### Sunday, December 31, 2006

## JSH: Extreme problem solving, legal

Some of you may wonder about all the posting if I am serious about a possible civil action.

Shouldn't I just quiet down and go forward with suing someone?

Well, for one thing, I haven't decided the legal option must be taken but am now seriously considering it, which means several problems have to be solved first.

I solve problems by talking them out as I explore possibilities which I used with mathematics to get my research results.

I am now using it with the legal problem as I explore solutions, so I toss the ideas out, and get feedback, as you'll notice posters are helping me consider how various approaches in a court of law might work, and as I move forward I refine how a case might proceed.

That is extreme problem solving.

Now what I used to get things like my prime counting function, I'll use to get a legal option.

The biggest thing if I decided to move forward legally would be convincing attorneys to pursue, so I try things out here first, as once I convince some attorneys, yeah, the Usenet posting would be over.

But now I'm a lot further along with HOW to convince than I was just a few days ago as extreme problem solving can work VERY FAST, and solutions found by it can be unbeatable, which is why they can also be public.

So, yeah, I can work out a legal strategy in posts, and potential targets can know what's coming ahead of time and it not matter at all. They will still lose no matter how much time they have to prepare and what legal resources of their own they can bring to bear.

And my hope now is that all the big court battles would be over within five years.

I still want another option. Remember, Usenet will be pulled in to the current legal strategy that I'm currently brainstorming, though I don't mind necessarily if it gets out.

Shouldn't I just quiet down and go forward with suing someone?

Well, for one thing, I haven't decided the legal option must be taken but am now seriously considering it, which means several problems have to be solved first.

I solve problems by talking them out as I explore possibilities which I used with mathematics to get my research results.

I am now using it with the legal problem as I explore solutions, so I toss the ideas out, and get feedback, as you'll notice posters are helping me consider how various approaches in a court of law might work, and as I move forward I refine how a case might proceed.

That is extreme problem solving.

Now what I used to get things like my prime counting function, I'll use to get a legal option.

The biggest thing if I decided to move forward legally would be convincing attorneys to pursue, so I try things out here first, as once I convince some attorneys, yeah, the Usenet posting would be over.

But now I'm a lot further along with HOW to convince than I was just a few days ago as extreme problem solving can work VERY FAST, and solutions found by it can be unbeatable, which is why they can also be public.

So, yeah, I can work out a legal strategy in posts, and potential targets can know what's coming ahead of time and it not matter at all. They will still lose no matter how much time they have to prepare and what legal resources of their own they can bring to bear.

And my hope now is that all the big court battles would be over within five years.

I still want another option. Remember, Usenet will be pulled in to the current legal strategy that I'm currently brainstorming, though I don't mind necessarily if it gets out.

## JSH: Simpler explanation of my legal position

My fear is that mathematicians at universities don't think they have to report on mathematical research that is important if it does not help their own careers.

That is breaking the trust the public gives them as I think if you talk to the a typical citizen they'd say that mathematicians are expected to report on ANY important mathematical research results.

It makes my legal problem just proving the importance of my research and that I did my part in informing universities through their mathematics professors but they failed to do their jobs.

If I prove that then mathematicians and the universities responsible for them would have no defense and could be forced to pay for damages.

Usenet could be impacted because some mathematicians on math newsgroups have abused the system to not only not report accurately about my research but actually to try and talk it down and convince others falsely that it is not important.

While specific laws exist to punish individuals, I think it is also clear that it takes a whole lot of effort to stop these people, they clearly are confident they can run wild on Usenet, and a reasonable person could consider their behavior strong evidence of a lack of proper protection from the current Usenet format.

Society just can't have a lot of lawsuits all the time over Usenet posts, especially when society spends a lot of money keeping Usenet up, so Usenet might have to change so that abusers of the system are not so confident they can get away with it.

[A reply to someone who tried to explain James that nobody ever earned any money by creating new prime counting methods.]

Well, I know how important my research actually is, which is why there have been mathematicians so willing to risk so much rather than face it.

But others might not realize just how much some mathematicians are willing to risk to protect themselves.

I suggest to people not on math newsgroups that mathematicians are more than willing to risk changes to Usenet itself rather than just do their jobs as my point is they are breaching the public trust.

And why would they if there weren't something in it for them?

There must be some huge things at stake, right?

Remember an entire math journal has already died as part of this story.

There are HUGE things at stake, whether you understand what they are or not.

But not for most of you. It is your trust they are breaking.

Clearly for me legal strategies are the last options, but at this point it is starting to look like I have no other choice as that is a lot about why we have a legal system, for when no other civil means remains.

And yes, this public notification would be part of a case as well as I point out that there are mathematicians who are willing to sacrifice the needs of others to protect themselves, showing they just don't care about the public trust, at all.

That is fair warning. Everything on Usenet is public.

That is breaking the trust the public gives them as I think if you talk to the a typical citizen they'd say that mathematicians are expected to report on ANY important mathematical research results.

It makes my legal problem just proving the importance of my research and that I did my part in informing universities through their mathematics professors but they failed to do their jobs.

If I prove that then mathematicians and the universities responsible for them would have no defense and could be forced to pay for damages.

Usenet could be impacted because some mathematicians on math newsgroups have abused the system to not only not report accurately about my research but actually to try and talk it down and convince others falsely that it is not important.

While specific laws exist to punish individuals, I think it is also clear that it takes a whole lot of effort to stop these people, they clearly are confident they can run wild on Usenet, and a reasonable person could consider their behavior strong evidence of a lack of proper protection from the current Usenet format.

Society just can't have a lot of lawsuits all the time over Usenet posts, especially when society spends a lot of money keeping Usenet up, so Usenet might have to change so that abusers of the system are not so confident they can get away with it.

[A reply to someone who tried to explain James that nobody ever earned any money by creating new prime counting methods.]

Well, I know how important my research actually is, which is why there have been mathematicians so willing to risk so much rather than face it.

But others might not realize just how much some mathematicians are willing to risk to protect themselves.

I suggest to people not on math newsgroups that mathematicians are more than willing to risk changes to Usenet itself rather than just do their jobs as my point is they are breaching the public trust.

And why would they if there weren't something in it for them?

There must be some huge things at stake, right?

Remember an entire math journal has already died as part of this story.

There are HUGE things at stake, whether you understand what they are or not.

But not for most of you. It is your trust they are breaking.

Clearly for me legal strategies are the last options, but at this point it is starting to look like I have no other choice as that is a lot about why we have a legal system, for when no other civil means remains.

And yes, this public notification would be part of a case as well as I point out that there are mathematicians who are willing to sacrifice the needs of others to protect themselves, showing they just don't care about the public trust, at all.

That is fair warning. Everything on Usenet is public.

## JSH: Not just about libel

I think that a problem many of you have is that you think you are very experienced with what you may perceive as a threat of a libel lawsuit. While I think libel is definitely a potential area for consideration of a civil action it is not the only one.

I am not a legal expert but I have read that the law recognizes various duties and responsibilities that all citizens have in actions towards each other and also can give people designated "expert" special responsibilities.

In talking with mathematicians I have sensed a belief that a mathematician need not concern himself with mathematical research that does not promote that particular person's career, which may be an attitude at odds with the law.

That means that civil actions may take more complex forms than a simple libel suit and may, though this post is not meant to declare they will, include a wider array of potential tortfeasors, which can include universities.

I will say though that I would not think it likely that a civil action could be made attractive to attorneys without the potential of bringing in defendants like universities, and it is my belief that legal precedent can be set on the basis of common law, specifically good faith.

That is, there is an expectation that mathematicians are bound by social contracts that would expect that in acting with good faith they would report on mathematical research that is important WITHOUT REGARD to its value to their own research or careers and that failure to do so is a BREACH OF THE PUBLIC TRUST, and more specifically is an act of bad faith, which can be seen as a tort against an individual who is harmed by such behavior, where such harm can be specific and/or general.

Under that legal principle both the mathematicians and their universities could be brought into a civil action, which asserts there is a great social good to be had from holding such institutions and their members responsible at a level commensurate with the great trust and prestige which is accorded to them in good faith by a society that expects the same in return.

In short, I am talking about a case I'd guess is unlike anything you have heard of before.

I read a lot so I can mention some legal stuff without asserting expertise or claiming necessarily that the principles mentioned would actually hold in any courts of law. But I suggest that those of you who think you know about threats of libel suits and how difficult those are, re-think and possibly send a copy of this post to an actual legal expert.

In my view our academic world has clear flaws which have been shown by this situation, and it may take court action which could impact how academics is done.

That is not just a case about libel.

[A reply to someone who wrote that it would be an interesting world if courts felt themselves obliged or able to rule on whether mathematical research was correct or interesting.]

Yup and I argue that mathematicians clearly feel confident that because of that they can ignore provably important research.

So the legal challenge would be proving that my research is important and that mathematicians are ignoring it because it does not help their own careers, possibly relying on their knowledge that the system trusts them to not do so.

That is the breach of the public trust which would allow me to not only pursue civil actions against mathematicians but against their universities as well, and pursue mathematicians who have made no public statements about my research.

If I won those cases which would be the big ones, where the heavy fighting would be done, I'd come back to the libel cases AFTERWARDS, and quickly mop those up, internationally pursuing certain Usenet posters and others who made libelous public statements, like on web pages.

May be some fights there like even with civil liberties groups but I think I could convince them that this is a special situation with a huge abuse of the public trust by people who felt certain they could not be held accountable because of the past difficulty in punishing abuses on Usenet and the web.

It'd change the landscape by creating a way to make it worthwhile for attorneys to pursue such cases.

So yes, I'd think libel would come up, but later. First I'd be going after universities.

And yes, if I succeed it'd change the system, opening up for the courts an area that has previously been left alone—and fraud has festered as society's dubious reward—which is why it is crucial that I pursue every other option first so that the egregious nature of the situation makes it clear that going to court is the only option left.

Four years plus have gone by since my computer screen filled up with prime numbers—the situation is clearly egregious.

[A reply to someone who wrote that James would have to pursue civil actions against every single mathematician in the world, except for those few who actually had a word to say about his research.]

To make a legal case I'd need to show they had every opportunity so that would mean mathematicians who could be proven to have known, for instance, because I contacted them.

Making the case could involve a paid expert on the stand testifying about my research versus what was previously known.

If you were someone who was of interest you could be called to the stand and forced to testify under oath about specific features of my research.

So no, you wouldn't be able to make a global statement against it, but like you'd face a question like, was anything like this previously known?

Or you could be asked, is there any other known multi-dimensional prime counting function?

Is there any other known prime counting function that recursively calls itself?

Can any other known prime counting function lead to a partial differential equation?

Under oath and before a judge or jury, all the childish replies that work on Usenet would just be shut down, and if you lied, you could face perjury charges and that's just you.

You're just one person as I'd have a gamut of people that could be called to the stand or deposed and forced to testify under oath.

Since no one would be able to claim my research is not of major interest without being impeached and maybe even facing perjury charges that aspect of a legal case is the easy part.

To interest attorneys I have to convince that someone could pay penalties, and that someone would be universities.

For instance, Harvard University alone has an over $2 billion US endowment.

I am not a legal expert but I have read that the law recognizes various duties and responsibilities that all citizens have in actions towards each other and also can give people designated "expert" special responsibilities.

In talking with mathematicians I have sensed a belief that a mathematician need not concern himself with mathematical research that does not promote that particular person's career, which may be an attitude at odds with the law.

That means that civil actions may take more complex forms than a simple libel suit and may, though this post is not meant to declare they will, include a wider array of potential tortfeasors, which can include universities.

I will say though that I would not think it likely that a civil action could be made attractive to attorneys without the potential of bringing in defendants like universities, and it is my belief that legal precedent can be set on the basis of common law, specifically good faith.

That is, there is an expectation that mathematicians are bound by social contracts that would expect that in acting with good faith they would report on mathematical research that is important WITHOUT REGARD to its value to their own research or careers and that failure to do so is a BREACH OF THE PUBLIC TRUST, and more specifically is an act of bad faith, which can be seen as a tort against an individual who is harmed by such behavior, where such harm can be specific and/or general.

Under that legal principle both the mathematicians and their universities could be brought into a civil action, which asserts there is a great social good to be had from holding such institutions and their members responsible at a level commensurate with the great trust and prestige which is accorded to them in good faith by a society that expects the same in return.

In short, I am talking about a case I'd guess is unlike anything you have heard of before.

I read a lot so I can mention some legal stuff without asserting expertise or claiming necessarily that the principles mentioned would actually hold in any courts of law. But I suggest that those of you who think you know about threats of libel suits and how difficult those are, re-think and possibly send a copy of this post to an actual legal expert.

In my view our academic world has clear flaws which have been shown by this situation, and it may take court action which could impact how academics is done.

That is not just a case about libel.

[A reply to someone who wrote that it would be an interesting world if courts felt themselves obliged or able to rule on whether mathematical research was correct or interesting.]

Yup and I argue that mathematicians clearly feel confident that because of that they can ignore provably important research.

So the legal challenge would be proving that my research is important and that mathematicians are ignoring it because it does not help their own careers, possibly relying on their knowledge that the system trusts them to not do so.

That is the breach of the public trust which would allow me to not only pursue civil actions against mathematicians but against their universities as well, and pursue mathematicians who have made no public statements about my research.

If I won those cases which would be the big ones, where the heavy fighting would be done, I'd come back to the libel cases AFTERWARDS, and quickly mop those up, internationally pursuing certain Usenet posters and others who made libelous public statements, like on web pages.

May be some fights there like even with civil liberties groups but I think I could convince them that this is a special situation with a huge abuse of the public trust by people who felt certain they could not be held accountable because of the past difficulty in punishing abuses on Usenet and the web.

It'd change the landscape by creating a way to make it worthwhile for attorneys to pursue such cases.

So yes, I'd think libel would come up, but later. First I'd be going after universities.

And yes, if I succeed it'd change the system, opening up for the courts an area that has previously been left alone—and fraud has festered as society's dubious reward—which is why it is crucial that I pursue every other option first so that the egregious nature of the situation makes it clear that going to court is the only option left.

Four years plus have gone by since my computer screen filled up with prime numbers—the situation is clearly egregious.

[A reply to someone who wrote that James would have to pursue civil actions against every single mathematician in the world, except for those few who actually had a word to say about his research.]

To make a legal case I'd need to show they had every opportunity so that would mean mathematicians who could be proven to have known, for instance, because I contacted them.

Making the case could involve a paid expert on the stand testifying about my research versus what was previously known.

If you were someone who was of interest you could be called to the stand and forced to testify under oath about specific features of my research.

So no, you wouldn't be able to make a global statement against it, but like you'd face a question like, was anything like this previously known?

Or you could be asked, is there any other known multi-dimensional prime counting function?

Is there any other known prime counting function that recursively calls itself?

Can any other known prime counting function lead to a partial differential equation?

Under oath and before a judge or jury, all the childish replies that work on Usenet would just be shut down, and if you lied, you could face perjury charges and that's just you.

You're just one person as I'd have a gamut of people that could be called to the stand or deposed and forced to testify under oath.

Since no one would be able to claim my research is not of major interest without being impeached and maybe even facing perjury charges that aspect of a legal case is the easy part.

To interest attorneys I have to convince that someone could pay penalties, and that someone would be universities.

For instance, Harvard University alone has an over $2 billion US endowment.

