 wasn't counted because it's not composite!!!

And of course 6 and 12 were left off because they are even.

Don't think the math can be that smart with such a simple expression?

Now try x=15, as now you get floor((15-3)/6) = 2.

It just counted 15 because it has 3 as a factor and is NOT even!!!

It's just a smarter way to count primes and it leads to a compact prime counting function in its sieve form.

Now then, when you have a better idea that a LOT of people are fighting you have to wonder what might be the deep secret to why.

Answer here is, the sieve form is boring. It turns out that you can go to a more complex fully mathematicized form, which uses what's called a partial difference equation. You keep pulling that thread and you get to a partial differential equation.

You work it all out logically and you have a strong implication that the Riemann Hypothesis is false.

As a group MOST mathematicians though say the Riemann Hypothesis is true!!!

By ignoring my research they can hold on to the conclusion democratically held.

Sunday, November 12, 2006


JSH: My prime counting, speed

Posters lie to you all the time about my research and one of the most telling areas is with my prime counting function.

I've talked recently about the sieve form giving the LaTex as that can give you a better look at it, if you paste it somewhere where you can process LaTex:

With natural numbers x and n, where p_i is the i_th prime:

:<math>P(x,n) = x - 1 -\sum_{i=1}^n {(P(x/p_i,i-1) - (i-1))}</math>

where if n is greater than the count of primes up to and including <math>\sqrt{x}</math> then n is reset to that count.

One correction I have to make to what I've said previously on this subject is that it is true that solving that expression out explicitly will give the same expression as Legendre's Method.

It does.

So no, the simple expression even in its sieve form is not going to be fast, but the first speed-up is to not iterate from i=1, as that covers evens. Here's a faster version:

With natural numbers x and n, where p_i is the i_th prime:

:<math>P(x,n) = floor(x/2) -\sum_{i=2}^n {(P(x/p_i,i-1) - (i-1))}</math>

where if n is greater than the count of primes up to and including <math>\sqrt{x}</math> then n is reset to that count.

Now that makes it quite a bit more than twice as fast. Now I posted recently that the sieve form was fast, as I haven't played with this all for some time, and I always would correct out the evens, and it IS fast if you do that simple thing.

But it doesn't stop there. It turns out that the iteration at i=2 can be given by


so you can do yet another speed up by using:

With natural numbers x and n, where p_i is the i_th prime:

:<math>P(x,n) = floor(x/2) - floor((x-3)/6) - \sum_{i=3}^n {(P(x/p_i,i-1) - (i-1))}</math>

where if n is greater than the count of primes up to and including <math>\sqrt{x}</math> then n is reset to that count.

And those of you who bother to try that out—hoping I got the math right on that last, I think I did—will find that it is far faster than Legendre's Method can be made to be.

So what's the point here?

I made some mistakes in talking about an area I haven't delved into for years, as I got bored with the speed issue, and some posters maintained one thing based on exploiting my mistakes, when the mathematical reality—the full story—wasn't too far away.

So why do those slight changes make for very fast prime counting?

They don't care. They don't care to let you know about those changes. They don't care what the mathematical reality is.

My research covers a lot of ground, and I often forget details about it, as I go away from one particular area for years, so I do apologize for getting some of the facts wrong.

But I'll come back and correct. I knew there were fast ways to count primes from my idea, so it was just a matter of getting the details right.

The people I'm facing, well, I think for them it's just a game, where a lot of times you don't even know who they are as they're using pseudonyms, and clearly think that they can never be held accountable for what they say on Usenet.

Saturday, November 11, 2006


JSH: What are your limits?

Yup, many of you were played for fools, but what will you do now?

What are your limits?

Will you still just accept the weird group of people who manipulated and lied to you for years about my math?

Or will you FINALLY go with the math?

How can they exist? How could such people do what they did?

Who cares, how could they so easily get you all to ignore publication in a math journal?

And even keep manipulating you when the poor journal collapsed and died?

The bigger question now is, are they connected even higher up?

How far up the math chain does this all go?


JSH: Connecting the dots

So I note that Wiles' work fails the null test, which involves assuming the opposite of what he claims to have proven at the outset and tracing through his paper trying to find a contradiction.

