Monday, January 29, 2007


Lying in mathematics

One of the most profound things I now realize is completely true is that in areas where people can lie and get away with it, often they do.

And in mathematics, in areas where only people check people, people do lie.

It might be strange to consider that as I think a lot of people know that mathematics is HUGELY important to a lot of science and technology, so how can people lie about it?

Well, there they don't.

Where they can be checked with other than human eyeballs, the mathematicians are ok.

They don't lie. Their math works and we have the technology and science that proves it.

Those mathematicians are OK.

Where they cannot be checked with the real world, they are not.

They lie.

Now computers could check ANY valid mathematical argument, if they were allowed, as in, if people would program them to, but today as I type this post, mathematicians in areas where they only need other mathematicians claiming they are correct, don't have to worry about some damn machine checking them too.

But why not?

Ask them and see what bizarre and wacky answer you get because, well, they lie!

The real answer is they don't want computers checking them because then all of mathematics would be like the areas that are useful in science and technology, and well, people couldn't lie—claim results are true when they are not knowing that other people in it with them, who need the lies to survive in the field, will just go along.

Or ignore results from people like me because they can be nasty, vicious people who are nothing like what most people think, let alone brilliant.

As if they WERE brilliant, they'd WANT computers to check their research to remove the tedium from human beings who could do better things with their time than check behind other mathematicians, like figure out new math of their own!

Friday, January 26, 2007


JSH: Single star rating

Google Groups allows people to rate posts. I look now and I see 733 ratings, where now I sit at a single star.


I think that's important.

No matter what one might like to think, it is true that so much depends on how people look at you.

And I see, rejection.

In deference to that rating and the opinion given to me by Google Groups and its rating system, I feel a need to lessen my postings.

I dare not say I'll stop, as I find the activity addictive, but I dare not deny the reality of the world's disdain for me. The rejection that tells me that I am not wanted.

But Usenet is not all about being wanted. Or about popularity.

The world may reject me, but I say FUCK THE WORLD to the extent that I will still speak.

But I say, respect the world to the extent that I acknowledge, that my ideas are not wanted.

I can rant and rave as I wish, but deep down, I accept that the world does not accept me.

Hell yeah. Fuck the world. It doesn't want me. Fuck it.

After all, the world if fucking stupid anyway. Just look at it.
If fucking stupid? I say, no doubt. It's fucking stupid.

The world's disdain for me, as shown by Google, so much a controller is more a validation than anything else.

Like Google knows anything other than how to control people who don't know they're being controlled.

I welcome it.

Give me your rejection little people.

And I take the future.

[A reply to someone who suggested that maybe James' ideas will be wanted in the next one and that he should save them till then.]

Oh please. Princeton still hasn't rejected my paper yet.

Does it not occur to any of you, that I am mocking your world?

That in my postings you see nails being driven into it?

I think that somehow, someway you people lack even the most basic of intelligence.

It's like, you have devolved.

You're not even human.

You're apes, jumping up and down and screaming for dominance…in a game you've already lost.

Monday, January 22, 2007


JSH: Wikipedia article on difference equations?

It seems the Wikipedia doesn't have an article on difference equations. There is now just a re-direct to recurrence relations.

For those of you who don't know, a few years back the Wikipedia didn't have a prime counting function article either, until I wrote the first one.

I may start a difference equation article, but I'll let you people get
your chance first.

[A reply to someone who wrote that James should write it so that someone else could have the pleasure of deleting it like all his other worthless crap.]

You clearly don't know anything about the Wikipedia.

But you sci.math people—yes for those who don't know just more sci.math regulars who track me to other newsgroups replying so far—are all about rage. So sad.

I'm just being nice by not going ahead and writing the article anyway, though I do admit that while I have rough drafts in mind I'm not settled on any one thing as of yet.

But it is not as simple a matter of deleting off an article once I start one.

You'd have to justify doing so before the Wikipedia community.

And rage would not work with that group. You'd need to at least attempt to argue objectively.

Sunday, January 21, 2007


JSH: What's a partial difference equation?

There seems to be this huge divergence I think between what I see the point of all the discussion is and what other people see it as, where I think the thrill of knowledge itself is being lost, so I have a question that can go to the heart of what matters with my prime counting research:

What is a partial difference equation?

[A reply to someone who wrote that there is some pretty intense stuff out there concerning this subject.]

Discrete mathematics is much more difficult, which is one of the reasons for a LOT of resistance within the scientific community to discretization of physics.

But that doesn't mean it's not right.

The real story about the revolution behind my research is the transformation of how we look at our world, and our universe.

And my real hope at the heart of my efforts is the movement from our planet…to the stars.

There are more forces fighting that than it's worth talking about, but let's just say, stopping humanity now, is of great importance for beings most of you would never understand.

But the good news is they don't quite succeed, at least, not entirely.

Thursday, January 18, 2007


JSH: Just a basic screw-up

People don't argue for years over basic algebra that is actually wrong.

And all the rationalizations given do not explain why a mathematical journal would publish a paper from an amateur that relied on basic algebra that was wrong.

There just isn't enough material in a simple argument with basic algebra for people to go on and on for years.

Or for any mathematicians to accidentally think it might be correct when it's wrong.

What I found was a basic screw-up over a hundred years ago that just wasn't caught until now.

But mathematics professors sitting at universities who have built careers around the screw-up, who idolize dead mathematicians who were part of the screw-up would just as soon forget about it and keep teaching math that is no longer about what is mathematically correct.

And I see no way to stop them.

They just failed. People fail.

These mathematicians just failed. But they won't accept they failed, so they keep failing.

And there's not a lot I can do.

Sunday, January 14, 2007


JSH: So why is it fraud?