### Saturday, December 30, 2006

## Other options, please

I want other options than civil litigation.

I'm now making the point that you may think this is unimportant to you, but this could change all of Usenet.

At issue is research easily proven to be correct, where there is no doubt about correctness, but mathematicians are ignoring it while some people have used Usenet to berate it.

I think I can show a real world impact from their behavior.

Other research was actually published. Usenet posters conspired online to attack its publication and managed to get it yanked.

You people are not a math newsgroup, but nevertheless if I have to push this thing into the courts you could have your posting here affected as could everyone on Usenet, just because some math people decided to commit fraud over some math research.

Your life impacted by their refusal to accept important and easily proven results.

I do not think Usenet should be punished for them, so I want other options. I need to see some other way to resolve this situation other than civil litigation.

As believe me, I explain how my prime counting research is different, and a jury can just see it explained in very simple terms as it is clearly different in important ways, then I don't see my losing the case, especially up against a group like mathematicians.

You may be overly impressed by their ability to be unintelligible with complicated explanations and abstruse discussions, but that is what will get their case lost in front of a jury, where people will want to actually understand what the math means.

I can explain it simply. Mathematicians by nature will try to overpower a jury with being incomprehensible and relying on their status.

I'm now making the point that you may think this is unimportant to you, but this could change all of Usenet.

At issue is research easily proven to be correct, where there is no doubt about correctness, but mathematicians are ignoring it while some people have used Usenet to berate it.

I think I can show a real world impact from their behavior.

Other research was actually published. Usenet posters conspired online to attack its publication and managed to get it yanked.

You people are not a math newsgroup, but nevertheless if I have to push this thing into the courts you could have your posting here affected as could everyone on Usenet, just because some math people decided to commit fraud over some math research.

Your life impacted by their refusal to accept important and easily proven results.

I do not think Usenet should be punished for them, so I want other options. I need to see some other way to resolve this situation other than civil litigation.

As believe me, I explain how my prime counting research is different, and a jury can just see it explained in very simple terms as it is clearly different in important ways, then I don't see my losing the case, especially up against a group like mathematicians.

You may be overly impressed by their ability to be unintelligible with complicated explanations and abstruse discussions, but that is what will get their case lost in front of a jury, where people will want to actually understand what the math means.

I can explain it simply. Mathematicians by nature will try to overpower a jury with being incomprehensible and relying on their status.

## JSH: You're screwing Usenet too

Usenet gives a lot of freedoms cheaply, but a lot of this case now is about public statements made on Usenet and what impact they may have had.

I can put a dollar amount on that and then consider civil litigation options.

What I have is mathematical research easily shown to be different than what was known before, like my prime counting function while similar to previous results is a multi-dimensional one that leads to a partial differential equation.

So, say that is put in front of a jury in a civil litigation and what is your defense?

Mathematicians on trial in front of ordinary citizens asked to look at some mathematics that counts primes, where I can not only take some of you posting on Usenet to court, but journal editors as well.

And there is the possibility of court ordered turning over of who made postings anonymously or using pseudonyms, as well as the possibility of an international turn to this thing with a team of attorneys going after posters and journals in other countries.

ALL I'd have to do is convince some attorneys that there is a case here.

And Usenet itself could change, paying the price for what you people have done.

I can put a dollar amount on that and then consider civil litigation options.

What I have is mathematical research easily shown to be different than what was known before, like my prime counting function while similar to previous results is a multi-dimensional one that leads to a partial differential equation.

So, say that is put in front of a jury in a civil litigation and what is your defense?

Mathematicians on trial in front of ordinary citizens asked to look at some mathematics that counts primes, where I can not only take some of you posting on Usenet to court, but journal editors as well.

And there is the possibility of court ordered turning over of who made postings anonymously or using pseudonyms, as well as the possibility of an international turn to this thing with a team of attorneys going after posters and journals in other countries.

ALL I'd have to do is convince some attorneys that there is a case here.

And Usenet itself could change, paying the price for what you people have done.

## JSH: It IS fraud

I think many of you think of this as meaningless and inconsequential where you argue with me and attack mathematical research easily proven to be correct and you win as long as no one realizes what is going on.

But it is fraud.

Some of you may believe that you are protected by various devices you use in your own comments or by claiming that you had agreement from others, but like with my prime counting research, it is obviously different in crucial ways from what was known before, despite similarities.

It may seem inconsequential posting here on Usenet, but posts are public comments so they can be used against you later.

There are a lot of precedents that could be set by this situation, and it is likely that Usenet itself could face much greater legal scrutiny.

As obviously some of you are using the freedoms given by Usenet in perpetuating a fraud to block acceptance of easily proven mathematical results, where it is also easy to prove their value.

Consider a world looking at my equations versus what was there before, hearing explanations for how they are different and just being able to SEE they are different as well, as it contemplates punishments for some of you who may have wanted that money for your retirement versus seeing it go to someone else because of some stuff you said on Usenet thinking you'd never be accountable for it.

It IS fraud to make false claims that cause harm to others, and in this case, making false claims against mathematical research can be shown to be a harm against humanity itself.

But it is fraud.

Some of you may believe that you are protected by various devices you use in your own comments or by claiming that you had agreement from others, but like with my prime counting research, it is obviously different in crucial ways from what was known before, despite similarities.

It may seem inconsequential posting here on Usenet, but posts are public comments so they can be used against you later.

There are a lot of precedents that could be set by this situation, and it is likely that Usenet itself could face much greater legal scrutiny.

As obviously some of you are using the freedoms given by Usenet in perpetuating a fraud to block acceptance of easily proven mathematical results, where it is also easy to prove their value.

Consider a world looking at my equations versus what was there before, hearing explanations for how they are different and just being able to SEE they are different as well, as it contemplates punishments for some of you who may have wanted that money for your retirement versus seeing it go to someone else because of some stuff you said on Usenet thinking you'd never be accountable for it.

It IS fraud to make false claims that cause harm to others, and in this case, making false claims against mathematical research can be shown to be a harm against humanity itself.

## Math fraud, any options?

So let's say for the sake of argument that an outsider makes some mathematical discoveries that challenge enough of the established ideas in the field that mathematicians uniformly over a period of years just refuse to acknowledge the results, are there any options?

I think the uniformity of it is what has been the biggest surprise for me, and it's a bit more complicated as at times I've gotten agreement from mathematicians on a lot of my major research, like that publication in the math journal.

What happens afterwards is the SOCIETY of mathematicians in some way come in to clean up, and this mathematician or that just chooses to go quiet or reverse themselves.

Usually they just go quiet.

So I'm the only champion of my own research unable to get any sustained support from any mathematicians.

So it's not like I don't get support or agreement, it's that individual mathematicians refuse to face the group, while you can see a lot of outright group hostility on math newsgroups.

Any options with such a situation?

[A reply to someone who wondered whether James had considered not using Usenet, since it such a source of pain for him.]

Usenet is a PUBLIC resource. People like you who push others to leave Usenet are like a gang of teenagers trying to take over a public park for "their" people.

Repeatedly though posters will admit they attack me in posts simply to try and convince me to quit, as they abuse the freedoms given by Usenet, which goes to the argument that Usenet is too free, and provably that is bad for society as abusers of the system run wild, and that has a social impact as can be seen with what has happened with my research.

That is how this case can impact Usenet, as if I pursue civil litigation and win, the next step will be arguing that the format of Usenet is too open, and that there is a substantial social cost in letting it remain so open because abusers find it too easy to operate forcing victims to go to extreme measures—like court—and abusers clearly are confident under this current system.

So Usenet would have to change and could be forcibly changed.

I want other options people. Many of you sit back while others abuse this system thinking nothing can change, but I'm telling you it can. So when it does, remember you were notified. And you had the opportunity to be heard.

I have given lots of public notice here.

I think the uniformity of it is what has been the biggest surprise for me, and it's a bit more complicated as at times I've gotten agreement from mathematicians on a lot of my major research, like that publication in the math journal.

What happens afterwards is the SOCIETY of mathematicians in some way come in to clean up, and this mathematician or that just chooses to go quiet or reverse themselves.

Usually they just go quiet.

So I'm the only champion of my own research unable to get any sustained support from any mathematicians.

So it's not like I don't get support or agreement, it's that individual mathematicians refuse to face the group, while you can see a lot of outright group hostility on math newsgroups.

Any options with such a situation?

[A reply to someone who wondered whether James had considered not using Usenet, since it such a source of pain for him.]

Usenet is a PUBLIC resource. People like you who push others to leave Usenet are like a gang of teenagers trying to take over a public park for "their" people.

Repeatedly though posters will admit they attack me in posts simply to try and convince me to quit, as they abuse the freedoms given by Usenet, which goes to the argument that Usenet is too free, and provably that is bad for society as abusers of the system run wild, and that has a social impact as can be seen with what has happened with my research.

That is how this case can impact Usenet, as if I pursue civil litigation and win, the next step will be arguing that the format of Usenet is too open, and that there is a substantial social cost in letting it remain so open because abusers find it too easy to operate forcing victims to go to extreme measures—like court—and abusers clearly are confident under this current system.

So Usenet would have to change and could be forcibly changed.

I want other options people. Many of you sit back while others abuse this system thinking nothing can change, but I'm telling you it can. So when it does, remember you were notified. And you had the opportunity to be heard.

I have given lots of public notice here.

## Fraud in the math field

I can easily prove the correctness of some of my more dramatic mathematical research as it counts prime numbers, and I can just show what it looks like versus what mathematicians had before, and what it leads to, versus what they had before, and it's easy to do all of that.

Yet over four years since I first saw my computer screen fill up with prime numbers I'm still labeled a crackpot, my research is not taught, and mathematicians seem to have no need to fear that this situation will change.

But why not?

Quite simply, they have the power to ignore results they don't like, and my results challenge some well-established views that mathematicians have built careers upon.

So they are committing fraud with very little fear of consequences.

And this is with mathematics, where it's easy to show what I have, that it is correct, that it is different from what was known before in crucial and unique ways—while being simpler in many aspects as well—and there's nothing I can do but whine about it on Usenet.

They have that kind of power.

And with results like mine that would just change the landscape in a huge way, they have the motivation—if they ignore the importance to humanity of advancements in knowledge and our understanding.

And why shouldn't they?

Why should they care about how we advance as a species if that means they are diminished?

Why should a professor with years of experience believing things he worked hard to learn accept it when some outsider makes discoveries that challenge what he was taught, when doing so could impact his own income?

Would you?

I don't think you would.

I think it's nice to talk about ideals and the importance to humanity of this or that, but you need to eat, to feed your family, and you like status.

Why accept changes to all of that when you can just go on with your world as it is, as if the advancement of this species means anything?

Isn't your ability to do it proof that it means nothing at all?

Isn't the capacity of mathematicians to avoid research that is this clearly unique and important to protect themselves proof that they are right in doing what they do?

And wouldn't you do the same.

[A reply to someone who wanted to know if James' post meant that the Annals of Mathematics had rejected his paper.]

No. It is still under review.

But it might help you to know that for a long time I haven't wanted to be bothered with a lot of civil litigations, but increasingly I'm just tired of this situation.

And yes, if Princeton accepts the paper then your legal defense would be that much harder.

And your identities can be pulled so that you can be litigated against.

But Usenet would change I'm afraid. Maybe if Princeton does accept the paper I'll go back to my earlier disdain for personally using the courts, but I'm gearing up just in case.

It's past time to end this situation and if I have to do it with a civil case in front of a jury, then so be it.

Yet over four years since I first saw my computer screen fill up with prime numbers I'm still labeled a crackpot, my research is not taught, and mathematicians seem to have no need to fear that this situation will change.

But why not?

Quite simply, they have the power to ignore results they don't like, and my results challenge some well-established views that mathematicians have built careers upon.

So they are committing fraud with very little fear of consequences.

And this is with mathematics, where it's easy to show what I have, that it is correct, that it is different from what was known before in crucial and unique ways—while being simpler in many aspects as well—and there's nothing I can do but whine about it on Usenet.

They have that kind of power.

And with results like mine that would just change the landscape in a huge way, they have the motivation—if they ignore the importance to humanity of advancements in knowledge and our understanding.

And why shouldn't they?

Why should they care about how we advance as a species if that means they are diminished?

Why should a professor with years of experience believing things he worked hard to learn accept it when some outsider makes discoveries that challenge what he was taught, when doing so could impact his own income?

Would you?

I don't think you would.

I think it's nice to talk about ideals and the importance to humanity of this or that, but you need to eat, to feed your family, and you like status.

Why accept changes to all of that when you can just go on with your world as it is, as if the advancement of this species means anything?

Isn't your ability to do it proof that it means nothing at all?

Isn't the capacity of mathematicians to avoid research that is this clearly unique and important to protect themselves proof that they are right in doing what they do?

And wouldn't you do the same.

[A reply to someone who wanted to know if James' post meant that the Annals of Mathematics had rejected his paper.]

No. It is still under review.

But it might help you to know that for a long time I haven't wanted to be bothered with a lot of civil litigations, but increasingly I'm just tired of this situation.

And yes, if Princeton accepts the paper then your legal defense would be that much harder.

And your identities can be pulled so that you can be litigated against.

But Usenet would change I'm afraid. Maybe if Princeton does accept the paper I'll go back to my earlier disdain for personally using the courts, but I'm gearing up just in case.

It's past time to end this situation and if I have to do it with a civil case in front of a jury, then so be it.

## JSH: Counting prime numbers

The standard argument against "crackpots" should be that what they have does not work.

It also should be that they have no support for their arguments from experts in the field.

Given a situation where you find a person labeled a crackpot where neither of those applies, there is a puzzle, whether people acknowledge it or not, as you have a situation without explanation.

Did you know that opposition in posts and websites against me exploded after December 1999 when I came up with a crucial yet simple way to analyze algebraic expressions which I typically call tautological spaces?

Over three years ago when I started talking about figuring out a way to count prime numbers on Usenet, I was facing the usual ridicule and nasty replies in posts that maybe I unfortunately have just gotten too used to, as it's expected behavior.

For a couple of weeks I tried various ideas, which did not work as I started from scratch figuring out a way to count prime numbers and posting about my research—part of a process I call extreme mathematics.

Posters dutifully—yeah, I know kind of odd—checked these various ideas I came up with, and there was derision as they did not work, and then one day I posted something I knew had to work.

I knew it worked as I was puzzling over my approach and trying out various ideas with a computer program, and suddenly with one change, the test output was nothing but prime numbers.

So my screen filled up with prime numbers and I knew I had succeeded.

I posted. There was some derision, then quiet as some posters noted that it worked.

Then someone claimed it was nothing new and the derision began again.

I had some other mathematical research published in a peer reviewed mathematical journal.

Someone posted that my paper was published—not me—and there was this outpouring of hatred on sci.math and they went after the journal.

I mean they went after that journal in post after post after post, ripping on it, until a couple of posters had the brilliant idea of emailing the journal claiming they had refutations to the mathematical proof it contained.

The bushwhacked editors—as I didn't realize I needed to warn them that Usenet posters might make false claims in emails attacking the paper—simply yanked my paper.

It was an electronic journal so they just pulled it from its position as the second paper published, as if they just wanted to erase it completely, but eventually they put the title back with "Withdrawn" underneath.

Posters on sci.math ripped on the journal.

They also berated it when later it quietly shut down after just one more edition.

Posters berated the now dead journal.