So how does he or anyone else think the argument proves Taniyama-Shimura?

That goes back to the problem with the ring of algebraic integers!!!

That ring is quirky and has a coverage problem so you can come up with arguments that just don't work, and can do weird things like appear to prove something when you look at them one way, and then logically fail in various ways, like failing a null test.

So I have two ways of knowing that Wiles failed:
  1. The logical error Cum Hoc, Ergo Propter Hoc.

  2. From non-polynomial factorization and the demonstration of the coverage problem with the ring of algebraic integers.
What is remarkable about how mathematics works is that you get one thing wrong and all kinds of things fall apart in other places.

So yes, the coverage problem of the ring of algebraic integers is a big deal, and you can connect my research back to issues with major papers in current number theory.

And that's just one piece of my research.

If you go to prime counting and start working through implications there you end up questioning the Riemann hypothesis, which is why the partial difference equation and partial differential equation that follow from it are such a big deal.

And if you look over some of my recent musings on considering p_1 mod p_2, that is, taking the residues of one prime modulo another, and considering that the result is random, you can answer the Twin Primes Conjecture, and refute Goldbach's Conjecture.

Taken all together my research has a huge impact over number theory.

In considering resistance to my research you can keep running into the same reality of demonstrated results with my research, like the sieve form of my prime counting function being VERY short and VERY fast, versus the political behavior of opponents to that research.

They lie, mislead and ignore direct evidence, while engaging in smear tactics and coordinated group behavior meant to convince people by making it appear that a large crowd—it's about a dozen of them—have substantive disagreements with my research.

And then somehow an entire math journal keeling over and dying after publishing a paper of mine, only to pull it when sci.math'ers do an email assault is evidence against me, according to these people.

Political parties here in America could learn a thing or two from them!!!

Math journals do not just die. And a crappy math journal would be LESS likely to take a risk with an admitted amateur mathematician. And a vanity journal wouldn't open the doors to some unknown.

Reality is that only a top-notch journal with a brave (briefly though) editorial board would publish a HUGE paper that lead down the line to unseating major players in the field like Andrew Wiles.

The revolution in mathematics on the verge of taking place is possibly the hugest in its history as there is a shift in the understanding of numbers themselves with one of the greatest events in the intellectual history of our world being the gaining of the knowledge of what I call the object ring.

Here and now it's difficult to grasp how huge it all is, or how important it all is to the intellectual future of our world, but I can assure you that no matter how effective some of you think you are in blocking this mathematical revolution, you have not the power to halt something on this big of a scale.

Without mathematics making this revolution, the scientific and technological progress of humanity itself has nearly reached a ceiling.

Mathematics is that important. Without this revolution there is no future.


JSH: Lying is how they live

We're talking about the fate of the world here.

So yes, there are bad guys in this story.

The great stories always have bad guys.

And some of you may feel like now is the time to just cut off from the entire mess, and try to find something to believe in, when you already have something—mathematical proof.

Go with the math.

Usenet is a lot about people pretending to be something they are not.

But I'm here because mainstream math society has pushed me to the fringe.

But one thing you can be certain of, I am James Harris.

And you can check my math.

Friday, November 10, 2006


JSH: Attack the discoverer

They are frauds. People who figured out how to use "pure math" to techno-babble and take home paychecks for doing of value to humanity have to fear real discoverers.

So they attack them.

That's why you have such a well-formed structure in the math community against "cranks" and "crackpots" not because such people are dangerous, as truly disturbed people don't make a lot of sense so it's not like they can be very convincing with rigid logic and in vigorous debate.

You have an attack culture against such people to catch the people who are neither.

Some of you I think rationalize by saying it's me and my personality, so I say do a web search on Britney Gallivan.

Who did she piss off? Is she some person angering people on the web?

Why does her research get marginalized?

Maybe you think if you play by their rules and learn within the system, getting a math degree, they'll let you make real discoveries.

Think again.

They'll teach you to claim that people who aren't making real discoveries actually are, but if you make real discoveries of your own, you'll be sidelined, and if you complain, you're a crank.

Do a web search on Perti Lounesto.

You have no idea how bad this is, or what happens when you have spent years working at being a mathematician and maybe figure something out that makes you a threat and none of that matters.