I uncovered a major error in number theory that entered the field over a hundred years ago that hasn't been noticed because no one did the type of analysis I did—it's kind of creative—and because it is in a "pure math" area, so with no practical application there was no indication from the real world that the stuff they were doing didn't work.

I stumbled across the problem after working—unsuccessfully for much of the time—for over four years trying to find a simple proof of Fermat's Last Theorem.

The paper I wrote that got published was actually about demonstrating the error.

That's how sci.math'ers attacked it, by using the error to claim the paper was wrong—not admitting there was this error.

It's a big enough error that the journal dying is not a big surprise.

But I talked out that paper and its techniques on more than Usenet, as I emailed mathematicians as well, including Barry Mazur a top ranked mathematician at Harvard University. I also worked out the argument in person at Vanderbilt University talking to a Professor McKenzie, using the chalkboard in his office, at his request. He suggested I explain in person, after I forwarded an email I go in reply from Barry Mazur.

What should have happened is that without me even having to get published at least one of the people I contacted should have raised the alarm about the problem I found.

After all, it entered the mathematical field before any of them were born.

That's not the fault of any of them.

But teaching it now is a fault, and that is entirely on them.

It is academic fraud.

Why would an entire mathematical journal die over this?

Because it is that big. As the years go by the fraud aspect of it gets bigger as do the costs associated with the fraud.

Consider some undergraduate in mathematics, who thinks they are learning great things, who finds out that part of what they have learned is just wrong, and it was known that it was wrong, years ago.

Do you want to be the one to try and rescue that person back to believing in the system?

Today that undergraduate can learn the teachings are wrong by coming across my research on the web, and what is their choice?

To leave.

How can they confront math professors?

Or they can decide this world is just crap anyway, they're just there to do whatever it takes to get something, and just repeat what they're told without believing in any of it, just playing a dumb game.

The facts in this case leave no doubt about what is the real truth:

Mathematical journals do not just publish anyone. And they do not just die.

People do not spend a lot of energy where they do not have serious investment, so Usenet posters claiming they do so because there is nothing to what I say, are saying you must be either dumb about human nature, or with them.

And mathematics professors who do not reveal to the world a serious flaw in their field are not decent or ethical people.


JSH: So why the fraud from the world's mathematicians

Mathematics is one of our greatest disciplines without which we would not have our modern world, for instance, you wouldn't be reading these words because computers wouldn't exist.

We have a world of beautiful results and brilliant insights that have given us powerful tools with which civilization can do more and more.

Mathematics is the backbone of the sciences, crucial in technology, and mathematicians around the world get a lot of credibility immediately with most people—even if what they actually do in mathematics has nothing whatsoever to do with any of that.

How many of you think you understand the mathematical field?

Would it surprise you that "pure" mathematicians can have an entire career with results that have nothing to do with science, nothing to do with technology, and nothing to do with anything at all that is practical, where every result they have has simply been looked over by other people and never tested any other way?

If that would surprise you then you don't understand the modern mathematical world.

MOST of the mathematics used in science and technology was figured out centuries ago, for instance, think of geometry. Euclid did quite a bit over a thousand years ago. High school, or secondary school for people outside the US, geometry would not have surprises for Euclid, who properly gets credited with collecting what was known in his time for a work relied upon for generations.

So we build on what was known before that worked, which is a great thing, but it can be problematic if a mistake is made!

Mistakes made in practical areas lead to things that DO NOT WORK but in "pure math" areas, how do you know?

Such results are only looked over by people. Yup, people look them over looking for mistakes in the reasoning, and there is a strongly held assumption that if a lot of people look at something for long enough, then they would catch any and all mistakes.

But that is just dumb. It defies what we know in the modern world about how groups operate, as sometimes the MORE people who look something over, believing it must be right, the less likely an error is to be found.

With mathematical ideas that can be used to build a better engine for an automobile, wrong assertions can reveal themselves by the engine not working better, but if you just had engineers looking over an idea who never built the engine, what might they think could work even when it doesn't?

Well in number theory with some impractical research, there was a mistake made in the late 1800's.

While pursuing a short proof of Fermat's Last Theorem I uncovered the mistake.

To date, modern mathematicians in number theory have not fully acknowledged the mistake and corrected it, but instead, keep teaching it.

To date, nothing has worked in stopping these people, as I've gotten publication—some sci.math posters managed to break the much vaunted formal peer review system with some emails to the editor claiming I was wrong, and the editor pulled my paper, and later the journal died.

I've put my research on web pages, where it is at right now.

I have emailed mathematicians around the world, and even gone back to my alma mater Vanderbilt University and explained my mathematical ideas to a professor there.

Remember, these are university mathematics professors who can hear of my results, understand that they are correct, and then go on teaching wrong stuff because the alternative is to feel very invalidated, and as the years go by they can just see that nothing I do works anyway, so it's not like there is much pressure on them to change.

But they are "beautiful minds" right?

No. They aren't. If they were, they would have figured out what I did.

They are people who now realize they are NOT as brilliant as they thought, and that will not change, no matter what they do.

Don't you get it?

Like Andrew Wiles. He is currently credited as one of the great mathematical minds of all time, but my research takes all that away, but it keeps going, as the full story is he may be no better at math than most of you are.

He may be worse, as his instincts didn't tell him that the methods he was learning in school didn't actually work.

Why would he tell the truth?

If he were great, he wouldn't be in the position he is in.


JSH: Not like football, they cheated

After watching a great playoff game today I am impressed with how sports is purer than academics because you have rules, people go out and play the game and to a large extent you can be certain that people have to play within the rules.

But academics can break their own rules, like how I have a unique mathematical find—as unique today as it was back in the summer of 2002—and it doesn't matter because math professors sitting at their desks at universities don't have to follow rules while the college students and coaches of their sports teams do.

With some of my other research I even got published—as I followed rules.