To me the one consistent thing in what I face from math society is their recognition that nothing happens unless they accept a result.

It does not matter what you can prove.

They have to accept the proof, or it's like you have nothing at all, no matter what happens.

[A reply to someone who asked if James' life is really so pathetic that he has nothing better to do than to waste it.]

Tell it to the judge as they say.

I'm tired of this situation and looking to get a lot more serious.

One option is to make a case that proper acceptance of my work would be worth a certain amount of dollars and go convince some attorneys to take up a precedent setting case.

The biggest problem I see is with the international scope of this thing in terms of going after some of you, but for the people in the US, all that matters is I find some attorneys willing to take the case.

It also should be that they have no support for their arguments from experts in the field.

Given a situation where you find a person labeled a crackpot where neither of those applies, there is a puzzle, whether people acknowledge it or not, as you have a situation without explanation.

Did you know that opposition in posts and websites against me exploded after December 1999 when I came up with a crucial yet simple way to analyze algebraic expressions which I typically call tautological spaces?

Over three years ago when I started talking about figuring out a way to count prime numbers on Usenet, I was facing the usual ridicule and nasty replies in posts that maybe I unfortunately have just gotten too used to, as it's expected behavior.

For a couple of weeks I tried various ideas, which did not work as I started from scratch figuring out a way to count prime numbers and posting about my research—part of a process I call extreme mathematics.

Posters dutifully—yeah, I know kind of odd—checked these various ideas I came up with, and there was derision as they did not work, and then one day I posted something I knew had to work.

I knew it worked as I was puzzling over my approach and trying out various ideas with a computer program, and suddenly with one change, the test output was nothing but prime numbers.

So my screen filled up with prime numbers and I knew I had succeeded.

I posted. There was some derision, then quiet as some posters noted that it worked.

Then someone claimed it was nothing new and the derision began again.

I had some other mathematical research published in a peer reviewed mathematical journal.

Someone posted that my paper was published—not me—and there was this outpouring of hatred on sci.math and they went after the journal.

I mean they went after that journal in post after post after post, ripping on it, until a couple of posters had the brilliant idea of emailing the journal claiming they had refutations to the mathematical proof it contained.

The bushwhacked editors—as I didn't realize I needed to warn them that Usenet posters might make false claims in emails attacking the paper—simply yanked my paper.

It was an electronic journal so they just pulled it from its position as the second paper published, as if they just wanted to erase it completely, but eventually they put the title back with "Withdrawn" underneath.

Posters on sci.math ripped on the journal.

They also berated it when later it quietly shut down after just one more edition.

Posters berated the now dead journal.

To me the one consistent thing in what I face from math society is their recognition that nothing happens unless they accept a result.

It does not matter what you can prove.

They have to accept the proof, or it's like you have nothing at all, no matter what happens.

[A reply to someone who asked if James' life is really so pathetic that he has nothing better to do than to waste it.]

Tell it to the judge as they say.

I'm tired of this situation and looking to get a lot more serious.

One option is to make a case that proper acceptance of my work would be worth a certain amount of dollars and go convince some attorneys to take up a precedent setting case.

The biggest problem I see is with the international scope of this thing in terms of going after some of you, but for the people in the US, all that matters is I find some attorneys willing to take the case.

### Monday, December 25, 2006

## Confounding the critics

With

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

and

7g(x) = 5a_2(x)

along with

2f(x) = 5a_1(x) + 5

it is reasonable to suppose that a_2(x) has 7 as a factor, but critics who have argued with me for some time over approaches like this have continually maintained it does not in the ring of algebraic integers, and for that to be true g(x) must not be an algebraic integer.

With my generalized solution:

(49x^2+7Q(x))5^2 - (3x-1+5Q(x))(5)(7) + 7^2 = (5a_1(x)+7)*(5a_2(x)+7)

giving the a's as roots of

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0

that claim can be rigorously tested, as you can simply shift to

7f(x) = 5a_2(x)

and

2g(x) = 5a_1(x) + 5

so that if g(x) is not an algebraic integer as the critics need then a_1(x) is not either, which forces Q(x) to not be, so assume instead you have Q'(x)/w(x) where w(x) is some factor of 7.

Then you'd have

a^2 - (3x - 1 + 5Q'(x)/w(x))a + (49x^2 + 7Q'(x)/w(x)) = 0

which solves as

a(x) = (3x - 1 + 5Q'(x)/w(x) +/ sqrt((3x - 1 + 5Q'(x)/w(x))^2 - 4(49x^2 + 7Q'(x)/w(x)))/2

but you'd still need the radicals to be the same as all you're doing is switching from multiplying one solution by 7, to multiplying the other, while with the other you multiply by 5 and add 5, which can't change the radicals.

But that forces Q'(x)/w(x) to equal the original Q(x), forcing w(x)=1 and

Q'(x) = Q(x)

so you just get back what you had before.

So it's absolute mathematics with perfect argument, otherwise known as a proof, and no room for a mathematical objection.

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

and

7g(x) = 5a_2(x)

along with

2f(x) = 5a_1(x) + 5

it is reasonable to suppose that a_2(x) has 7 as a factor, but critics who have argued with me for some time over approaches like this have continually maintained it does not in the ring of algebraic integers, and for that to be true g(x) must not be an algebraic integer.

With my generalized solution:

(49x^2+7Q(x))5^2 - (3x-1+5Q(x))(5)(7) + 7^2 = (5a_1(x)+7)*(5a_2(x)+7)

giving the a's as roots of

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0

that claim can be rigorously tested, as you can simply shift to

7f(x) = 5a_2(x)

and

2g(x) = 5a_1(x) + 5

so that if g(x) is not an algebraic integer as the critics need then a_1(x) is not either, which forces Q(x) to not be, so assume instead you have Q'(x)/w(x) where w(x) is some factor of 7.

Then you'd have

a^2 - (3x - 1 + 5Q'(x)/w(x))a + (49x^2 + 7Q'(x)/w(x)) = 0

which solves as

a(x) = (3x - 1 + 5Q'(x)/w(x) +/ sqrt((3x - 1 + 5Q'(x)/w(x))^2 - 4(49x^2 + 7Q'(x)/w(x)))/2

but you'd still need the radicals to be the same as all you're doing is switching from multiplying one solution by 7, to multiplying the other, while with the other you multiply by 5 and add 5, which can't change the radicals.

But that forces Q'(x)/w(x) to equal the original Q(x), forcing w(x)=1 and

Q'(x) = Q(x)

so you just get back what you had before.

So it's absolute mathematics with perfect argument, otherwise known as a proof, and no room for a mathematical objection.

### Sunday, December 24, 2006

## JSH: Dumb as rocks

So the weird reality at the heart of the debates that have gone on for years is that I say that functions like sqrt() return more than one value while posters maintain that it has one solution—because it is defined to have one.

So I say, sqrt(4) is 2 or -2, and they claim it's just 2.

I say, look (-2)(-2) = 4, and they claim, so what, mathematicians DEFINED sqrt(4) to be 2, so who cares if (-2)(-2) = 4?

It may seem trivial, but by getting away with that dumb argument, posters can with that single small logical error keep going with bigger and bigger errors that grow from it, which is why these arguments don't get resolved.

So I say they are dumb as rocks because I'd think most of you can comprehend that people can DEFINE something to be true, even with the best of intentions, and it just fall apart as a concept with more advanced knowledge.

And while to many of you it may see this trivial thing which you think you always handle—mentally shifting as needed if you need sqrt(4) to be -2—it turns out that it breaks a lot of mathematics to make even one, small, seemingly trivial, logical mistake.

No matter how much you hate it, sqrt(4) has TWO SOLUTIONS.

And if you can get away with saying it only has one, you break mathematical reasoning at a low enough level that it's pointless to explain and explain and explain and mathematical proofs just bounce off of you as you are a rock, at such a basic level of denial about mathematics that more advanced concepts are totally beyond you.

So the debates continue because posters hold on to the most obvious error, refusing to accept that sqrt() has TWO SOLUTIONS, and that has implications over much of number theory.

Hard to believe but that is how mathematics escapes people who don't understand it is about perfection.

Even seemingly trivial mistakes can break huge swathes of mathematics.

In contrast in your daily lives little errors are just a fact of life.

So you carry over your mundane existence to an area where the tiniest of mental mistakes break so much, and then can't accept that it's happening because your mind keeps telling you that it is too small of a thing.

But in mathematics there is no such thing as too small of an error.

So I say, sqrt(4) is 2 or -2, and they claim it's just 2.

I say, look (-2)(-2) = 4, and they claim, so what, mathematicians DEFINED sqrt(4) to be 2, so who cares if (-2)(-2) = 4?

It may seem trivial, but by getting away with that dumb argument, posters can with that single small logical error keep going with bigger and bigger errors that grow from it, which is why these arguments don't get resolved.

So I say they are dumb as rocks because I'd think most of you can comprehend that people can DEFINE something to be true, even with the best of intentions, and it just fall apart as a concept with more advanced knowledge.

And while to many of you it may see this trivial thing which you think you always handle—mentally shifting as needed if you need sqrt(4) to be -2—it turns out that it breaks a lot of mathematics to make even one, small, seemingly trivial, logical mistake.

No matter how much you hate it, sqrt(4) has TWO SOLUTIONS.

And if you can get away with saying it only has one, you break mathematical reasoning at a low enough level that it's pointless to explain and explain and explain and mathematical proofs just bounce off of you as you are a rock, at such a basic level of denial about mathematics that more advanced concepts are totally beyond you.

So the debates continue because posters hold on to the most obvious error, refusing to accept that sqrt() has TWO SOLUTIONS, and that has implications over much of number theory.

Hard to believe but that is how mathematics escapes people who don't understand it is about perfection.

Even seemingly trivial mistakes can break huge swathes of mathematics.

In contrast in your daily lives little errors are just a fact of life.

So you carry over your mundane existence to an area where the tiniest of mental mistakes break so much, and then can't accept that it's happening because your mind keeps telling you that it is too small of a thing.

But in mathematics there is no such thing as too small of an error.

## JSH: Re-visiting planet Contrary

After years of acting as if expressions like 1+sqrt(2) give you one number so that 1 - sqrt(2) is a different number, many of you have no clue about the mistakes in mathematical reasoning you are making so I will re-visit the concept of a strange planet I call Contrary where people do things differently than on planet Earth.

Like on planet Contrary philosophers recently decided it was immoral to resolve the square root when you use the quadratic formula, so when they use it on

x^2 - 5x + 4 = 0

they get

x = (5 +/- sqrt(9))/2

and they say they have (5 + sqrt(9))/2 and (5 - sqrt(9))/2 and that each is a number, which you may think, hey, that's ok! Because to you they ARE single numbers where one is 4 and the other is 1, but the people on planet Contrary have one upped you, as thinking those are single numbers they have developed Contrary Galois Theory which is just like that used here on Earth except they have "numbers" in their Contrary Galois Theory where we'd just resolve the freaking square root.

And with their Contrary Galois Theory they can "prove" all kinds of things!

Like they can "prove" to you that no integer unit can be the root of a monic primitive with integer coefficients of degree 2 or higher, and they can even "factor" roots of monic polynomials with integer coefficients with remarkable adeptness giving convoluted expressions that are roots of polynomials we can just work out to integer

roots—but on Contrary they look get things like

(3 + sqrt(25))^{1/3}

and ooh and awe over the wonder of such complexity!!!

Recently things are restless though on planet Contrary as one person has dared to stand up to the philosopher overlords and proclaimed that they are silly and that

5 + sqrt(9)

is TWO NUMBERS and not just one, and that no, it's NOT true that it can't be the root of some other monic primitive with integer coefficients.

In fact he can PROVE that ONE of its solutions can be the root of <gasp>

x^2 + 9x + 8 = 0

and that it is just silly anyway to keep saying that sqrt(9) can't be evaluated, as in fact it can be evaluated to give two integers and people should toss out the ruling philosopher overlords for just being nasty turkeys.

Well the furor that has erupted on planet Contrary is something to behold!

Angry mathematicians and philosophers rant and rave about the crackpot who dares to say square roots should be evaluated, and foam at the mouth over the brazen heresy that the venerable square root function would be such a lowly beast as to give TWO SOLUTIONS??!!!

No way they argue, and the debate goes back and forth on planet Contrary where some philosophers DEFINED the square root function as too holy to give ANY solution at all!!!

[A reply to someone who wrote that sqrt(2) = 1.414213562…, 1 + sqrt(2) = 2.414213562…, and 1 − sqrt(2) = 0.414213562&hellip, and then asked James why it was so hard for him to understanding that.]

It's not true.

Consider

(3 + sqrt(25))^{1/3}

and if you could not do that simple thing of evaluating sqrt(25) and later evaluating one solution to find a cubic, you could go on and on about this special number that is an algebraic integer root of some other number as if you were doing something major, when you're not.

But when you can resolve the square root—you do it.

So people don't go around talking about 3 + sqrt(25), as instead they use A NUMBER.

But if it's sqrt(2) or some other expression where you haven't figured out a way to get beyond that square root, you drag it around in expression like 1 + sqrt(2).

Now you wouldn't drag around sqrt(4) in 1 + sqrt(4) because you can evaluate out of the square root and pick a solution.

But you DO drag around something like sqrt(5) because you CANNOT.

Get it, yet?

And in number theory approximations are no solution at all.

People drag around expressions asking to be evaluated, when they don't quite have the mathematical machinery in place to evaluate them.

So they'd resolve 1 + sqrt(25) but drag around 1 + sqrt(5).

Understand yet? Has anything seeped through the wall of stupidity which may be protecting you from basic knowledge about mathematics?

[A reply to someone who said that, despite all the maths books he read, he never saw “proof by invocation of imaginary alien civilization” used as a proof method before]

I think it's an excellent way to try and get people to look at what is being done in a different way, as consider some aliens who go even further than declaring sqrt(4) as only having one solution to saying it has NO solutions, and they can build Contrary Galois Theory with exactly the same machinery human beings have built up their Galois Theory with, so that it'd look exactly the same except you'd look at it and go, hey, wait, you can just evaluate things like sqrt(4) in there.

Taking the silly idea that you can declare away one solution to the square root to the limit of declaring away ALL solutions shows how dumb it is, I hope.

I've proven and proven and proven the mathematical truth.

Yet even publication in a mathematical journal meant nothing to people like you who can explain away just about anything.

But I'll make sure that on some level you understand how stupid your position is, and realize it also ultimately rests on refusing to acknowledge that sqrt(4) is 2 or -2.

Real aliens contemplating the inability of human beings to get over this hurdle and start developing number theory again would probably just conclude that our species has just kind of gone as far as it can go, and might just keep going themselves rather than deal with such an obstinate and clueless species. Oh that and how we keep destroying our own world, of course.

[A reply to someone who said that if

Yes it does—on planet Contrary.

Dude, to get Galois Theory with integers all you have to do is NOT take the square root with squares!!!

That's it!

You get the exact same damn theory with integers if you with sqrt(4) you just leave it as sqrt(4) versus resolving it.

Don't you get the story?

On planet Contrary the weird aliens DEFINE the square root to have NO SOLUTIONS AT ALL, as it's immoral or something according to their philosophers who are terrible overlords.

By DEFINING the square root of squares to not have a solution they managed to create Contrary Galois Theory, and it looks just like Galois Theory on this planet, except you have things like sqrt(25) in there while humans would have sqrt(5).