The best minds simply leave. The story does not get told. The parasites remain and party.

It's not about me. They'd do the same to you if you had my discoveries but you'd be an easier target than I am.

That's the only difference. You'd have probably given up by now and been silenced and bittered.

Crying quietly to yourself about the evils of this world and in your disillusionment, giving the parasites the victory they want and seek.

Why else do you think they engage in so many psychological attacks?

The ploy is to attack the discoverer—into silence.


JSH: Some prime counting facts, facing the swarm

I've given the conciser sieve form of my prime counting function to dramatically show how clear it is that certain people are ignoring important mathematical research.

The LaTex won't be processed but hopefully some of you who use LaTex will be able to see what it is anyway.

With natural numbers x and n, where p_i is the i_th prime:

:<math>P(x,n) = x - 1 -\sum_{i=1}^n {(P(x/p_i,i-1) - (i-1))}</math>

where if n is greater than the count of primes up to and including <math>\sqrt{x}</math> then n is reset to that count.

Here's an interesting tidbit, you can SEE the equivalent to the above in a specific range in what is called Meissel's Formula:


where it is P_2(x,a).

That is the form when

x/p_i < i - 1

as then P(x/p_i, i-1) = pi(x/p_i).

So the actual mathematical reality is that my prime counting function in its sieve form in a specific range is equivalent to a key piece of Meissel's Formula.

Now I figured out my prime counting function as a thinking exercise a few years back, and have had to argue, and argue, and argue with mathematicians about it ever since as the real world is not that people celebrate your discoveries in the math world, they try to ignore them because they didn't make them.

That community is the one you don't understand which is why I'm trying to educate you with easily checkable facts.

Notice how posters swarm over these threads as I create them, babbling nonsense to block out the facts?

Read through those threads and see the same names over and over again, and consider, how many of those people are actually acting alone?

Top mathematicians can ignore me, but how can they be sure that maybe some of you might not pick up on these ideas and start asking uncomfortable questions?

So why wouldn't they have an attack squad out here on Usenet to protect them?

[A reply to someone who wanted to know how James could say that he was being ignored, since his result was published on the Internet and it was acknowledged as correct.]

It is one of the shortest prime counting functions known:

With natural numbers x and n, where p_i is the i_th prime:

:<math>P(x,n) = x - 1 -\sum_{i=1}^n {(P(x/p_i,i-1) - (i-1))}</math>

where if n is greater than the count of primes up to and including <math>\sqrt{x}</math> then n is reset to that count.

And in that form, also one of the fastest.

Because of that unique form it can be fully mathematicized into a summation of a partial difference equation:

If <math>y\le\sqrt{x}</math> then

:<math>P(x,y) = \mathrm{floor}(x) - 1 -\sum_{k=2}^y {((P(x/k,k-1) - P(k-1,\sqrt{k-1}))( P(k,\sqrt{k}) - P(k-1,\sqrt{k-1})))}</math>

else <math>P(x,y) = P(x,\sqrt{x})</math>.

In that form, it doesn't need to be given a list of primes because it uses a partial difference equation, and yes, there is a partial differential equation that follows from it.

All of that sounds like exciting mathematics to me. Lots of places where there is uniqueness and a clear route to a partial differential equation connecting the discrete to the continuous.

Mathematicians ignoring it is like if physicists ignored…um, I don't know.

But mathematicians don't just ignore my research, some of you come on Usenet and lie about it, manipulating newsgroups and telling them bogus math.

There has to be a reason for that behavior.

Simplest reason is that you're con artists who are protecting your con. You know if you properly acknowledge my research your fraud will be outed and you'll lose a money source, so you fight it.


Prime numbers, counting tells it all

So notice there is no debate about correctness.

I found that you can count prime numbers using a short and simple method, which I call my prime counting function.

Easiest way to read about it now is to go to the Wikipedia and the talk pages of the prime counting function, where you can also see at the bottom the short sieve form:

My prime counting function is actually most closely related to something discovered by Meissel and at its top iterations is equivalent to that, and sieve forms—in the top iterations—are equivalent to the fastest known in the world as all the top algorithms do that part the same way.