Some sci.math'ers send emails claiming I'm wrong, and the university math professors who were editors at the journal—broke the rules and pulled my paper after publication.

These university math professors do not follow their own rules, and what can you do with that?

I mean, think about it, you can go out to a bookstore today and get popular works about how these people supposedly care so much about big questions like the Riemann Hypothesis, and I have unique research in that area that might lead to an answer, and they try to act like it doesn't exist.

But the coaches at these schools have to follow all kinds of rules that have to do with having a fair game, when the academics don't.

Why wouldn't they?

I say, it's because the answers that come from my research don't suit the careers of the guys sitting at the desks writing their own papers and teaching kids about mathematics, telling them it's one way, when my discoveries say it can be another.

They say it's about listening to them for years, to learn as much as you can about what came before, so maybe if you're lucky, you can build on what came before, and you need to do everything a certain way, where mathematics is about academics and requires—professors.

I say mathematics can be about solving problems, and like the rest of the world, where what matters is whether or not you have a solution or not, answers can come from unlikely sources and people you wouldn't expect.

So I challenge the status quo, and that shouldn't matter as before I'd have said, hey, these are probably decent people who care at some level about what they're doing, and at the end of the day, yeah, they might fight a bit, hate it, but they'll go with what's proven to be true.

But it's been over four years now.

And there is no referee to make these math professors stop cheating. No clock to push them to do what's right.

And no real fans who care more about mathematics than they do about playing at mathematics.

Eggheads can hate sports, but eggheads can lie, when in sports you have a purity that would not have allowed this to happen, as people there can actually be counted on to follow the rules of the game, as best they can, or get caught by the referees.

So yeah, football is better than "pure" mathematics, as at the end of the game, with sports, you can usually feel good about how the rules were followed, but "pure" math professors can cheat, and you have no options, but I guess, whining about it on Usenet, where the "fans" just don't give a damn anyway.

Friday, January 12, 2007


JSH: Yeah from scratch

I started thinking about counting prime numbers having never bothered to read what mathematicians had on the subject. It just didn't seem that important to check on what was previously known so I did it all from scratch.

So I discovered what had never been found before, which can be forced down to something very similar to what was found, but you have to force it.

Naturally it's like nothing else—it finds the list of primes it needs on its own.

I think that story really upsets mathematicians because they don't do anything from scratch.

They love this monolithic building on what came before, so to get started on research they first immerse themselves on what was already done.

If I'd bothered to even do a web search on "prime counting" I'd never have made my discovery as I'd have looked at what was known and wandered off from the subject.

Mathematicians HATE from scratch. It may be for them the worst part of my story, as I found results not far from what was already known, but generation after generation of mathematicians just travel down the same trails first and then try to extend on what was already known.

I just set off in my own direction never bothering to check, as I just didn't care about what was previously known.

I simply did not care.


My prime counting, understanding forms

I talk about two forms with my prime counting function, where a lot of discussion ends up about the sieve form.

Here's the sieve form:

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))}

except when n is greater than the number of primes up to sqrt(x), as if it is, it is reset to that count.

It's a sieve form because p_i is the i_th prime number. For instance 3 is the second prime number so

p_2 = 3

and p_3 = 5, as 5 is the third prime number.

So if you want to count prime numbers with the sieve form, you have have a list of primes up to the positive value of sqrt(x), like to calculate P(100,4), you first need to know the first four primes: 2, 3, 5 and 7.

To calculate P(1000000,168) you need to know the first 168 primes.

The other form is NOT a sieve and relies on a partial difference

With all natural numbers:

P(x,y) = x - 1 - sum for k=2 to y of {(P([x/k,k-1) - P(k-1,sqrt(k-1)))dP(k,sqrt(k)}

where dP(k,sqrt(k)) = P(k,sqrt(k)) - P(k,sqrt(k-1))

where if y is greater than sqrt(x) then y is reset to sqrt(x).

The sieve form can be related to past known research with counting primes:

P(x,n) = phi(x,n) + n - 1

as has been pointed out, but to my knowledge, no one wrote it that way.

Mathematicians always wrote the prime counting function as

pi(x) = phi(x,n) + n -1

as they saw it as a single variable function that had a multi-variable helper function, which is a sieve function.

They didn't make the leap to looking at it as a multi-variable function as there didn't seem to be a point with the prime count.

But I did things my own way, as I did all my discovery from scratch, not having bothered to read about what mathematicians had done on prime counting and I naturally went to a multi-variable prime counting function that is not a sieve function, and can't be directly related to past research unless you force it to a sieve function.

So the natural form for what I discovered is NOT a sieve, it does not need you to give it a list of primes, and it relies on summing a partial difference equation, with a special constraint on how you do that sum.

That form leads to a partial differential equation and you can integrate that to get an approximate count of prime numbers explaining the prime number theorem.

But in so doing you can see that the exact count is different from those results because of that requirement about cutting y off at sqrt(x), so you have this simple explanation for the 'why' of the prime number theorem, as to why there is a gap.

Mathematicians since Gauss were curious about that gap, and Riemann was looking for an explanation when he made his famous hypothesis.

My research gives a simpler explanation and may give a way to check the Riemann Hypothesis that mathematicians did not realize existed, by directly comparing with the function that results from the partial differential equation that follows from the partial difference equation of my prime counting function.


JSH: My best guess about why

So if I am correct I am an amateur mathematician with some of the most dramatic results in mathematical history—some of them formally peer reviewed and published--who for years has had a mathematical community denying his results.

But why?

My best guess considering the nature of my results is that I simplified a HUGE swath of number theory.

Like with my prime counting function, compare the simple definition I have, for either the sieve form or the fully mathematicized form with the partial difference equation, to just about any page on prime counting you'd find anywhere else, and it's just more compact.