It's a great analogy showing how stupid it is to define away a solution to the square root as someone can just go further and define away ALL solutions and get—Galois Theory with integers.

Surely you're not too dumb to realize that if you just don't resolve square roots you can get Galois Theory with integers, are you?

Like on planet Contrary philosophers recently decided it was immoral to resolve the square root when you use the quadratic formula, so when they use it on

x^2 - 5x + 4 = 0

they get

x = (5 +/- sqrt(9))/2

and they say they have (5 + sqrt(9))/2 and (5 - sqrt(9))/2 and that each is a number, which you may think, hey, that's ok! Because to you they ARE single numbers where one is 4 and the other is 1, but the people on planet Contrary have one upped you, as thinking those are single numbers they have developed Contrary Galois Theory which is just like that used here on Earth except they have "numbers" in their Contrary Galois Theory where we'd just resolve the freaking square root.

And with their Contrary Galois Theory they can "prove" all kinds of things!

Like they can "prove" to you that no integer unit can be the root of a monic primitive with integer coefficients of degree 2 or higher, and they can even "factor" roots of monic polynomials with integer coefficients with remarkable adeptness giving convoluted expressions that are roots of polynomials we can just work out to integer

roots—but on Contrary they look get things like

(3 + sqrt(25))^{1/3}

and ooh and awe over the wonder of such complexity!!!

Recently things are restless though on planet Contrary as one person has dared to stand up to the philosopher overlords and proclaimed that they are silly and that

5 + sqrt(9)

is TWO NUMBERS and not just one, and that no, it's NOT true that it can't be the root of some other monic primitive with integer coefficients.

In fact he can PROVE that ONE of its solutions can be the root of <gasp>

x^2 + 9x + 8 = 0

and that it is just silly anyway to keep saying that sqrt(9) can't be evaluated, as in fact it can be evaluated to give two integers and people should toss out the ruling philosopher overlords for just being nasty turkeys.

Well the furor that has erupted on planet Contrary is something to behold!

Angry mathematicians and philosophers rant and rave about the crackpot who dares to say square roots should be evaluated, and foam at the mouth over the brazen heresy that the venerable square root function would be such a lowly beast as to give TWO SOLUTIONS??!!!

No way they argue, and the debate goes back and forth on planet Contrary where some philosophers DEFINED the square root function as too holy to give ANY solution at all!!!

[A reply to someone who wrote that sqrt(2) = 1.414213562…, 1 + sqrt(2) = 2.414213562…, and 1 − sqrt(2) = 0.414213562&hellip, and then asked James why it was so hard for him to understanding that.]

It's not true.

Consider

(3 + sqrt(25))^{1/3}

and if you could not do that simple thing of evaluating sqrt(25) and later evaluating one solution to find a cubic, you could go on and on about this special number that is an algebraic integer root of some other number as if you were doing something major, when you're not.

But when you can resolve the square root—you do it.

So people don't go around talking about 3 + sqrt(25), as instead they use A NUMBER.

But if it's sqrt(2) or some other expression where you haven't figured out a way to get beyond that square root, you drag it around in expression like 1 + sqrt(2).

Now you wouldn't drag around sqrt(4) in 1 + sqrt(4) because you can evaluate out of the square root and pick a solution.

But you DO drag around something like sqrt(5) because you CANNOT.

Get it, yet?

And in number theory approximations are no solution at all.

People drag around expressions asking to be evaluated, when they don't quite have the mathematical machinery in place to evaluate them.

So they'd resolve 1 + sqrt(25) but drag around 1 + sqrt(5).

Understand yet? Has anything seeped through the wall of stupidity which may be protecting you from basic knowledge about mathematics?

[A reply to someone who said that, despite all the maths books he read, he never saw “proof by invocation of imaginary alien civilization” used as a proof method before]

I think it's an excellent way to try and get people to look at what is being done in a different way, as consider some aliens who go even further than declaring sqrt(4) as only having one solution to saying it has NO solutions, and they can build Contrary Galois Theory with exactly the same machinery human beings have built up their Galois Theory with, so that it'd look exactly the same except you'd look at it and go, hey, wait, you can just evaluate things like sqrt(4) in there.

Taking the silly idea that you can declare away one solution to the square root to the limit of declaring away ALL solutions shows how dumb it is, I hope.

I've proven and proven and proven the mathematical truth.

Yet even publication in a mathematical journal meant nothing to people like you who can explain away just about anything.

But I'll make sure that on some level you understand how stupid your position is, and realize it also ultimately rests on refusing to acknowledge that sqrt(4) is 2 or -2.

Real aliens contemplating the inability of human beings to get over this hurdle and start developing number theory again would probably just conclude that our species has just kind of gone as far as it can go, and might just keep going themselves rather than deal with such an obstinate and clueless species. Oh that and how we keep destroying our own world, of course.

[A reply to someone who said that if

*d*is an integer which is not a square, then there is an automorphism of*Q*(sqrt(*d*)) which sends sqrt(*d*) to −sqrt(*d*) and that if*d*is a square, then that's not the case.]Yes it does—on planet Contrary.

Dude, to get Galois Theory with integers all you have to do is NOT take the square root with squares!!!

That's it!

You get the exact same damn theory with integers if you with sqrt(4) you just leave it as sqrt(4) versus resolving it.

Don't you get the story?

On planet Contrary the weird aliens DEFINE the square root to have NO SOLUTIONS AT ALL, as it's immoral or something according to their philosophers who are terrible overlords.

By DEFINING the square root of squares to not have a solution they managed to create Contrary Galois Theory, and it looks just like Galois Theory on this planet, except you have things like sqrt(25) in there while humans would have sqrt(5).

It's a great analogy showing how stupid it is to define away a solution to the square root as someone can just go further and define away ALL solutions and get—Galois Theory with integers.

Surely you're not too dumb to realize that if you just don't resolve square roots you can get Galois Theory with integers, are you?

## JSH: Generalized non-polynomial factorization

Considering continuing debates over the latest simplified approach to non-polynomial factorization I've concluded that some of you got confused on the specificity of the solution I gave for the a's, which actually is a conclusion helped by some responses from mathematicians I emailed.

So here is a generalized approach which removes that area of potential confusion.

This time starting with

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

in an integral domain, begin determining the functions f(x) and g(x) with

f(x) = 5a_1(x) + 5

and

7g(x) = 5a_2(x)

and now for the generalized approach I introduce another polynomial Q(x):

(49x^2+7Q(x))5^2 - (3x-1+5Q(x))(5)(7) + 7^2 = (5a_1(x)+7)*(5a_2(x)+7)

so that I have as solutions for the a's:

a_1(x)*a_2(x) = 49x^2 + 7Q(x)

and

a_1(x) + a_2(x) = 3x - 1 + 5Q(x)

so they must be roots of

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0.

That is the generalized solution for the a's rather than a highly specific one, so assume that an f(x) and g(x) exist in the ring of algebraic integers with the start

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

and if such exist, then the a's will be algebraic integers as well, and ALL possible solutions for the a's are defined by

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0

meaning variation is just with Q(x), and with the a's algebraic integers it must be true that Q(x) is an algebraic integer; therefore, it must be true that ONE of the roots for a Q(x) that works, will have 7 as a factor, while the other will not.

So what if f(x) and g(x) can't be algebraic integers when x is an integer?

Well, why not? And even if they aren't, at best you can hope they'd be ratios of algebraic integers with a denominator having non-unit factors in common with 2, not 7.

So that wouldn't change anything important.

Now some of you may refuse to acknowledge that there can exist functions f(x) and g(x) that behave as needed but then you're not people who are thinking rationally on the subject.

My original posts used Q(x) = -2x and I think doubt was cast on the specificity of THAT solution as maybe it seemed too arbitrary, while putting in the general solution to cover all possible solutions for the a's no matter what f(x) and g(x) are, should take away any concerns in that area.

So how might some of the people who obsessively argue with me still try to disagree?

Well, considering

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0

they'd have to claim that Q(x) does not have integer coefficients if neither f(x) nor g(x) would divide off factors from 7 as they wish, so that they could claim that if you get to a monic with integer coefficients it would be reducible over Q, and they'd have to claim that NEVER when Q(x) has integer coefficients, except when Q(x) = 0, of

course, could you have 7f(x) and 7g(x) both be algebraic integers.

Maybe the only way for some of you to understand what is happening and to comprehend how big a mistake it makes in your mind to declare the sqrt() function has only one solution and start down that road to some really big errors is to just figure out a Q(x) that will work with an integer x so that you can SEE the freaking 7 as a factor—once you resolve the square roots.

So with

(49x^2+7Q(x))5^2 - (3x-1+5Q(x))(5)(7) + 7^2 = (5a_1(x)+7)*(5a_2(x)+7)

where the a's are roots of

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0

and Q(x) is some polynomial YOU can pick so that with some integer x, you get integer roots, then I want you to do something simple, pause with your solution for the quadratic formula, and consider, what if?

What if you couldn't just resolve that square root?

Now go back to

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

where now you'll have integer values for f(x) and g(x) as well, and just ask yourself, how would you write that in terms of square roots?

So how did this error in thinking with the square roots propagate and flourish?

I say because of simple failure as mathematicians had no idea how to figure out something like one root having 7 as a factor if they didn't have integers with even something as simple as a monic quadratic with integer coefficients.

So they made stuff up.

Maybe it was a lot of ego, or maybe it was just a refusal to accept a limitation that there was something they didn't know with math they thought was so simple, but for whatever reason, they started making stuff up, and part of doing that was declaring the sqrt() had only one solution so they could escape the reality of two solutions and run off into error.

And now holding on to the errors in thinking so that I STILL get in arguments with people declaring that -2 is not a solution for sqrt(4) is just willful stupidity and foolish pride.

So you have all kinds of machinery with Galois Theory that will work the EXACT SAME WAY with integers, if you just refuse to do things like resolve sqrt(25).

If you just use the quadratic formula, and refuse to evaluate the square root when you get integers, everything works the exact same way.

So here is a generalized approach which removes that area of potential confusion.

This time starting with

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

in an integral domain, begin determining the functions f(x) and g(x) with

f(x) = 5a_1(x) + 5

and

7g(x) = 5a_2(x)

and now for the generalized approach I introduce another polynomial Q(x):

(49x^2+7Q(x))5^2 - (3x-1+5Q(x))(5)(7) + 7^2 = (5a_1(x)+7)*(5a_2(x)+7)

so that I have as solutions for the a's:

a_1(x)*a_2(x) = 49x^2 + 7Q(x)

and

a_1(x) + a_2(x) = 3x - 1 + 5Q(x)

so they must be roots of

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0.

That is the generalized solution for the a's rather than a highly specific one, so assume that an f(x) and g(x) exist in the ring of algebraic integers with the start

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

and if such exist, then the a's will be algebraic integers as well, and ALL possible solutions for the a's are defined by

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0

meaning variation is just with Q(x), and with the a's algebraic integers it must be true that Q(x) is an algebraic integer; therefore, it must be true that ONE of the roots for a Q(x) that works, will have 7 as a factor, while the other will not.

So what if f(x) and g(x) can't be algebraic integers when x is an integer?

Well, why not? And even if they aren't, at best you can hope they'd be ratios of algebraic integers with a denominator having non-unit factors in common with 2, not 7.

So that wouldn't change anything important.

Now some of you may refuse to acknowledge that there can exist functions f(x) and g(x) that behave as needed but then you're not people who are thinking rationally on the subject.

My original posts used Q(x) = -2x and I think doubt was cast on the specificity of THAT solution as maybe it seemed too arbitrary, while putting in the general solution to cover all possible solutions for the a's no matter what f(x) and g(x) are, should take away any concerns in that area.

So how might some of the people who obsessively argue with me still try to disagree?

Well, considering

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0

they'd have to claim that Q(x) does not have integer coefficients if neither f(x) nor g(x) would divide off factors from 7 as they wish, so that they could claim that if you get to a monic with integer coefficients it would be reducible over Q, and they'd have to claim that NEVER when Q(x) has integer coefficients, except when Q(x) = 0, of

course, could you have 7f(x) and 7g(x) both be algebraic integers.

Maybe the only way for some of you to understand what is happening and to comprehend how big a mistake it makes in your mind to declare the sqrt() function has only one solution and start down that road to some really big errors is to just figure out a Q(x) that will work with an integer x so that you can SEE the freaking 7 as a factor—once you resolve the square roots.

So with

(49x^2+7Q(x))5^2 - (3x-1+5Q(x))(5)(7) + 7^2 = (5a_1(x)+7)*(5a_2(x)+7)

where the a's are roots of

a^2 - (3x - 1 + 5Q(x))a + (49x^2 + 7Q(x)) = 0

and Q(x) is some polynomial YOU can pick so that with some integer x, you get integer roots, then I want you to do something simple, pause with your solution for the quadratic formula, and consider, what if?

What if you couldn't just resolve that square root?

Now go back to

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

where now you'll have integer values for f(x) and g(x) as well, and just ask yourself, how would you write that in terms of square roots?

So how did this error in thinking with the square roots propagate and flourish?

I say because of simple failure as mathematicians had no idea how to figure out something like one root having 7 as a factor if they didn't have integers with even something as simple as a monic quadratic with integer coefficients.

So they made stuff up.

Maybe it was a lot of ego, or maybe it was just a refusal to accept a limitation that there was something they didn't know with math they thought was so simple, but for whatever reason, they started making stuff up, and part of doing that was declaring the sqrt() had only one solution so they could escape the reality of two solutions and run off into error.

And now holding on to the errors in thinking so that I STILL get in arguments with people declaring that -2 is not a solution for sqrt(4) is just willful stupidity and foolish pride.

So you have all kinds of machinery with Galois Theory that will work the EXACT SAME WAY with integers, if you just refuse to do things like resolve sqrt(25).

If you just use the quadratic formula, and refuse to evaluate the square root when you get integers, everything works the exact same way.

## JSH: Perspective is weird

One of the odder things that has emerged recently as I have expressed my opinion of posts with ratings on Google Groups as they give that option is that people who replied to me so obsessively actually care about getting an honest assessment of the reality of how much their posting is valued by both the number of ratings they get—few—and the reality that there are maybe 3 or 4 other people who try to combat my low ratings.

It gives them some perspective on their real social ranking on the newsgroup.

Before, they must have just looked at replies, where as I've noted, maybe 3 or 4 people can make it look like there is a LOT of support for them by replying a lot in a thread, but the ratings tell you how many people are rating and give you some idea of how it goes.

I am highly critical, not surprisingly, so I mostly give out 1 star, as I see a lot of crap posts and rate them accordingly.

Their supporters, all three or four of them, come back to give them 5 stars, an outlandish overrating as their posts ARE crap, but still it seems to settle in that hey, they are not the newsgroup celebrities they thought they were.

These people didn't know where they actually stood.

But my guess is they thought they were very popular with most of the newsgroup, of which they seem to believe there are a few hundred readers with a few dozen regular readers based on the posts they notice.

Weird, but from what I've read from these people in the past, consistent with their gut feeling of the size of the sci.math newsgroup.

In contrast I measure my impact off of the newsgroup and don't count replies to my posts because I know there are a few very obsessive people who skew things to the negative because they think they are some kind of stars or something posting negatives the newsgroup wants to see.