If you do not know those things then consider how little you actually know despite how much you may think you know on the subject.

Regardless, even if it were just a re-hash mostly, the shortness and simplicity of my prime counting function in its sieve form would make it worth noting and teaching with, as it's just easier to learn about prime counting using it and a lot easier to program it than other methods.

So why do these people not only keep fighting me about my research in this area but manage to keep getting important details wrong?

Simple answer is that the math field is now corrupted. Some people learned that they could do a lot by acting at being mathematicians because they could just support each other—claiming that they succeeded—when they actually failed to find proofs.

Such a system has one fatal flaw—real discoverers mess things up.

So these people use various ways to attack real discoverers.

And you can consider that prime counting function in its shortness and simplicity having to be shown on the Wikipedia in talk page as proof of how powerful they are and how ruthless.

Of course my research covers a lot more than just counting primes, and that's where these people really have a lot to fear.

Reality is that "pure math" as it is now implemented is a communal system relying on the opinion of one group to claim that some person or person's have perfect mathematical arguments, otherwise known as mathematical proofs.

It is a great system for fraud, as long as you have a critical mass of people willing to just agree with what they are supposed to, which is why it's so hard for a discoverer like me to break it because they TRAIN you all to agree, and think consensus is a great thing, which allows them to lie about mathematics and hide research from discoverers.

So no Andrew Wiles did not prove Fermat's Last Theorem. But he can rely on supporters around the world claiming he did no matter how many ways you prove he failed. Their word against the mathematics.

How could people do such a thing?

Easy. People around the world routinely do much worse if you hadn't noticed.

But how do you know they are doing such a thing?

You go to the Wikipedia talk page on the prime counting function and look at that short, simple little prime counting function, my prime counting function in its short form and realize just how far they will go, and how dangerous they really are.

These people do fake math, for their own gain. They make money. Gain prestige, and they are ruthless.

Count the primes. Step back to think objectively about the smear campaign that is used against my research. Ask yourself how a highly creative individual who could make major discoveries would actually react to coming upon stinking corruption.

And start ending the con.

These people depend on your trust, following a system they have managed, and on you just being dumb about basics, like how I point out that computers aren't used to check mathematical arguments.

They will block anything they can. Including progress at using computers to check claims of mathematical proof.

They have to to survive. For our species to survive you have to look at the truth.

[A reply to someone who wished to know why, if it is true that James proved Fermat's last theorem and destroyed the foundations of number theory, he is particularly worried about prime counting.]

I have LOTS of research in multiple areas while the easiest area to attack is research related to FLT as mathematicians have a field day with comparing you to crackpots and cranks through the ages who have hacked at the problem.

In contrast counting prime numbers is as direct and real as you get with numbers and it has a very intuitive aspect.

Also, my prime counting function in its sieve form just looks dramatic, as it's so short.

People who compare that with what they see on the main prime counting function page of the Wikipedia can feel deep in their bones that something must be wrong.

And there is no other good explanation except that the math field is corrupted by people who pretend they are making major discoveries, supported by other people who pretend, and they all get paid that way.

Which is why computers are a threat as well so they have to keep coming up with excuses for why computers can't check all those supposed proofs, even though mathematics is a logical subject.

These people are slime of the earth.

They found a way to suck the life out of humanity by attaching themselves in an important but vulnerable area as "pure math" opened the door for them, and now it's just hard getting them out.

Like trying to burn leeches off of a patient covered with them.

The mathematical world is full of parasites who have figured out a way to beat the system, but they have to block out real discoverers to do it—and computers as well.

My prime counting function is a way to help people see the parasites for what they are, and the parasites can't react to it, as in accepting it, because they know that I won't stop there, so there is a pause.

Wednesday, November 08, 2006


JSH: So they broke the rules

So yes, for YEARS now you've had a steady diet of people ripping on me and my research, where it looks like I can't win.

You have people who gang together and make a mission out of posting carefully and in concert to convince you that I'm wrong, while I keep at mathematical research like a damn fool so that I can check the research I have and maybe discover something new.

And in the process I make a lot of mistakes.

And you can believe that in this world maybe the bad guys just are better at winning public opinion so I don't have a chance.

But I know a little bit about time, and about process, as well as about why values matter.