And yes, still no word from Princeton. I may bug them early February if the quiet continues, and ask what's going on.

So think about it people—results posters on sci.math have proclaimed boring or meaningless re-writes of Legendre's have been at Princeton University for over a month, even subtracting for the holidays.

You have already been shown up by one of the top schools in the world, as your newsgroup's blanket dismissal has been rejected.

Partial difference equation.

Posters on sci.math say stuff about the subject of difference equations that is childishly wrong, as in, it's so dumb you get embarrassed looking at it.

But a partial difference equation is just the discrete version of a partial differential equation.

They are interchangeable depending on the ring. One is in the ring of integers, the other is in the full field of complex numbers.

Yet posters here can say bizarrely dumb things about the partial difference equation from the full form of my prime counting function, but this newsgroup follows along.

But why? Why are editors at a journal yet again at odds with the newsgroup?

They are supposed to follow rules, that's why.

By the rules the paper should be considered on its merits without regard to anything outside of mathematics, which is what the Southwest Journal of Pure and Applied Mathematics was faced with years ago with my other paper.

By the rules the mathematics should be judged only by its merits.

So yeah, I'm sure there are readers here who think it matters if I talk about the paper being at Princeton as if that should influence what happens.

By the rules it should not.

You forget that sci.math doesn't have rules.

Usenet is not about rules.

Mathematical journals are about rules.

Here it's a free-for-all, and many posters clearly don't fear being held accountable for what they say.

So, yeah, the secret is that journals are different environments.

To break their rules editors at journals have to lose their society, lose their structure—lose their civilization.

You people in contrast lose nothing here because this environment is not about rules.

In contrast, editors get broken by a failure to follow the rules, which is how your newsgroup killed SWJPAM as the editors broke down under social pressure, and then could not continue.

So the journal died.

If the editors at the Annals didn't follow the rules, they could find themselves unable to continue as well.

It could end their careers as editors, just like that, as something inside would get lost.

But Usenet posters can babble on without concern no matter how wrong they are. It's the nature of the environment.

It's a place to babble on.

Thursday, January 11, 2007


JSH: What did I do?

Maybe it'd help if I told you all the bigger picture of what I actually accomplished over four years ago.

Yes, I found my prime counting function, but did so right after finishing a proof of Fermat's Last Theorem using some creative new analytical tools based on what I call tautological spaces.

Arguing about the proof of Fermat's I realized posters were focusing on one area, so I pulled that area out and wrote a paper on it, which is the paper that got published, then retracted by the editors, and then the journal died.

That paper was expanded from a couple of sentences in the full proof of Fermat's Last Theorem, but it shows a subtle error in a huge part of number theory.

So the big picture is that my research resets the way mathematicians around the world look at themselves.

I simplified a HUGE amount of number theory with some interesting new techniques.

One dead math journal is NOTHING compared to the big picture.

I think nothing like this has happened in history before.

[A reply to someone who wondered why people bothered with a clown like James.]

Yeah, if I were wrong, then they could do that, but I'm right so they can't.

It's simple.

Why did the entire sci.math newsgroup erupt in a fury when I got published, and go after the paper?

Because it was wrong?

Why not then be puzzled at it getting through? Why not just a little bit of self-reflection to be sure that maybe it wasn't right? Why go hot after the paper IMMEDIATELY?

But instead the newsgroup did not pause, did not consider but jumped to verbal attacks and then an email assault because deep down THEY KNOW IT IS RIGHT!!!

There is no need to reflect or pause when they know the real answer is they are wrong, my research is correct and that is why they are angry.

The anger is over the math. They hate what is mathematically correct.

An analogy would be if physicists had decided they couldn't stand quantum mechanics and hounded after people who talked about it.

Here is the mathematical revolution that can't occur because members of the math community hate the next step, like if physics people had hated to oddity and quirkiness of QM, then we could have had a drama like this one in that area.

Monday, January 08, 2007


JSH: Fact check, showing the reality

I am going to list several facts about my research, just to show you how far this has gone in terms of simple denial as you consider replies:
  1. My prime counting function is the only known multi-variable prime counting function in all of human history.

  2. My prime counting function, unlike any other prime counting function known, while having a sieve form, which can be related to past research, also has a purer math form, where it is what is called a partial difference equation, where it finds primes on its own in a way unlike any other known in human history.

  3. My prime counting function because it is a P(x,y) function can be graphed in three dimensional space.

  4. My prime counting function does not follow from any other known, though in its sieve form as mentioned above it can be related to other known research, where nothing other than the sieve form was known.

  5. I have other mathematical research published in a peer reviewed mathematical journal, sci.math posters assaulted the journal when they heard I was published and some of them sent emails falsely claiming my paper was wrong, convincing the editors who pulled it.

  6. To date, no one has refuted any mathematical argument that I currently hold as correct, and nothing that even appears to be a refutation can be given, as instead as you've seen in recent threads, posters just lie.

  7. My research is all about simple methods so that there is little room for error to hide, and no one has shown any error with any of my current research and cannot, even in reply to this thread.
Remember, these people lie. They may reply claiming refutation but mathematical proofs cannot be refuted. So they have to turn to lying to convince against proof.

Mathematicians today live in a world of complicated, where complicated gets them prestige, and for those who work professionally, funding.

My research in contrast is about simple. Simple explanations. Simple answers.

And that's why they hate it. Not because it's wrong, but because, to them, it's too simple.


JSH: Consider the letdown

Imagine you have decades working on one of the most prestigious areas of mathematics and have countless "deep" conversations with other "great" minds who have pondered, thought about, and considered the mysteries of those enigmatic wonders—prime numbers.