But they are actually minor hanger's on, drawing attention to themselves at the expense of my research which I can measure as having an ever growing worldwide impact by using a lot of tools, which yes are mostly as a result of Google, that tell me what the real impact is, versus the skewed view you'd get from posts on the newsgroup.

Perspective is weird that way. Most people have no clue about their worldwide impact and in a situation where there is worldwide attention—like here—they just screw up figuring out where they stand as they don't take the proper view that it takes work to figure out what is going on.

Especially in a world like ours does it take work.

Like how many of you have the slightest hint of a clue how many people are likely to read this post in the next 24 hours?

Dozens? Hundreds? Thousands?

Or in how many countries?

1? 2 or 3? 20 or more?

If you accept that your answer is you do not know, then maybe you are on the path to realizing that unlike me, you have no clue what is actually going on.

It gives them some perspective on their real social ranking on the newsgroup.

Before, they must have just looked at replies, where as I've noted, maybe 3 or 4 people can make it look like there is a LOT of support for them by replying a lot in a thread, but the ratings tell you how many people are rating and give you some idea of how it goes.

I am highly critical, not surprisingly, so I mostly give out 1 star, as I see a lot of crap posts and rate them accordingly.

Their supporters, all three or four of them, come back to give them 5 stars, an outlandish overrating as their posts ARE crap, but still it seems to settle in that hey, they are not the newsgroup celebrities they thought they were.

These people didn't know where they actually stood.

But my guess is they thought they were very popular with most of the newsgroup, of which they seem to believe there are a few hundred readers with a few dozen regular readers based on the posts they notice.

Weird, but from what I've read from these people in the past, consistent with their gut feeling of the size of the sci.math newsgroup.

In contrast I measure my impact off of the newsgroup and don't count replies to my posts because I know there are a few very obsessive people who skew things to the negative because they think they are some kind of stars or something posting negatives the newsgroup wants to see.

But they are actually minor hanger's on, drawing attention to themselves at the expense of my research which I can measure as having an ever growing worldwide impact by using a lot of tools, which yes are mostly as a result of Google, that tell me what the real impact is, versus the skewed view you'd get from posts on the newsgroup.

Perspective is weird that way. Most people have no clue about their worldwide impact and in a situation where there is worldwide attention—like here—they just screw up figuring out where they stand as they don't take the proper view that it takes work to figure out what is going on.

Especially in a world like ours does it take work.

Like how many of you have the slightest hint of a clue how many people are likely to read this post in the next 24 hours?

Dozens? Hundreds? Thousands?

Or in how many countries?

1? 2 or 3? 20 or more?

If you accept that your answer is you do not know, then maybe you are on the path to realizing that unlike me, you have no clue what is actually going on.

### Saturday, December 23, 2006

## JSH: Reasoning behind the hostility

For years I have wondered why there was so much anger from math people where none of the explanations made sense, until now with this remarkably simple and perfect argument that among other things proves that just one root of

x^2 - 6x + 35 = 0

has 7 as a factor in the ring of algebraic integers.

Why would so many mathematicians get upset with such a result?

Well, when Hilbert was talking about the great problems in mathematics, if mathematicians were being honest they could have added finding how factors of 7 distribute among roots of a simple quadratic like that to the list.

But compare that to the 10 problems he did give and you can get some sense of why a proud group of people would rather run from an annoying reality that would escape most people because of point of view, as, after all, we have the quadratic formula, and lots of methods for APPROXIMATING the solution for the roots.

You need such in science, construction and practical areas, but in number theory, approximate is no solution at all.

To understand how little the quadratic formula actually tells you without evaluating the square roots consider the roots of

x^2 -12x + 35 = 0

from

x = (12 +/- sqrt(4))/2

where I don't evaluate the square root though it's trivial, so you can understand how little you actually know there, until you evaluate the square root.

But with x^2 - 6x + 35 = 0, you have

x = (6 +/- sqrt(-104))/2

and while you can divide out that 2 to get

x = 3 +/- sqrt(-26)

at that point you're stuck, and how does 7 distribute?

No one knew, so they made stuff up.

What I did was figure out an easy way to figure out that one root has 7 as a factor, while it still doesn't say which root, but it gets around actually evaluating that square root with some simple analytical tools, and there's the problem.

Now the truth would come out about the previous refusal to acknowledge a hard problem in a seemingly trivial area, where mathematicians made up a solution which doesn't actually work.

For instance, you may think that a non-monic primitive polynomial with integer coefficients irreducible over Q cannot have algebraic integer roots, when it can.

The fake argument actually proves that a monic primitive with integer coefficients irreducible over Q cannot have the root of a monic primitive with integer coefficients of lesser degree, and then there is one of those annoying leaps when people use what's true to leap to something that's not.

So it turns out that to have an algebraic integer root, a non-monic primitive with integer coefficients irreducible over Q must have the root of a monic primitive with integer coefficients irreducible over Q of HIGHER DEGREE.

Go back, check arguments you thought were proofs see the obvious and realize that people when pushed can lie—even in mathematics.

So no, Hilbert wouldn't have wanted to state that one of the great unknowns in mathematics was how 7 or its factors distributed with the roots of

x^2 - 6x + 35 = 0

and with the faked math, he didn't have to, but instead could put up really complicated and highly technical stuff that made mathematicians look like the brilliant people they want people to think they are—not people still working at what most people think of as trivially solved because they don't understand number theory.

In number theory, approximate is no solution at all.

[A reply to someone who said that James has alredy been exposed to three proofs of the fact that, given an equation like

You're wrong.

I have a perfect argument, simple proof which readers can see at my

Extreme Mathematics group:

http://groups.google.com/group/extrememathematics

What I did was settle another area where people seemed to be puzzled, as I showed how you get that neat little way of factoring into non-polynomial factors that I do.

By generalizing a bit I also give a final solution for the a's where you can actually check to see if it's possible for one of the a's to NOT have 7 as a factor and see the consequences if that possibility were to occur.

So I've added more detail and added more flash to the paper, before it goes to the next journal.

The next chief editor won't have the option, like the Bulletin one did, of saying the paper focuses on too narrow of an area to interest readers!

It is a beautiful argument. A wonderful proof so I'm glad I had to find it versus just having my previous line of attack shown in my old paper.

And it's so wild to be able to drop the negatives against Dedekind as the ring of algebraic integers is ok. He did good.

x^2 - 6x + 35 = 0

has 7 as a factor in the ring of algebraic integers.

Why would so many mathematicians get upset with such a result?

Well, when Hilbert was talking about the great problems in mathematics, if mathematicians were being honest they could have added finding how factors of 7 distribute among roots of a simple quadratic like that to the list.

But compare that to the 10 problems he did give and you can get some sense of why a proud group of people would rather run from an annoying reality that would escape most people because of point of view, as, after all, we have the quadratic formula, and lots of methods for APPROXIMATING the solution for the roots.

You need such in science, construction and practical areas, but in number theory, approximate is no solution at all.

To understand how little the quadratic formula actually tells you without evaluating the square roots consider the roots of

x^2 -12x + 35 = 0

from

x = (12 +/- sqrt(4))/2

where I don't evaluate the square root though it's trivial, so you can understand how little you actually know there, until you evaluate the square root.

But with x^2 - 6x + 35 = 0, you have

x = (6 +/- sqrt(-104))/2

and while you can divide out that 2 to get

x = 3 +/- sqrt(-26)

at that point you're stuck, and how does 7 distribute?

No one knew, so they made stuff up.

What I did was figure out an easy way to figure out that one root has 7 as a factor, while it still doesn't say which root, but it gets around actually evaluating that square root with some simple analytical tools, and there's the problem.

Now the truth would come out about the previous refusal to acknowledge a hard problem in a seemingly trivial area, where mathematicians made up a solution which doesn't actually work.

For instance, you may think that a non-monic primitive polynomial with integer coefficients irreducible over Q cannot have algebraic integer roots, when it can.

The fake argument actually proves that a monic primitive with integer coefficients irreducible over Q cannot have the root of a monic primitive with integer coefficients of lesser degree, and then there is one of those annoying leaps when people use what's true to leap to something that's not.

So it turns out that to have an algebraic integer root, a non-monic primitive with integer coefficients irreducible over Q must have the root of a monic primitive with integer coefficients irreducible over Q of HIGHER DEGREE.

Go back, check arguments you thought were proofs see the obvious and realize that people when pushed can lie—even in mathematics.

So no, Hilbert wouldn't have wanted to state that one of the great unknowns in mathematics was how 7 or its factors distributed with the roots of

x^2 - 6x + 35 = 0

and with the faked math, he didn't have to, but instead could put up really complicated and highly technical stuff that made mathematicians look like the brilliant people they want people to think they are—not people still working at what most people think of as trivially solved because they don't understand number theory.

In number theory, approximate is no solution at all.

[A reply to someone who said that James has alredy been exposed to three proofs of the fact that, given an equation like

*x*² − 6*x*+ 35 = 0, then both roots either are, or are not, divisible by 7 in the algebraic integers.]You're wrong.

I have a perfect argument, simple proof which readers can see at my

Extreme Mathematics group:

http://groups.google.com/group/extrememathematics

What I did was settle another area where people seemed to be puzzled, as I showed how you get that neat little way of factoring into non-polynomial factors that I do.

By generalizing a bit I also give a final solution for the a's where you can actually check to see if it's possible for one of the a's to NOT have 7 as a factor and see the consequences if that possibility were to occur.

So I've added more detail and added more flash to the paper, before it goes to the next journal.

The next chief editor won't have the option, like the Bulletin one did, of saying the paper focuses on too narrow of an area to interest readers!

It is a beautiful argument. A wonderful proof so I'm glad I had to find it versus just having my previous line of attack shown in my old paper.

And it's so wild to be able to drop the negatives against Dedekind as the ring of algebraic integers is ok. He did good.

### Tuesday, December 19, 2006

## JSH: Latest paper submitted

In case you hadn't guessed it, I now talk out ideas before I submit papers.

Having hashed and re-hashed the main points of this latest approach to non-polynomial factorization, I made my last changes to my latest paper and submitted it to the Bulletin of the AMS.

Thanks for your help!

And yes, now things can quiet down.

With extreme mathematics things get really loud when something new is about to happen.

In this case I was working out some annoying little details until I was certain enough, as I'm trying to submit better papers than in the past as before they tended to be rather messy.

At first I kind of thought that was part of extreme mathematics but it's just un-professional and tedious as it's so much harder dealing with updates with the math journals than just tossing out another post on Usenet or updating my own sites.

[A reply to someone who wanted to know which where James' reaction to previous refutations of his paper.]

You didn't refute anything. If you did, I wouldn't have submitted the paper today.

My suggestion to you is to take a deep breath, think about automorphisms, and consider that it is now out of your hands anyway as I suggest to you that the staff and editors of the Bulletin of the AMS are more than capable of considering the mathematical issues carefully and making the right decision.

You really went way out there into la la land, so I read your posts less and less.

Maybe extreme mathematics is getting too familiar for me to get good critiques any more.

Oh well, that's how it goes. Kick back dude. Enjoy the holidays.

It's not like I'm going to look over any posts when the paper is at the Bulletin.

So those things are just out there for anybody else who cares.

As now, I don't give a damn, and there is no reason I should.

Having hashed and re-hashed the main points of this latest approach to non-polynomial factorization, I made my last changes to my latest paper and submitted it to the Bulletin of the AMS.

Thanks for your help!

And yes, now things can quiet down.

With extreme mathematics things get really loud when something new is about to happen.

In this case I was working out some annoying little details until I was certain enough, as I'm trying to submit better papers than in the past as before they tended to be rather messy.

At first I kind of thought that was part of extreme mathematics but it's just un-professional and tedious as it's so much harder dealing with updates with the math journals than just tossing out another post on Usenet or updating my own sites.

[A reply to someone who wanted to know which where James' reaction to previous refutations of his paper.]

You didn't refute anything. If you did, I wouldn't have submitted the paper today.

My suggestion to you is to take a deep breath, think about automorphisms, and consider that it is now out of your hands anyway as I suggest to you that the staff and editors of the Bulletin of the AMS are more than capable of considering the mathematical issues carefully and making the right decision.

You really went way out there into la la land, so I read your posts less and less.

Maybe extreme mathematics is getting too familiar for me to get good critiques any more.

Oh well, that's how it goes. Kick back dude. Enjoy the holidays.

It's not like I'm going to look over any posts when the paper is at the Bulletin.

So those things are just out there for anybody else who cares.

As now, I don't give a damn, and there is no reason I should.

## JSH: Signal to noise

I get a good deal of feedback from people who tell me I should not be posting.

And I think some of you wonder why I bother if a bunch of people just call me names and repeatedly claim I'm wrong.

Well I'm an amateur dabbler who likes to play with simple math ideas and talk about them.

There are people who hate you for that, and no, it's not my manner as I've been posting for over ten years and I've tried different ways of going about talking out my ideas—never mattered.

If I was polite, people still called me names.

When I was careful about details and tried to sound closer to standard terminology, they'd still question my sanity.

One poster who at least is honest about his intentions would just tell me—if I wanted the verbal attacks to stop I had to stop posting.

Now if I had somewhere else to go, maybe I would, but who do you talk out math with?

So should I have to get a math degree to talk out simple ideas on Usenet in public forums?

I don't think so.

But maybe some of you think that you should be able to make up the rules for your groups and DEMAND a math degree or that people follow some outline of posting that fits in with your way of thinking.

Hey, that's un-Usenet in flavor but you have the right to your opinion—and I have the right to ignore it.

So there's a lot of noise. I know that no matter how I post there will always be some people who will reply in a nasty way, but there's a freedom in that as well!

If I want, I can let loose as well knowing it does not matter either way. Whatever I do as long as I post there will be people replying nastily as intention is—to stop me from posting.

Your culture has some issues which it gets away without addressing by forcing people out, so then you can all tell each other what you want to hear and act like you fit with mainstream social values, yet in the mainstream society I know it's considered bad form to impinge on the rights of others in public places to try and make them your own.

One analogy I like is to a gang of teenagers who decide that a public park is THEIR space, so they harass and intimidate others who try to use the public space, and as long as the police don't roust them out, they congratulate themselves on their accomplishment.

What you have are gangs of posters who harass and intimidate other posters they decide are unwanted, and usually they get away with it, so you have the noise.

But I have nowhere else to go to talk out math ideas, so I stay, but in so doing I also remind you that your society is sick. You act out from your hatreds and can be intolerable of free speech that you disagree with, to an absurd degree, while lying about your own behavior and intolerance.

And I think some of you wonder why I bother if a bunch of people just call me names and repeatedly claim I'm wrong.

Well I'm an amateur dabbler who likes to play with simple math ideas and talk about them.

There are people who hate you for that, and no, it's not my manner as I've been posting for over ten years and I've tried different ways of going about talking out my ideas—never mattered.

If I was polite, people still called me names.

When I was careful about details and tried to sound closer to standard terminology, they'd still question my sanity.

One poster who at least is honest about his intentions would just tell me—if I wanted the verbal attacks to stop I had to stop posting.

Now if I had somewhere else to go, maybe I would, but who do you talk out math with?

So should I have to get a math degree to talk out simple ideas on Usenet in public forums?

I don't think so.

But maybe some of you think that you should be able to make up the rules for your groups and DEMAND a math degree or that people follow some outline of posting that fits in with your way of thinking.

Hey, that's un-Usenet in flavor but you have the right to your opinion—and I have the right to ignore it.