Values matter not because you can get a poll one day saying that most people believe you.

Values matter because at the end of the day you can say you did your best.

If you can say you did your best, then if people don't believe you, at least you can be satisfied that you did your best.

I really do not care a lot about what people around the world think of me, but I have to accept the responsibility that is forced upon me by this situation I'm in.

Those before me did not fail. If they had I wouldn't have this computer to talk to the world through.

I will not fail. But it may take time. It may take more years. Years when there will be people who will be insulting me, and fighting effectively to deny the truth as they fight mathematical proof.

But I can only do my best, and part of my best is not giving up, and not deciding that the bad guys have to win.

The weight of the world is on my shoulders simply because I found a mistake from over a hundred years ago, and found that some people were not who they claimed, and realized that mathematics is a crucial discipline to our future, so I must not fail.

So some people broke the rules and appeared to get away with it. I got published but they could just kill the journal, after convincing some editors to go against their rules.

When you believe that that's all that matters you may as well lay down and die because every day there are people who seem to get away with breaking the rules.

Enough talk. It's past time to move beyond politics and go with the math.

>From my prime counting function to my ideas on three logic, to my excursions into factoring polynomials into non-polynomial factors I have been blessed with brilliant and effective ideas.

The pain that has gone along with them is just proof of how big they are as you are not allowed to just win. You do not just waltz up and take victory. You have to earn it through pain, blood, sweat and tears.

Or die trying.


JSH: Change is reality

So much changes but human nature is to look to the past to conclude what must be the future.

As my nation goes through changes I want to make the point to you that what you think is possible may simply be what you have seen before, and what is actually possible, may be what you cannot imagine.

I imagine.

My journey has been about going from hypothetical to reality, from dreams of success to accomplishments so great that they are difficult to grasp, even by me.

Moving forward there will be less of the brainstorming, casting about, and direct communication that has made the early part of this journey such a trial.

As time progresses I can escape this dungeon and move beyond postings, so I guess later I'll never make a direct posting like this, and even if something ends up on Usenet it will go past some committee first—people who will make sure the message is the "correct" one and that there is some message that I stay on, and that I don't stick my foot into some pile of dung.

The break that I took as I tried to absorb what I'd discovered, and tried to absorb the world's ability to ignore it is almost over, and going forward I'll turn back to those abilities that have made my life so extraordinary so that I can post a reply from Marvin Minsky, or from Jeff Lagarias, or from people I haven't talked to you yet about because I can contact them, and be heard.

As my country goes through changes where the ability of some people to claim one thing and do another fades, and the ability of some people to escape the truth, for a while, fades, so too will the ability of you people to do the same.

The Universe has sent a message and you can ignore that message, but you will face the consequences anyway.

Like the Democrats fighting here in the US to no avail, with so much failure against a seemingly indomitable Republican party, I have fought against a seemingly indomitable wall of denial from an incumbent mathematical party, which has learned how to use people to its advantage against mathematical proof.

Change is that which confounds the plans of mere mortals, and damns the designs of mice and men.

We are facing change.

The story here will just get bigger as Usenet people fight to make it small. Already the battles cross out of Usenet to the Wikipedia across Google and into countries around the world as I track.

The story gets ever sadder as mathematicians are nailed to the wall with no defense in their denial of simple mathematics and direct mathematical proof.

And in their contempt for humanity, their quest to stop progress, to end the movement forward of number theory, their attempts to stop—for the first time in human history—a discoverer.

Going forward you may not know where the next move will be. You may not know—until it's too late—what person I know who is on my side, or in my corner, and you will not know the consequences for your life, until those consequences are a reality.

Open information and open source were cornerstones of my philosophy—but no longer.

The math wars have convinced me that some ideals are meant to be lost, and that letting your opponents know too much about what is coming is just a bad idea.

You will not know nearly as much about what I'm doing as you have known before, except that it will be so much more than ever before with more players with more power than before as I've learned from the past.

I need the most powerful people on the planet on my side FIRST before anyone in the mathematical community has a clue what's coming or can react.

Your will to deny demands a stronger will to catch you at your weaknesses, take you from your blind spots, and remove your defenses before you even know that some senator or governor is breathing down your necks.

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