You are in awe at the beauty and complexity locked within mathematics you barely grasp and maybe only two or three people in the world completely understand, and it is your dream to someday just barely scratch the surface a little deeper just to understand a little bit more, just a bit more…

And then some loudmouth on Usenet posts a simple—to you—function that is the key to understanding it all, just like that, and he's not even a mathematician.

His degree is in PHYSICS!!!!!!!

What's this? Some Cosmic Joke? God laughing at you?

It cannot be. So what to do? What to do…

Ignore him! That'll teach the Universe!

Like you can be forced to comprehend what you thought was incomprehensible! Like you'll sit by and understand what you thought would never make complete sense to you.



If that sounds like some joke to you, try hard, really hard, to imagine putting years of your life into something, working very hard, believing one thing, only to have it shattered.

Answers might not be what most people really want.

Ever consider that?

[A reply to someone who said that James' algorithm yields no new insights whatsoever.]

So why lie? Why do posters like you keep fighting admitting even the simplest thing like it is the only known multi-variable prime counting function?

Why not acknowledge that no other known prime counting function can do what human beings do and find the helper primes on its own?

Lying about simple stuff betrays the reality here, which is that the simplicity of what I found is what people like you deny.

It's like if you're arguing with some person claiming that 2+2=5, and you count out 2 fingers and count out 2 more fingers and they say, FIVE!!!

You know it's not about what's true at all.

My research is simple. It's far simpler than most prime research.

Gut check people—my research is far simpler.

And in the lies told by other about that simplicity, you can see the real tale about how far mathematicians can be willing to go to hold on to complicated, when simple truth hurts too much to accept.


JSH: Rhetoric aside

So without all the drama the simple answer is that I found a function that counts primes in a way never before seen, so it has inside of it answers never before found.

Turns out you can go quickly and simply to a way to check some of the most complicated mathematical ideas ever known, and I wrote a paper on that and sent it to Princeton late November of last year, and it is, still under review.

That "simple" is what gets me in trouble.

Turns out that what I have is so damn simple it's easy for math people to lie about it as many of you WANT complicated. You need mathematical ideas that are incomprehensible as that's what mathematicians usually give you, so you hate simple like they do.

None of you really wants to know how prime numbers operate, you want the satisfaction of reading some popular work that tells you that it is all beyond you but brilliant and beautiful minds understand it, somewhere.

So my research is hampered by its simplicity. As notice how dumb the stuff posters had to lie about is, as it IS so simple.

But mathematicians hate simple, and the people who cheer them on hate it as well, like soft tackling in American football.

You want complexity to feel like something impressive is actually going on.


JSH: Re-cap, when is unique also important?

What is not in doubt is that back in 2002 after a problem solving effort I found my own way to count prime numbers where last week I kept talking about the sieve form of my prime counting function.

But that's not what I found years ago.

To understand the issues now you need to understand just a bit about counting prime numbers, as in all of human history there have been only two basic ways to count them:
  1. Brute force, like from 1 to 10, you check that no natural numbers below 2 divide it, except 1, so it is prime, as is 3, then you find that 2 divides 4 so it's not, and then no naturals except 1 divide 5 so it is, and so on…

  2. Get smarter and notice that you can count the primes by first finding primes. That is, you find the primes below the positive square root of the number you're counting up to, and get counts using those primes.
Natural numbers are just the counting numbers, starting at 1, next 2, then 3 and so forth.

The brute force method doesn't work that well, so people have figured out smart ways with the second approach. And with it you have sieve methods, where again, you use primes to count more primes.

In thousands of years of human history there have been just these two ways known to exactly count prime numbers, until I found my prime counting function, where crucial here is in understanding what hasn't been mentioned.

I did not find a sieve function. Years ago when I posted I did not post a sieve function.

What I found is a function that unlike any other previously known, finds the primes it needs to do counting the smarter way, where you just tell it that 2 is prime and it figures out the rest.

That is a P(x,y) function. Where y is like x, just another natural number.

In contrast with sieve functions like my prime counting function in its sieve form P(x,n), there n is a count of prime numbers—the helper primes you need to count primes.

Guess what? I didn't first give the sieve form of my prime counting function as it was a sci.math poster named Wim Benthem who did so, years ago, after I put up something unlike anything mathematicians had ever seen before—a function that did what people did, count primes by first finding primes, on its own.

For days last week I argued with posters about whether or not there is another known multi-variable prime counting function, as several posters lied until cornered and then switched to saying my prime counting function could be trivially related to a previously known phi function.

But they lied again, as that's not the function I actually discovered.

And the one I actually discovered cannot be so related to anything else known. It cannot be directly related to any sieve function.

If I am wrong a poster should relate my P(x,y) function to something previously known.

Those who followed the discussion may remember I asked posters if there was anything else unique about my prime counting function besides being multi-variable, and you may notice they did not give you the answer I give to you now.

So you have the lies about there being another multi-variable prime counting function, collapsing into lies that my prime counting function was just trivially related to another multi-variable function, when in fact what I actually discovered and posted about those years ago, can't be related to anything else known, and it can do what no other known mathematical function can do.

So what gives?

Why would mathematicians lie if it's so grand, and is there anything else to this prime counting function of mine?

Well some of you know that modern mathematics can get a little complicated. You may also know that mathematicians can get a lot of schooling to study difficult topics for years to gain expertise in their subject areas.

It can be a difficult business with extreme complexity, difficult arguments and years of effort just to understand the basics.

And I might have cut the Gordian knot in one of the most high profile areas—prime numbers.

Imagine you are a Ph.D in mathematics specializing in prime numbers, and you sent a grant proposal for federal funds totalling $500,000 US to fund your research where most of that is your SALARY for five years of research. And then some nobody, from nowhere comes up with a simple damn function that opens the door to a simple explanation and your research is not needed.

Do you just give up on half a million dollars over the next five years?

Didn't think of it that way? Don't understand how mathematical research gets funded?