So there's a lot of noise. I know that no matter how I post there will always be some people who will reply in a nasty way, but there's a freedom in that as well!

If I want, I can let loose as well knowing it does not matter either way. Whatever I do as long as I post there will be people replying nastily as intention is—to stop me from posting.

Your culture has some issues which it gets away without addressing by forcing people out, so then you can all tell each other what you want to hear and act like you fit with mainstream social values, yet in the mainstream society I know it's considered bad form to impinge on the rights of others in public places to try and make them your own.

One analogy I like is to a gang of teenagers who decide that a public park is THEIR space, so they harass and intimidate others who try to use the public space, and as long as the police don't roust them out, they congratulate themselves on their accomplishment.

What you have are gangs of posters who harass and intimidate other posters they decide are unwanted, and usually they get away with it, so you have the noise.

But I have nowhere else to go to talk out math ideas, so I stay, but in so doing I also remind you that your society is sick. You act out from your hatreds and can be intolerable of free speech that you disagree with, to an absurd degree, while lying about your own behavior and intolerance.

## JSH: Automorphisms and political behavior

I figured out a simplified proof of an important assertion where it's obvious to anyone with a math degree or anyone who has bothered to study much mathematics at all that what I'm talking about is an automorphism(?) I think that's the right word.

So it's an easy proof with well-known ideas, but then I did something wacky.

I brainstormed a bit and said something wrong!!!

And then posters who argue with me, in particular Arturo Magidin and David Ullrich decided to try and exploit the mistake in replies in some of my threads.

Now that is deliberate behavior. Now it's an accident as I brainstorm as I see fit and part of the process is making mistakes as you try ideas, but it's a useful accident because they did reply in those threads showing their contempt for what is mathematically correct.

So what is the argument and what does it have to do with automorphisms (hoping I'm using the right word)?

In an integral domain I have an approach starting with what I want to be a factorization

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

where of course there is a simple non-monic quadratic on the left with the factorization on the right with functions f(x) and g(x) to be determined.

The next steps go against the gain immediately as I multiply through f(x) + 1 by 2 and multiply both sides by 7, introducing versus dividing away:

7*(175x^2 - 15x + 2) = 7*(2f(x) + 2)*(g(x) + 1)

then I fiddle with the left side some and multiply through g(x) + 1 by 7, still doing things against the grain:

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2 = (2f(x) + 2)*(7g(x) + 7)

and now I bring in new functions, in a kind of odd way as I work towards a conclusion:

Let

2f(x) = 5a_1(x) + 5

and

7g(x) =5a_2(x)

then substitute to get

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 49 = (5a_1(x) + 7)*(5a_2(x) + 7)

where now I finally solve for the a's using

a_1(x)*a_2(x) = 49x^2 - 14x

and

a_1(x) + a_2(x) = 7x-1

so the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

And what do automorphisms have to do with anything?

Well f(x) and g(x) are indistinguishable in the original factorization, so I should be able to shift them around without changing anything.

But the a's are roots of that last quadratic like expression thingy, which has only TWO SOLUTIONS.

So the weird answer is that f(x) = g(x), and you can work things out from there, but most importantly you have that only one root of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

can have 7 as a factor.

But if you solve for the functions using the quadratic formula, you find that a lot is wrapped up in that solution so that it's hard to pull out the actual solution for f(x) and g(x), which is where I made a mistake yesterday and posters worked hard to exploit it as you can see in those threads.

But there is no way that Ullrich and Magidin could have gotten their math Ph.D's and not known about automorphisms or whatever the right word is, so they DELIBERATELY lied in their recent posts trying to exploit my most recent brainstorming mistakes showing their absolute contempt for mathematics.

And to make matters worse, Magidin is supposedly a specialist in Galois Theory where automorphisms I think are kind of important, right?

So his contempt is especially acute. He tried to hide a simple conclusion that follows from the most basic idea in the area he is supposedly a specialist.

So it's an easy proof with well-known ideas, but then I did something wacky.

I brainstormed a bit and said something wrong!!!

And then posters who argue with me, in particular Arturo Magidin and David Ullrich decided to try and exploit the mistake in replies in some of my threads.

Now that is deliberate behavior. Now it's an accident as I brainstorm as I see fit and part of the process is making mistakes as you try ideas, but it's a useful accident because they did reply in those threads showing their contempt for what is mathematically correct.

So what is the argument and what does it have to do with automorphisms (hoping I'm using the right word)?

In an integral domain I have an approach starting with what I want to be a factorization

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

where of course there is a simple non-monic quadratic on the left with the factorization on the right with functions f(x) and g(x) to be determined.

The next steps go against the gain immediately as I multiply through f(x) + 1 by 2 and multiply both sides by 7, introducing versus dividing away:

7*(175x^2 - 15x + 2) = 7*(2f(x) + 2)*(g(x) + 1)

then I fiddle with the left side some and multiply through g(x) + 1 by 7, still doing things against the grain:

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2 = (2f(x) + 2)*(7g(x) + 7)

and now I bring in new functions, in a kind of odd way as I work towards a conclusion:

Let

2f(x) = 5a_1(x) + 5

and

7g(x) =5a_2(x)

then substitute to get

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 49 = (5a_1(x) + 7)*(5a_2(x) + 7)

where now I finally solve for the a's using

a_1(x)*a_2(x) = 49x^2 - 14x

and

a_1(x) + a_2(x) = 7x-1

so the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

And what do automorphisms have to do with anything?

Well f(x) and g(x) are indistinguishable in the original factorization, so I should be able to shift them around without changing anything.

But the a's are roots of that last quadratic like expression thingy, which has only TWO SOLUTIONS.

So the weird answer is that f(x) = g(x), and you can work things out from there, but most importantly you have that only one root of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

can have 7 as a factor.

But if you solve for the functions using the quadratic formula, you find that a lot is wrapped up in that solution so that it's hard to pull out the actual solution for f(x) and g(x), which is where I made a mistake yesterday and posters worked hard to exploit it as you can see in those threads.

But there is no way that Ullrich and Magidin could have gotten their math Ph.D's and not known about automorphisms or whatever the right word is, so they DELIBERATELY lied in their recent posts trying to exploit my most recent brainstorming mistakes showing their absolute contempt for mathematics.

And to make matters worse, Magidin is supposedly a specialist in Galois Theory where automorphisms I think are kind of important, right?

So his contempt is especially acute. He tried to hide a simple conclusion that follows from the most basic idea in the area he is supposedly a specialist.

## JSH: Weird if correct

Thinking about the latest failed idea, it seems to me that the correct answer may be simpler than I thought but kind of weird.

Still with

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

in an integral domain, it may be true that if

a_1(x) = ((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2

and

2f(x) = 5a_1(x) + 5

then f(x) = g(x), so you have that

f(x) = sqrt((175x^2 - 15x + 2)/2) - 1

and if that is true then f(x) is an algebraic integer factor of a_1(x).

If not, then hey, another weird idea wrong, but I think it should be correct, but it still seems weird.

Wacky, but I think it's right.

Still with

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

in an integral domain, it may be true that if

a_1(x) = ((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2

and

2f(x) = 5a_1(x) + 5

then f(x) = g(x), so you have that

f(x) = sqrt((175x^2 - 15x + 2)/2) - 1

and if that is true then f(x) is an algebraic integer factor of a_1(x).

If not, then hey, another weird idea wrong, but I think it should be correct, but it still seems weird.

Wacky, but I think it's right.

## JSH: Clarified disproof

Remarkably a simple refutation of claims against my research is easy enough to obtain, where I noticed that I could just directly give a solution that ends the debate. After brainstorming through it a bit I'll go ahead and give the clarified disproof.

Consider

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

in an integral domain, where f(x) and g(x) are functions I'll soon give.

With

a_1(x) = ((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2

it can be shown that

2f(x) = 5a_1(x) + 5

so 2f(x) is an algebraic integer.

Solving then I have

2f(x) = 5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

and it follows that

2g(x) = 5((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

proving that both 2f(x) and 2g(x) are algebraic integers.

The solution for a_1(x) follows from it being a root of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

Using x=1, I have that the quadratic that follows is

a^2 - 6a + 35 = 0

which gives

a = 3 +/- sqrt(-26)

as the solutions that follow from the quadratic formula, where now it is clear that one solution has 7 as a factor, while the other does not, in the ring of algebraic integers.

But let a = 7z, and you have

49z^2 - 42a + 35 = 0

which is

7z^2 - 6a + 5 = 0

which is a non-monic primitive polynomial irreducible over Q, which has been shown to have on root that must be an algebraic integer.

This disproof of a previously widely held belief—if sci.math'ers are to be believed and you may notice I tested them on this all day—is remarkable for its conciseness and reliance on very elementary algebra.

Previous to this disproof, it seems some people wrongly believed that an algebraic integer could not be the root of a non-monic primitive polynomial irreducible over Q.

[A reply to someone who said that James should get a grip on his life an put it back on track.]

You people have gotten away way too long with babbling in posts versus doing mathematics.

You show no respect whatsoever for proof and instead are lead around like dumb cows by ANY reply from people like Rupert or Magidin without paying attention to their errors or avoidance of the obvious.

If Rupert posted 1+1=3, you'd probably be right there cheering him on talking about how great it was, and respond with derision if I pointed out that 1+1=2.

Oh and yes, in case you people are too dumb to get it, your behavior with absolute proof is useful for political operators who yes, do wish to know how to get away with not telling the truth or ignoring the obvious in their better understanding of how to manipulate large groups of supposedly highly intelligent people.

So the rest of your crime is in helping people like George W. Bush understand how to keep power no matter what the truth is.

And you people give everything away, including your credibility as mathematicians, for what?

Nothing. You're giving it away for absolutely nothing in return, which is the lesson for real political players.

The best way to really win is to make sure you give your patsies nothing in return, as rather than acknowledge they've been completely taken for nothing, they will make up their own rewards.

They'll do all the work to convince themselves they are getting something.

NONE of you noticed that Bush's rise has been coincident with my arguments with you knuckleheads?

[A reply to someone who told James that he and Bush “are both symptoms of the sorry state of the nation”.]

Bush is even brainstorming now, which at least is a good thing.

Some of you must have noticed similarities between what you could see on the newsgroup and political machinations different than at any other time in US history.

But of course you will simply explain it all away versus considering that by being recalcitrant and resistant to mathematical proof you provide a roadmap for how politicians can, well, rule the world.

[A reply of James to his own assertion that “both 2f(x) and 2g(x) are algebraic integers”.]

Well I've thought about that and it should be correct but some posters are saying it's not, so I'll switch from brainstorming to critiquing.

For those who don't know I practice what I call extreme mathematics, which involves a creative brainstorming phase followed by a critiquing phase.

During brainstorming ideas are tossed out with little consideration for correctness as idea generation is the aim.

Now then I have asserted that with

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

it works to use

2f(x) = 5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

and

2g(x) = 5((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

So I guess I'll multiply that out. To make it a little easier I'll shift to

350x^2 - 30x + 6 = (2f(x) + 2)*(2g(x) + 2)

so

350x^2 - 30x + 6 = (5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5 + 2)*(5((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5 + 2)

Which is

1400x^2 - 120x + 24 = (5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x)) + 14)*(5((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x))+14)

which is

1400x^2 - 120x + 24 = (35x + 9 +/- 5sqrt((7x-1)^2 - 4(49x^2 - 14x)))*(35x + 9 -/+ 5sqrt((7x-1)^2 - 4(49x^2 - 14x)))

which is

1400x^2 - 120x + 24 = ((35x + 9)^2 - 25((7x-1)^2 - 4(49x^2 - 14x)))

which is

1400x^2 - 120x + 24 = ((35x + 9)^2 - 25(49x^2 - 14x + 1 - 196x^2 + 56x))

which is

1400x^2 - 120x + 24 = ((35x + 9)^2 - 25(-147x^2 + 42x + 1))

which is

1400x^2 - 120x + 24 = ((35x + 9)^2 - 25(-147x^2 + 42x + 1))

and I can already see they don't match, but continuing on the right:

Q(x) = (1225x^2 + 630x + 81 + 3675x^2 - 1050x - 25)

so I finally have

Q(x) = 4900x^2 - 420x + 56 = 7(700x^2 - 60x + 8)

so that idea failed. One thing is interesting though, as the two solutions for f(x) plus one multiply together to give 7 itself as a factor.

So using f(x) and f*(x) as the conjugate, I have that with integer x,

(f(x)+1)*(f*(x)+1)

is an integer with 7 itself as a factor.

But the original idea failed so it's back to brainstorming!

Some may wonder about a delay in my checking ideas, which is about me letting other people check them so I save time. During brainstorming I do little if any checking but toss the ideas out there and often some other person will go and check for me.

[Another reply of James to himself, this time to his assertion that “350x^2 - 30x + 6 = (2f(x) + 2)*(2g(x) + 2)”.]

Oh, inexplicably at this point I put 6 instead of 4.

Fix that then there are only extra factors of 2, as 2f(x) + 2 is just 5a_1(x) + 7, so I just went in a Big Freaking Circle.

Oh well, at least now it all makes sense. So though

2f(x) = 5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

I can't just say that 2g(x) is the conjugate, as that gives a wrong answer with the sides not matching up because of factors of 2.

But it's still true that g(x) and f(x) should be indistinguishable, unless I'm missing something.

More brainstorming needed!!!

Consider

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

in an integral domain, where f(x) and g(x) are functions I'll soon give.

With

a_1(x) = ((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2

it can be shown that

2f(x) = 5a_1(x) + 5

so 2f(x) is an algebraic integer.

Solving then I have

2f(x) = 5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

and it follows that

2g(x) = 5((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

proving that both 2f(x) and 2g(x) are algebraic integers.

The solution for a_1(x) follows from it being a root of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

Using x=1, I have that the quadratic that follows is

a^2 - 6a + 35 = 0

which gives

a = 3 +/- sqrt(-26)

as the solutions that follow from the quadratic formula, where now it is clear that one solution has 7 as a factor, while the other does not, in the ring of algebraic integers.

But let a = 7z, and you have

49z^2 - 42a + 35 = 0

which is

7z^2 - 6a + 5 = 0

which is a non-monic primitive polynomial irreducible over Q, which has been shown to have on root that must be an algebraic integer.

This disproof of a previously widely held belief—if sci.math'ers are to be believed and you may notice I tested them on this all day—is remarkable for its conciseness and reliance on very elementary algebra.

Previous to this disproof, it seems some people wrongly believed that an algebraic integer could not be the root of a non-monic primitive polynomial irreducible over Q.

[A reply to someone who said that James should get a grip on his life an put it back on track.]

You people have gotten away way too long with babbling in posts versus doing mathematics.

You show no respect whatsoever for proof and instead are lead around like dumb cows by ANY reply from people like Rupert or Magidin without paying attention to their errors or avoidance of the obvious.

If Rupert posted 1+1=3, you'd probably be right there cheering him on talking about how great it was, and respond with derision if I pointed out that 1+1=2.

Oh and yes, in case you people are too dumb to get it, your behavior with absolute proof is useful for political operators who yes, do wish to know how to get away with not telling the truth or ignoring the obvious in their better understanding of how to manipulate large groups of supposedly highly intelligent people.

So the rest of your crime is in helping people like George W. Bush understand how to keep power no matter what the truth is.