I give a simple answer, and mathematicians lose income—if they acknowledge it.

If they don't, and notice, they didn't, those research grants keep coming, the money keeps flowing, and that mathematics Ph.D is still worth something.

Alternative explanations?

Give them please.

You have a unique function that does what no other in human history has ever done in counting prime numbers. Yet mathematicians have done their best to completely ignore it for over four years.

Oh yeah, is there anything else to its uniqueness?

In its simplicity may be found the answers to the 'why' of prime numbers. Answers so simple, they might even make sense to non-mathematicians.

A slashing breakdown of complexity, replaced with beautiful simplicity.

Yet most mathematicians completely ignore it, while you get Usenet posters who lie about its details, continually getting caught in lies and omissions.

Come on, deep down, you knew it had to be about money.

So simple answer is, they lie about it because of the money.

[A reply to someone who said that James' algorithm is not essentially different from the very earliest work done on the subject, and that, although it is an achievement for James to come up with it independently, it yields no new insights.]

In actuality it explains the prime distribution giving answers looked for by some of the greatest minds in mathematical history, as the P(x,y) prime counting function, not the sieve function posters continually try to bring up instead, is a fully mathematicized prime counting function, which just kind of blabs out the answer at you.

It says that the prime count varies from other mathematical functions—the prime gap shown by the prime number theorem—because you have to specially constrain the partial difference equation on which the P(x,y) function relies.

So it just tosses the answer out there, easy. An easy answer in one of the areas where other research is quite complicated.

The partial difference equation on which my prime counting function in its full glory as a fully mathematicized function relies, leads to a partial differential equation, which can be integrated, to get an approximation to the prime count.

There is NOTHING even close in ANY of the mathematical literature.

And to lie about it posters have to just dodge that assertion in detail and depend on flatly denying it as there is NOTHING even close in ANY of the mathematical literature.


So they cannot show.

To lie here posters have to lie as flatly as if you asserted that 2+2=5, as there is nothing in all of human history that covers the territory I covered with some simple ideas.


Such an absolute statement does not need rhetoric in response but concrete facts.

To the extent that posters in reply rely on rhetoric, you know they are lying to you.

Saturday, January 06, 2007


My prime counting function

I've talked a lot in various formats across the web about a way to count prime numbers that I found back in 2002.

I am going to next give my prime counting function in its sieve form, where things might look a bit complicated but I'm going to break it all down simply to count the primes up to 100.

Sieve form of my prime counting function:

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.

The word "sieve" is used a lot like it is used in non-math areas to mean a way to block out certain things while getting just what you want. And to count the primes up to 100 the sieve part has to do with getting primes, as you first need to already know the primes up to the positive square root of 100, which is of course 10.

And those primes are 2, 3, 5, and 7, and there are 4 of them, so with x=100, n = 4, and I can go back and expand out what I had before:

P(100,4) = 100 - 1 - (P([100/2], 0)-0) - (P([100/3], 1) - 1) - (P([100/5, 2) - 2 )- (P([100/7], 3) - 3 )

where I want to explain the part with the brackets, as, for instance, [100/3] = 33.

The brackets are called the floor function and mean to drop off any remainder when you do the division, which is a good thing, as it makes it easier to do the calculation without worry about any decimal places or fractions. So, now I can go forward to get:

P(100,4) = 99 - P(50, 0) - P(33, 1) + 1 - P(20, 2) + 2 - P(14, 3) + 3

and there is a problem with the last one as the count of primes up to the positive of sqrt(14) is just 1, so that needs to be changed to 1, and I can simplify some so I have:

P(100,4) = 105 - P(50, 0) - P(33, 1) - P(20, 2) - P(14, 1)

So now what? Well the function has called itself 4 times so you go through each time, and the first is easy enough as you now have

P(50, 0) = 50 - 1 = 49

as the 0 means no other iterations, because you go from 1, in the definition above. But,

P(33, 1) = 33 - 1 - P([33/2], 0) + 0 = 32 - P[16,0] = 32 - 15 = 17

I know that P[16,0] equals 15 from what I learned with the previous case as the 0 means not to iterate so you just subtract 1, so that's easy. Next is

P(20, 2) = 20 - 1 - (P([20/2], 0) - 0) - (P([20/3], 1) - 1)


P(20, 2) = 19 - P(10, 0) - P(6, 1) + 1

and the P(10,0) is easy to get as that is just 9. And there is a short-cut for P(6,1) though you can go the long way if you want, or you can notice that there is only one prime less than the positive square root of 6 as that prime is 2, so P(6,1) must be the count of primes up to 6, and those are 2, 3 and 5, so it is 3. Then

P(20, 2) = 20 - 9 - 3 = 8

and you may notice that is the count of primes up to 20. As 2 is equal to the number of primes less than the positive square root of 20.

So now only P(14, 1) is left and you may think now this is a long process but I am explaining a lot so you can have a clear idea of how it works. Once you get a feel for it though, it's a fast and easy way to count primes.

Now with P(14, 1) is can use the formula or I can just notice that it is the count of primes up to 14, which is 6, as those are 2, 3, 5, 7, 11 and 13. (As an exercise you can go ahead with the formula and verify you get 6.)

So now finally I can get the count of primes up to 100:

P(100,4) = 105 - 49 - 17 - 8 - 6 = 25

To verify your prime counts you can go on to web to various sources. Here's one:

There is a table where you can see the count of primes for 100, or, of course you can just go through all the numbers up to 100 and count.

Ok, so that is a detailed explanation of how to use that formula which is the sieve form of my prime counting function.