And you people give everything away, including your credibility as mathematicians, for what?

Nothing. You're giving it away for absolutely nothing in return, which is the lesson for real political players.

The best way to really win is to make sure you give your patsies nothing in return, as rather than acknowledge they've been completely taken for nothing, they will make up their own rewards.

They'll do all the work to convince themselves they are getting something.

NONE of you noticed that Bush's rise has been coincident with my arguments with you knuckleheads?

[A reply to someone who told James that he and Bush “are both symptoms of the sorry state of the nation”.]

Bush is even brainstorming now, which at least is a good thing.

Some of you must have noticed similarities between what you could see on the newsgroup and political machinations different than at any other time in US history.

But of course you will simply explain it all away versus considering that by being recalcitrant and resistant to mathematical proof you provide a roadmap for how politicians can, well, rule the world.

[A reply of James to his own assertion that “both 2f(x) and 2g(x) are algebraic integers”.]

Well I've thought about that and it should be correct but some posters are saying it's not, so I'll switch from brainstorming to critiquing.

For those who don't know I practice what I call extreme mathematics, which involves a creative brainstorming phase followed by a critiquing phase.

During brainstorming ideas are tossed out with little consideration for correctness as idea generation is the aim.

Now then I have asserted that with

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

it works to use

2f(x) = 5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

and

2g(x) = 5((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

So I guess I'll multiply that out. To make it a little easier I'll shift to

350x^2 - 30x + 6 = (2f(x) + 2)*(2g(x) + 2)

so

350x^2 - 30x + 6 = (5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5 + 2)*(5((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5 + 2)

Which is

1400x^2 - 120x + 24 = (5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x)) + 14)*(5((7x-1) -/+ sqrt((7x-1)^2 - 4(49x^2 - 14x))+14)

which is

1400x^2 - 120x + 24 = (35x + 9 +/- 5sqrt((7x-1)^2 - 4(49x^2 - 14x)))*(35x + 9 -/+ 5sqrt((7x-1)^2 - 4(49x^2 - 14x)))

which is

1400x^2 - 120x + 24 = ((35x + 9)^2 - 25((7x-1)^2 - 4(49x^2 - 14x)))

which is

1400x^2 - 120x + 24 = ((35x + 9)^2 - 25(49x^2 - 14x + 1 - 196x^2 + 56x))

which is

1400x^2 - 120x + 24 = ((35x + 9)^2 - 25(-147x^2 + 42x + 1))

which is

1400x^2 - 120x + 24 = ((35x + 9)^2 - 25(-147x^2 + 42x + 1))

and I can already see they don't match, but continuing on the right:

Q(x) = (1225x^2 + 630x + 81 + 3675x^2 - 1050x - 25)

so I finally have

Q(x) = 4900x^2 - 420x + 56 = 7(700x^2 - 60x + 8)

so that idea failed. One thing is interesting though, as the two solutions for f(x) plus one multiply together to give 7 itself as a factor.

So using f(x) and f*(x) as the conjugate, I have that with integer x,

(f(x)+1)*(f*(x)+1)

is an integer with 7 itself as a factor.

But the original idea failed so it's back to brainstorming!

Some may wonder about a delay in my checking ideas, which is about me letting other people check them so I save time. During brainstorming I do little if any checking but toss the ideas out there and often some other person will go and check for me.

[Another reply of James to himself, this time to his assertion that “350x^2 - 30x + 6 = (2f(x) + 2)*(2g(x) + 2)”.]

Oh, inexplicably at this point I put 6 instead of 4.

Fix that then there are only extra factors of 2, as 2f(x) + 2 is just 5a_1(x) + 7, so I just went in a Big Freaking Circle.

Oh well, at least now it all makes sense. So though

2f(x) = 5((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2 + 5

I can't just say that 2g(x) is the conjugate, as that gives a wrong answer with the sides not matching up because of factors of 2.

But it's still true that g(x) and f(x) should be indistinguishable, unless I'm missing something.

More brainstorming needed!!!

### Monday, December 18, 2006

## JSH: So why did they bother?

Why would posters who spent so much energy in post after post to convince other Usenet readers of false mathematics still keep at it now, as you can see in threads where I give the simple proof, and now there is a growing response of just continued ridicule?

Because they see themselves as brilliant, and see you as seeing them as brilliant, and they wish to keep that role.

So it's simple delusion.

For those of you who do not understand the complexities of how some people seek attention, just consider the Jerry Springer Show.

They are like performers on an episode of that show and will continue as long as they can convince themselves that you like them.

Yup, they want you to like them.

As long as they think you like them, they will continue to reply in my threads, carefully going around the simple mathematical proofs which would destroy their delusion and congratulate themselves as they get the attention of the world as my research draws the attention of the world.

So they are getting a lot of attention, at the expense of my research, where I can prove all these things simply but have a lot of hanger's on because they think you people love them.

Now going forward I can try to move more to the mainstream, like with my paper still currently under review at the Annals of Mathematics at Princeton, and I can think more about what to do with my latest, newly revised paper.

I used Usenet as a brainstorming area and ended up with a lot of parasites who can't quite get it that it's over, as it's not for them!

Look at them in those threads, wallowing in it with ever more glee, despite some very simple algebra proving they are wrong.

They want you to love them, and believe you do, from "Tim Peters" to "Rupert", to "William Hughes", and even David Ullrich, despite being a math professor, and Arturo Magidin.

They believe you love them, love their show, and that they are giving you, the readership of these newsgroups, what you want.

Because they see themselves as brilliant, and see you as seeing them as brilliant, and they wish to keep that role.

So it's simple delusion.

For those of you who do not understand the complexities of how some people seek attention, just consider the Jerry Springer Show.

They are like performers on an episode of that show and will continue as long as they can convince themselves that you like them.

Yup, they want you to like them.

As long as they think you like them, they will continue to reply in my threads, carefully going around the simple mathematical proofs which would destroy their delusion and congratulate themselves as they get the attention of the world as my research draws the attention of the world.

So they are getting a lot of attention, at the expense of my research, where I can prove all these things simply but have a lot of hanger's on because they think you people love them.

Now going forward I can try to move more to the mainstream, like with my paper still currently under review at the Annals of Mathematics at Princeton, and I can think more about what to do with my latest, newly revised paper.

I used Usenet as a brainstorming area and ended up with a lot of parasites who can't quite get it that it's over, as it's not for them!

Look at them in those threads, wallowing in it with ever more glee, despite some very simple algebra proving they are wrong.

They want you to love them, and believe you do, from "Tim Peters" to "Rupert", to "William Hughes", and even David Ullrich, despite being a math professor, and Arturo Magidin.

They believe you love them, love their show, and that they are giving you, the readership of these newsgroups, what you want.

## JSH: Deepening puzzle

It is NOT true that an algebraic integer cannot be the root of a non-monic polynomial with integer coefficients irreducible over Q.

Now I'm trying to figure out if the assertion that it is true is a sci.math only claim, or if it is a wrong belief that was held outside of Usenet before my research, which has since been adjusted as so far the strongest support of the sci.math'ers claim I've seen has been on the Wikipedia.

That changes a lot. An algebraic integer CAN be the root of a non-monic polynomial irreducible over Q.

So no, my results do not contradict with what follows from the ring of algebraic integers, as the argument is valid within that ring.

One argument claimed to be a proof of the false assertion that I saw years ago that convinced me is broken just by noting that an algebraic integer root of a non-monic polynomial irreducible over Q, can be the root of some monic polynomial with integer coefficients of higher degree.

So now I'm trying to figure out what exactly is the big deal with my original argument, and in retrospect it was the poster Rupert who first made the assertion that I now point out is false, and in considering that poster's recent replies, like how he has made some wackily wrong mathematical statements in recent posts attacking a simplified proof with my non polynomial factorization research, it occurs to me that he may have some serious issues, if you know what I mean.

Was this all some sick sci.math game?

Other replies I've seen from posters raise the possibility of simple jealousy and spite possibly with some kind of weird sense of superiority felt from managing to convince me of some wrong mathematical ideas.

Whatever the reasons they are probably going to be nasty, low and mean.

In any event, again, it is NOT true that an algebraic integer cannot be the root of a non-monic polynomial irreducible over Q, and I doubt you'd find a decent mathematician who would claim it is true, while I cite my amateur status and gullibility as reasons for how I was convinced.

Now I'm trying to figure out if the assertion that it is true is a sci.math only claim, or if it is a wrong belief that was held outside of Usenet before my research, which has since been adjusted as so far the strongest support of the sci.math'ers claim I've seen has been on the Wikipedia.

That changes a lot. An algebraic integer CAN be the root of a non-monic polynomial irreducible over Q.

So no, my results do not contradict with what follows from the ring of algebraic integers, as the argument is valid within that ring.

One argument claimed to be a proof of the false assertion that I saw years ago that convinced me is broken just by noting that an algebraic integer root of a non-monic polynomial irreducible over Q, can be the root of some monic polynomial with integer coefficients of higher degree.

So now I'm trying to figure out what exactly is the big deal with my original argument, and in retrospect it was the poster Rupert who first made the assertion that I now point out is false, and in considering that poster's recent replies, like how he has made some wackily wrong mathematical statements in recent posts attacking a simplified proof with my non polynomial factorization research, it occurs to me that he may have some serious issues, if you know what I mean.

Was this all some sick sci.math game?

Other replies I've seen from posters raise the possibility of simple jealousy and spite possibly with some kind of weird sense of superiority felt from managing to convince me of some wrong mathematical ideas.

Whatever the reasons they are probably going to be nasty, low and mean.

In any event, again, it is NOT true that an algebraic integer cannot be the root of a non-monic polynomial irreducible over Q, and I doubt you'd find a decent mathematician who would claim it is true, while I cite my amateur status and gullibility as reasons for how I was convinced.

## JSH: Good news and bad news

I was going over my latest very simple proof and realized that it required that both f(x) and g(x) in my key factorization be algebraic integers.

That's the good news.

I am re-thinking my belief that the ring of algebraic integers is flawed.

Now the bad news.

The argument is correct and then shows that in the ring of algebraic integers, for instance,

3 + sqrt(-26)

has one solution that has 7 as a factor in that ring, while the other does not.

Now I accepted claims that there is a proof that a non-monic polynomial irreducible over Q cannot have an algebraic integer as a root, and the bad news is that cannot be a proof.

So the impact over number theory is probably just as big, but it seems the issue is more subtle than I realized.

I want someone to post again the argument claiming that a non-monic polynomial irreducible over Q cannot have an algebraic integer as a factor.

The key to breaking that argument is considering unit factors.

Oh, I'm kind of surprised none of you noticed that the latest argument I have actually does require that both f(x) and g(x) be algebraic integers.

I did and puzzled over that for a while. Back to brainstorming! Might get a bit messy now.

That's the good news.

I am re-thinking my belief that the ring of algebraic integers is flawed.

Now the bad news.

The argument is correct and then shows that in the ring of algebraic integers, for instance,

3 + sqrt(-26)

has one solution that has 7 as a factor in that ring, while the other does not.

Now I accepted claims that there is a proof that a non-monic polynomial irreducible over Q cannot have an algebraic integer as a root, and the bad news is that cannot be a proof.

So the impact over number theory is probably just as big, but it seems the issue is more subtle than I realized.

I want someone to post again the argument claiming that a non-monic polynomial irreducible over Q cannot have an algebraic integer as a factor.

The key to breaking that argument is considering unit factors.

Oh, I'm kind of surprised none of you noticed that the latest argument I have actually does require that both f(x) and g(x) be algebraic integers.

I did and puzzled over that for a while. Back to brainstorming! Might get a bit messy now.

### Sunday, December 17, 2006

## JSH: Least to lose?

I have a problem. While mathematicians I contact directly with my research don't call me names and insult me, they tend to run away from my results all the same. Yet you can look in recent threads and see how easy the mathematics is.

Trouble is, it wrecks the sense of self and belief in accomplishment of just about any modern mathematician, so I'm stuck with important and revolutionary results that are being blocked by simple human weakness.

I need to identify a group of people smart enough to understand the mathematics who do not have as much to lose as most mathematicians, or this thing could go on indefinitely.

One way to look at it is, most people accept that in our modern age we know many things that people in the past got wrong, from medicine to physics to even sports training, over time our species has learned corrections to past mistakes.

For some reason mathematicians decided their field was different, yet I found a mistake made over a hundred years ago. Other fields accepted changes, like surgeons now know they need to be very clean before surgeries when a hundred years ago is was considered a bad thing.

But mathematicians decided that previous mathematicians got it all right, and now with simple proofs that they too made mistakes, the denial is just about impenetrable.

I need to know of a group smart enough to understand the mathematics which is not as invested in the wrong ideas to get this thing going forward, and I haven't identified such a group yet so I'm throwing this out there in the hopes some of you might know of one.

I have the papers already written up, so it's not like there's anything to do but identify and distribute, knowing there will then be a hell storm to go through as mathematicians whose egos are shattered do just about anything but accept what is mathematically correct in what must be to them the worst possible thing on this earth. A nightmare they will fight for as long as they can even though they are mathematically incorrect in doing so.

Trouble is, it wrecks the sense of self and belief in accomplishment of just about any modern mathematician, so I'm stuck with important and revolutionary results that are being blocked by simple human weakness.

I need to identify a group of people smart enough to understand the mathematics who do not have as much to lose as most mathematicians, or this thing could go on indefinitely.

One way to look at it is, most people accept that in our modern age we know many things that people in the past got wrong, from medicine to physics to even sports training, over time our species has learned corrections to past mistakes.

For some reason mathematicians decided their field was different, yet I found a mistake made over a hundred years ago. Other fields accepted changes, like surgeons now know they need to be very clean before surgeries when a hundred years ago is was considered a bad thing.

But mathematicians decided that previous mathematicians got it all right, and now with simple proofs that they too made mistakes, the denial is just about impenetrable.

I need to know of a group smart enough to understand the mathematics which is not as invested in the wrong ideas to get this thing going forward, and I haven't identified such a group yet so I'm throwing this out there in the hopes some of you might know of one.

I have the papers already written up, so it's not like there's anything to do but identify and distribute, knowing there will then be a hell storm to go through as mathematicians whose egos are shattered do just about anything but accept what is mathematically correct in what must be to them the worst possible thing on this earth. A nightmare they will fight for as long as they can even though they are mathematically incorrect in doing so.

### Saturday, December 16, 2006

## Algebraic integers is a flawed ring

Excerpts taken from the math blog with some editing for size and clarity.

Simple algebra shows ring of algebraic integers is critically flawed by revealing factors blocked by special definition of ring. Significant error which has to be addressed by the mathematical community but it is not clear who has the nerve or the will to do anything about it.

Start with

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

with functions f(x) and g(x), and an integral domain with more to be specified later.

Choose to multiply through f(x) + 1 by 2 and multiply both sides by 7:

7*(175x^2 - 15x + 2) = 7*(2f(x) + 2)*(g(x) + 1)

note that the above is equivalent to

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2 = (2f(x) + 2)*(7g(x) + 7)

where 7 has been distributed through g(x) + 1.

Now introduce additional functions a_1(x) and a_2(x), and let

2f(x) = 5a_1(x) + 5

and

7g(x) = 5a_2(x)

make the substitutions:

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2 = (5a_1(x) + 7)*(5a_2(x) + 7)

solve for the a's using

a_1(x)*a_2(x) = 49x^2 - 14x

and

a_1(x) + a_2(x) = 7x-1

so it follows they are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

And that second quadratic gives the critical result.