Just for fun, I'll do a quick calculation for 120, as that's the last number before you get another prime, so n still equals 4, like before and

P(120,4) = 120 - 1 - (P([120/2], 0)-0) - (P([120/3], 1) - 1) - (P([120/5, 2) - 2 )- (P([120/7], 3) - 3 )


P(120,4) = 119 - 59 - P(40, 1) + 1 - P(24, 2) + 2 - P(17, 2) + 3

where P(17,3) goes to P(17,2) because there are only two primes up to the positive square root of 17. And now for some short-cuts, as P(24,2) is the count of primes up to 24, and I'll just count those off on my fingers to get P(24, 2) = 9, and doing the same with P(17,2) gives

P(17,2) = 7

and hope you caught that one as I didn't at first as 17 is prime, so it gets counted.

And P(40,1) = 40 - 1 - P(20,0) = 39 - 19 = 20, so I have

P(120,4) = 119 - 59 - 20 + 1 - 9 + 2 - 7 + 3 = 30.

So just like that you know there are 5 more primes after 100, before 120 and those are:

101, 103, 107, 109, and 113

And yes, if you just like playing with numbers you can easily keep doing prime counts where it's kind of a good idea to keep short-cut information handy.

I'll give you two additional short-cuts that always work:

P(x, 1) = [(x-2)/2]

which is just the count of evens minus 1 because 2 is a prime.

P(x, 2) = [(x-3)/6]

which is just the count of odds that have 3 as a factor minus 1 because
3 is prime.

And you should already have

P(x, 0) = x - 1

from what we noticed before.

If you're wondering if there are more short-cuts, the answer is yes, but things get more complicated from here.

Wednesday, January 03, 2007


JSH: Let's take a break, Jan 8th?

Part of extreme problem solving is, you toss out the ideas, and at some point you have to pause and kind of look over what might have bubbled through, or you might say, stuck to the wall.

I have been brainstorming a legal option, just in case.

A lot has been said over the last few days and a pause can give me time to consider that, while of course, I don't expect others to pause so feel free to keep replying in my threads as I will be looking at feedback as usual.

At this juncture my take on events is that once again—as I've done it before—I've caught posters lying about unique features of my research proving how important those features are, only to then claim that what they lied about wasn't really important when cornered!!!

I've come up with a basic argument that might mean that universities can be sued when their academics break the public trust.

And I've put out a teaser about how my prime counting function is unique in a special way that makes it a key that unlocks the door to what was previously never known—in all of human history—as I begin to wrap up the outlines of both how my research is important, and work at figuring out why math people would lie about it.

I will add that one of the puzzles for me over the four plus years since I first made my prime counting discovery has been how easily people who argue with me get away with lying about it, and my take on it is that we trust people.

Yup. I think mostly it comes down to basic human trust, which is so necessary in our modern world.

And it is so unimaginable that highly intelligent people would actually lie about an important mathematical discovery, and get away with it for years that a lot of people just decide it can't be important, or they figure, hey, yeah, rotten world, but it's not my problem.

So what? Mathematicians are just more corrupt people in a corrupt world?

Like that's news?

I think I'll try to let things percolate until Jan 8th. Until then.


JSH: Using people like you

So yes, mathematicians do lie a lot and yes, they will happily label a person a crackpot or kook who is just threatening when that person's research is actually perfect.

They use people like many of you.

And notice they lie to you as well as you can see in replies to my posts where kind of you might think maybe the math posters will now at least admit that it is the only known multi-variable prime counting function in history, but I have had these arguments before.

They just wait.

Later those posters would just say the same things.

They NEED people like you who will let them get away with blatant lies, contradictory behavior, and still cheer them later when they trot out what they claim are discoveries by the REAL mathematicians.

Now what could be so damn important that they'd sacrifice so much to lie so blatantly that I can show it in Usenet posts?

How dare those supposedly brilliant people let themselves look like blatant liars in arguments with a supposed crackpot!

Don't they realize how depressing that can be to those of you who spend so much times criticizing saying you are defending the real researchers?

You people are tools.

When mathematicians can just say "kook" in reply to a mathematical proof then they have power above mathematical proof, which you give to them.

And what do they give you in return?

Look at the lies. I'd suggest to you they give you contempt.


JSH: Unique in all the world

So yes, it turns out that I figured out this mathematics where you have something different than you'd find anywhere in the mathematical literature as instead of a pi(x) function, as mathematicians traditionally call the prime counting function, you have a P(x,n) function in the sieve form, so it has two variables instead of just one.

The second variable in the sieve form is the count of primes up to the integer square root of the first, that is, the largest natural number less than or equal to the square root of x.

Now if you know much about mathematics and mathematicians you may believe they get excited about unique things, even when those things are not practical as they call them "pure".

When they do not VISIBLY get excited over something, they would like you to think they don't think it's important, but what if it is, but is also threatening?

But how could a multi-variable prime counting function be threatening?

That is a question I want you to ponder so that the answer sinks in, and while you're pondering it, I'll note that hey, I found something UNIQUE in mathematical history about prime numbers!!!

The definition of my prime counting function in its sieve form is some of the most compact mathematics ever written to count primes. Actually, I say it is, but some posters argue with me saying other stuff is at least just as compact. Nothing is more.

So I have one of the most compact mathematical functions known for counting primes, which is unique in all of human history just for being a multi-variable prime counting function, yet mathematicians aren't cheering me for my "pure" math discovery!

What gives?

And it's not my only mathematical research.

I have other research that got published until some sci.math posters emailed the mathematical journal saying it was false, and the editors yanked it.

And later the journal died.

What could be so important as to quietly kill a math journal?

Any of you a published author of a mathematical paper?

Officially, I still am. Just check Mathematical Reviews.

This story is one of the biggest in mathematical history. And it is more than big enough that Usenet is tiny, and its fate is tiny in comparison.

It's also big enough that universities may be gearing up as we speak to go toe-to-toe against the legal ideas I've been brainstorming—in battles they are likely to lose.

Yup, some of the biggest universities around the world dwarfed by the size of it.

It is that big.

And a lot of it revolves around this compact mathematical function that counts primes—that is unique in all the world.


JSH: Why no counter demonstration?

Some of you may have noticed that I went ahead and gave a demonstration to show how my prime counting function is multi-variable:

In its sieve form, my prime counting function gives for 16, P(16,2) = 6.

The six primes up to 16, are of course, 2, 3, 5, 7, 11 and 13.

If you followed the discussions at all or know the area a little bit you may suppose people disagreeing with me about the worth of my research wouldn't give their own demonstration of a prime counting function over that range as it'd just reveal lies about there being other multi-variable prime counting functions.

But it's more complicated than that, and also more crucial to the question of what door of knowledge does my research open?

I would ask that those posters who are arguing with me go ahead and give a demonstration, showing the prime count for 16 with any other multi-variable prime counting function.

I say sieve form for P(16,2), because it also has another form, where P(16,4) gives the same count, and that is a clue to what that intelligent function can do that no other fully mathematical function in known human history could ever do.

How it mimics human beings, and shows mathematical intelligence in one of the most important mathematical areas—prime numbers.


JSH: So why is it important?

I go on about details about my prime counting function like it being multi-variable unlike any other known in human history, but hey, so what?

So let's say that it's just taken as known that it IS the only known multi-variable prime counting function in history, would mathematicians ignore something important?

So them ignoring it, while some Usenet posters argue about the details, isn't that proof that it IS not important?

After all, what can you do with it that you could not do before?


Any of you have a clue?

Of course, I do know the answer, but I want to know if anyone else will try to give you the simple answer, also I want to emphasize that posters who do lie, do so quite deliberately, and give you some sense of why mathematicians might not tell you about one of the biggest discoveries in all of human history related to prime numbers.

Yup, one of the greatest intellectual finds in all of human history, where the key to it, is not complicated, and once you grasp fully what that key is, you'll begin to understand why so many people in math circles would not want you to know the truth.

Tuesday, January 02, 2007


JSH: How much money?

I am brainstorming a legal solution to a problem where I am using the same problem solving tools that I used to get my mathematical research.

The outlines of the legal solution emerging from this process might open the door to lawsuits against universities anywhere in the world for a breach of trust by academics at those schools who just inexplicably decide to ignore research that doesn't help their own careers.

So how much money could be in this for trial attorneys seeking new territory?

Harvard University alone has over $2 billion US in its endowment.

And if people are listening to academics dragged to the stand to testify about why they decided that some provably important research wasn't worth their time, possibly all chanting the same mantra about academic freedom and their right to ignore anything they freaking well want to ignore?

Why not punitive damages in the tens of millions or even in the hundreds of millions when these Ivory Tower eggheads confront regular people who think that hey, living in society means taking care of more than just yourself?

Any of you who are professors really want to roll the dice? Face a legal argument that can put you on the stand talking to regular people instead of fawning students?

Why do it?

I still want another option.

But you people need to understand how fast extreme problem solving is.

I am starting to feel a little bit of concern on this one as I'm not actually interested at this time in taking a legal option, but was thinking it'd be better to start the problem solving process going just in case.

I started this thinking it was all just in case I needed it down the line.

Monday, January 01, 2007


JSH: Begin to see the point?

You may think your freedom of speech on Usenet has a great value, but I fear it can be shown to be a great social detriment.

Society then would have to solve the problem of how to change Usenet so that it IS a social good.

That is the other aspect of what I'm brainstorming as I use the techniques I used to figure out my mathematical research with the problem of getting past mathematicians thinking they can ignore it, or even lie about it, where some of them, unfortunately for Usenet, are using Usenet as their primary tool, clearly believing they can't be caught.

It's that acting like they can't be caught that really pushes the case that maybe all that freedom on Usenet is being so horribly abused that it is doing great harm to our world, and I hate to make that argument as I rely on Usenet myself and the freedoms it provides, but this case is just so obvious at this point.

The mathematicians and mathematician supporters arguing with me are doing things like fighting research on prime numbers, and lying repeatedly about it, using the freedom Usenet gives them, in a way that displays a belief in impunity.

What some of you may not realize though is that their behavior could change what you can do on Usenet in the future, and not just you, but anyone on Usenet.


JSH: Legal brainstorming, value of research

Continuing the process of brainstorming how a legal option might play out, I've noticed that posters make replies indicating they think that somehow a legal battle could be made to be about me.

But the issue is the value of my research, and how easily that is determined.

I like the diamond analogy.

Say there is this quirky fellow who is confident he is going to find a HUGE and very valuable diamond in an area where others think they've mined them all out.

In his quest he has often got it wrong, rushing to diamond experts with rocks that turned out to not be diamonds, and they have hooted and hollered and ridiculed him in return, or mostly ignored him.

But then, he finds a huge diamond.

The experts can of course just look and see whether he has a diamond or not, but instead of admitting that he has finally done this thing, and found a huge and valuable diamond, they claim that again he has just found a worthless rock, and seek to cheat him out of the value of the diamond.

So he takes them to court.

Can the diamond experts question his credibility in a court case as part of their own defense?

Can they even talk about his past failures in finding diamonds at all, and even if they could, do you think it'd matter to a judge and jury?

Or is it just about the diamond he found and what the diamond experts did?


Prime research

My prime counting function research continues to be the hot area in terms of possible quick acceptance and easy accessibility.

Succinctly, back in 2002 I found a way to count prime numbers that relies on a prime counting function that is multi-variable. It is a recursive function so that it can just call itself allowing a stepping away from sieve methods to a partial difference equation.

I have a page that covers a lot of what I have on this subject on this group:

Currently the paper on primes is under review at a peer reviewed journal.

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