For instance, let x=1, then

a^2 - 6a + 35 = 0

and

7g(1) = 5a_2(1)

would seem to indicate that a_2(1) has 7 as a factor, but so far it is only specified (as I added to the original argument from the blog above) that the domain is integral. But go to the ring of algebraic integers and it can be shown that 7 is not a factor of a_2(x) in that ring.

That is the back breaker result. The arbitrariness of the selection of g(x) to be multiplied by 7, completes the simple proof as you could have gone the other way:

175x^2 - 15x + 2 = (f(x) + 1)*(2g(x) + 2)

to get the same equation for the a's, but now with

7f(x) = 5a_2(x)

so now f(x) would also need to divide off factors from 7. QED

The argument with evens and odds is remarkably succinct in explaining the result.

What follows is just taken from the blog with very limited editing:

Well think if you wish to have only evens. Now consider that 2 is now not a factor of 6 as that will give you the odd 3, so just like that, with an arbitrary rule that excludes some numbers you get a result counter to what you know, as 2 is a factor of 6.

With algebraic integers, the rule is that an algebraic integer must be the root of some monic polynomial with integer coefficients, and the algebra above proves that some numbers are excluded by that rule so you get the odd result.

But now let's solve for the a's with x=1, as using the quadratic formula with

a^2 - 6a + 35 = 0

gives

a = 3 +/- sqrt(-26)

and you may wonder, which root has 7 as a factor?

The answer is, one root but it's ambiguous as to which as the sqrt() gives two answers while many of you may think that you can say that 3 + sqrt(-26) is one number while 3 - sqrt(-26) is another, but consider

1 + sqrt(4)

and if you say that's 3, well, what about -2? In the mathematical world I live in

(-2)(-2) = 4

so that is two solutions which can be represented as

1 +/- 2

and this may seem like a boring exercise given the importance of what I have above, but a lot of people are taught wrong on this point, and it's worth pointing out that when you have sqrt(), you have two numbers, no matter what.

Some math people will say that, no, they have one number as they have DEFINED the square root to be only the positive and they will also claim they can find a factor of 3 + sqrt(-26) in the ring of algebraic integers, so I'm wrong and there is nothing wrong with what they do.

But check this out:

(1 +/- 2)(3 +/- 2) = (7 +/- 8)

so you can do algebra with functions that have two values and even find factors that way, without it changing a thing.

(An interesting way to show the flaw in some objections I've noted from posters who seem to be taken seriously—though I don't know why—by readers on these newsgroups.)

Oddly enough though mathematicians got it wrong!

Some time ago some of them decided they didn't like functions that gave more than one answer so they defined sqrt() to have only one solution. But that couldn't get rid of the other solution! So -2 is still a solution to sqrt(4) as (-2)(-2) = 4, but math students learn to think it's not a solution to the square root function because it is defined not to be. That weird little error has consequences, as you have generations of people who think that 1+sqrt(2) is a single number different from 1-sqrt(2) when both actually give the same two numbers—just in different order.

Like

1+/-2 versus 1-/+2

as the first way gives 3 and -1, while the second gives -1 and 3.

So it's not hard to understand what is happening mathematically, and easy to prove a problem with the ring of algebraic integers, while also pointing out a weird thinking error with square roots which currently plagues a lot of people.

Want a paper? Then go to my page on this at my Extreme Mathematics group:

http://groups-beta.google.com/group/extrememathematics/web/non-polynomial-factorization-paper

Simple algebra shows ring of algebraic integers is critically flawed by revealing factors blocked by special definition of ring. Significant error which has to be addressed by the mathematical community but it is not clear who has the nerve or the will to do anything about it.

Start with

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

with functions f(x) and g(x), and an integral domain with more to be specified later.

Choose to multiply through f(x) + 1 by 2 and multiply both sides by 7:

7*(175x^2 - 15x + 2) = 7*(2f(x) + 2)*(g(x) + 1)

note that the above is equivalent to

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2 = (2f(x) + 2)*(7g(x) + 7)

where 7 has been distributed through g(x) + 1.

Now introduce additional functions a_1(x) and a_2(x), and let

2f(x) = 5a_1(x) + 5

and

7g(x) = 5a_2(x)

make the substitutions:

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2 = (5a_1(x) + 7)*(5a_2(x) + 7)

solve for the a's using

a_1(x)*a_2(x) = 49x^2 - 14x

and

a_1(x) + a_2(x) = 7x-1

so it follows they are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

And that second quadratic gives the critical result.

For instance, let x=1, then

a^2 - 6a + 35 = 0

and

7g(1) = 5a_2(1)

would seem to indicate that a_2(1) has 7 as a factor, but so far it is only specified (as I added to the original argument from the blog above) that the domain is integral. But go to the ring of algebraic integers and it can be shown that 7 is not a factor of a_2(x) in that ring.

That is the back breaker result. The arbitrariness of the selection of g(x) to be multiplied by 7, completes the simple proof as you could have gone the other way:

175x^2 - 15x + 2 = (f(x) + 1)*(2g(x) + 2)

to get the same equation for the a's, but now with

7f(x) = 5a_2(x)

so now f(x) would also need to divide off factors from 7. QED

The argument with evens and odds is remarkably succinct in explaining the result.

What follows is just taken from the blog with very limited editing:

Well think if you wish to have only evens. Now consider that 2 is now not a factor of 6 as that will give you the odd 3, so just like that, with an arbitrary rule that excludes some numbers you get a result counter to what you know, as 2 is a factor of 6.

With algebraic integers, the rule is that an algebraic integer must be the root of some monic polynomial with integer coefficients, and the algebra above proves that some numbers are excluded by that rule so you get the odd result.

But now let's solve for the a's with x=1, as using the quadratic formula with

a^2 - 6a + 35 = 0

gives

a = 3 +/- sqrt(-26)

and you may wonder, which root has 7 as a factor?

The answer is, one root but it's ambiguous as to which as the sqrt() gives two answers while many of you may think that you can say that 3 + sqrt(-26) is one number while 3 - sqrt(-26) is another, but consider

1 + sqrt(4)

and if you say that's 3, well, what about -2? In the mathematical world I live in

(-2)(-2) = 4

so that is two solutions which can be represented as

1 +/- 2

and this may seem like a boring exercise given the importance of what I have above, but a lot of people are taught wrong on this point, and it's worth pointing out that when you have sqrt(), you have two numbers, no matter what.

Some math people will say that, no, they have one number as they have DEFINED the square root to be only the positive and they will also claim they can find a factor of 3 + sqrt(-26) in the ring of algebraic integers, so I'm wrong and there is nothing wrong with what they do.

But check this out:

(1 +/- 2)(3 +/- 2) = (7 +/- 8)

so you can do algebra with functions that have two values and even find factors that way, without it changing a thing.

(An interesting way to show the flaw in some objections I've noted from posters who seem to be taken seriously—though I don't know why—by readers on these newsgroups.)

Oddly enough though mathematicians got it wrong!

Some time ago some of them decided they didn't like functions that gave more than one answer so they defined sqrt() to have only one solution. But that couldn't get rid of the other solution! So -2 is still a solution to sqrt(4) as (-2)(-2) = 4, but math students learn to think it's not a solution to the square root function because it is defined not to be. That weird little error has consequences, as you have generations of people who think that 1+sqrt(2) is a single number different from 1-sqrt(2) when both actually give the same two numbers—just in different order.

Like

1+/-2 versus 1-/+2

as the first way gives 3 and -1, while the second gives -1 and 3.

So it's not hard to understand what is happening mathematically, and easy to prove a problem with the ring of algebraic integers, while also pointing out a weird thinking error with square roots which currently plagues a lot of people.

Want a paper? Then go to my page on this at my Extreme Mathematics group:

http://groups-beta.google.com/group/extrememathematics/web/non-polynomial-factorization-paper

### Saturday, December 09, 2006

## JSH: Why would they tell the truth?

Ok, here's a different tack as I probe the mystery of resistance to the mathematical proofs I have on this newsgroup.

Let's say I were right, how would you know it? Would it be from poster's replies in agreement?

Or would it be from lack of objections?

If these results are correct and seriously impact results thought to have been proven such that mathematicians now considered tops in the field lose their major results, why would they tell the truth?

Do you think they would?

If I managed to contact Andrew Wiles and he followed the argument and agreed with it, and then concluded that it meant he did not find a proof of Fermat's Last Theorem, do you think he'd announce that or just quietly consider it?

Let's say I were right, how would you know it? Would it be from poster's replies in agreement?

Or would it be from lack of objections?

If these results are correct and seriously impact results thought to have been proven such that mathematicians now considered tops in the field lose their major results, why would they tell the truth?

Do you think they would?

If I managed to contact Andrew Wiles and he followed the argument and agreed with it, and then concluded that it meant he did not find a proof of Fermat's Last Theorem, do you think he'd announce that or just quietly consider it?

## JSH: Short explanation, why error is so big

I want to give a short post so that you can quickly understand what all the latest arguing about, but it looks like to cover everything it will be a bit long, but you need to have enough information to understand why this seemingly minor result could have such a huge impact, such that, for instance, it can tell you immediately that Andrew Wiles did not prove Fermat's Last Theorem, which then explains my concern for him and other leading mathematicians seriously impacted by the error.

I start with a factorization:

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

multiply by 7

7*(175x^2 - 15x + 2) = 7*(f(x) + 2)*(g(x) + 1)

re-order in a special way on the left side and pick one way to multiply through by 7 on the right:

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2 = (f(x) + 2)*(7g(x) + 7)

next I introduce new functions that I call the a's where

f(x) = 5a_1(x) + 5

and

7g(x) =5a_2(x)

substitute to get

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 49 = (5a_1(x) + 7)*(5a_2(x) + 7)

allowing me to find a solution of the a's where they are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

Well you can clearly see

7g(x) = 5a_2(x)

so it seems reasonable to think that 7 is a factor of a_2(x), but if you stick in some numbers, like x=1, you find that NEITHER of the a's can have 7 as a factor in the ring of algebraic integers.

The ring of algebraic integers is defined to be made up of numbers that are roots of monic polynomials with integer coefficients, and it will not allow just one of the a's to have 7 as a factor.

I say that is a flaw to the ring and that may seem odd, but think about, well, odds and evens, and if you only take evens then 2 is not a factor of 6, right? It's not because 3 is not even, so if you have a rule to only take evens then you can't divide 2 from 6 because that will give you an odd.

Similarly, the ring of algebraic integers excludes some numbers, like the odds are excluded with evens so you can get weird results, but a lot of modern mathematics was built on the idea that it means that neither of the a's has 7 as a factor, which means that with

7g(x) = 5a_2(x)

some factors of 7 would be divided off by g(x), like if w_1(x)*w_2(x) = 7, and you have

g(x) = c(x)/w_1(x)

then

7c(x)/w_1(x) = 5a_2(x)

would explain how a_2(x) does not have 7 as a factor in the ring of algebraic integers.

But now g(x) is like a fraction with g(x) = c(x)/w_1(x), but going back to

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

that would mean g(x) is different from f(x), because

f(x) = 5a_1(x) + 5

so f(x) cannot be like a fraction, so anyone arguing with this approach now need f(x) and g(x) to be distinct in this special way.

But I noticed that you can just move a factor of 2 around with

175x^2 - 15x + 2 = (f(x)/2 + 1)*(2*g(x) + 2)

and re-do the same analysis and get the same answer, which now would force f(x)/2 to be like a fraction, with some factor of 7 in the denominator, so don't let that 2 in the denominator throw you off.

Now that should end all debate as it's clear that the 2 can be moved around as described, but you can look in recent threads to see posters still arguing about it, and me talking about protecting leading mathematicians from the impact of the result.

So how could something this trivial looking be so big?

Well, mathematicians over a hundred years ago when algebraic integers were discovered, thought that what was true with algebraic integers was true in general, so to them 7 is NOT a factor of a_2(x), and somehow the 7 is getting split up, and they built mathematical ideas they thought were proofs on the flawed belief.

May not seem like a big deal, but that was over a hundred years ago.

Math people built on what came before, so the error has had over a hundred years to snowball, so now it shadows much of number theory, and is more than big enough to take away the techniques used by Andrew Wiles in his attempt to prove Taniyama-Shimura.

Math is a special discipline in that even seemingly small mistakes can take everything away.

So the arguing is over denying the basic math you see in this post to deny the huge impact over a lot of famous mathematical works, and famous mathematical people.

It would be unfair to just let this sock people like Wiles at random, as at first the impact could be very huge, while time would help to heal the wounds, so leading mathematicians need to be around people who care about them and understand what is going on in the early phases, so that they get through the hardest period ok.

Understand now?

I know it's a lot but in the modern age with so many incredible things happening. I'd hope that some of you can just follow the math, realize the implications, and understand that all of this is for real.

[A reply to someone who asked James to provide a reference for this claim: “what is true with algebraic integers is true in general”.]

Ok, maybe I'm wrong. I've been told this by posters on math newsgroups, so let's check.

For the sake of argument, consider the result that whether or not an algebraic integer has some number as a factor in the ring of algebraic integers means nothing important mathematically.

Just like it doesn't matter that 2 is not a factor of 6 with evens because we know it is a factor of 6 as 6 = 2*3. So let's say that now, for the sake of argument, it is clear that the ring of algebraic integers and results in that ring don't matter.

Would that impact any arguments accepted as proofs in the mathematical field?

I start with a factorization:

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

multiply by 7

7*(175x^2 - 15x + 2) = 7*(f(x) + 2)*(g(x) + 1)

re-order in a special way on the left side and pick one way to multiply through by 7 on the right:

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2 = (f(x) + 2)*(7g(x) + 7)

next I introduce new functions that I call the a's where

f(x) = 5a_1(x) + 5

and

7g(x) =5a_2(x)

substitute to get

(49x^2 - 14x)5^2 + (7x-1)(7)(5) + 49 = (5a_1(x) + 7)*(5a_2(x) + 7)

allowing me to find a solution of the a's where they are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

Well you can clearly see

7g(x) = 5a_2(x)

so it seems reasonable to think that 7 is a factor of a_2(x), but if you stick in some numbers, like x=1, you find that NEITHER of the a's can have 7 as a factor in the ring of algebraic integers.

The ring of algebraic integers is defined to be made up of numbers that are roots of monic polynomials with integer coefficients, and it will not allow just one of the a's to have 7 as a factor.

I say that is a flaw to the ring and that may seem odd, but think about, well, odds and evens, and if you only take evens then 2 is not a factor of 6, right? It's not because 3 is not even, so if you have a rule to only take evens then you can't divide 2 from 6 because that will give you an odd.

Similarly, the ring of algebraic integers excludes some numbers, like the odds are excluded with evens so you can get weird results, but a lot of modern mathematics was built on the idea that it means that neither of the a's has 7 as a factor, which means that with

7g(x) = 5a_2(x)

some factors of 7 would be divided off by g(x), like if w_1(x)*w_2(x) = 7, and you have

g(x) = c(x)/w_1(x)

then

7c(x)/w_1(x) = 5a_2(x)

would explain how a_2(x) does not have 7 as a factor in the ring of algebraic integers.

But now g(x) is like a fraction with g(x) = c(x)/w_1(x), but going back to

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

that would mean g(x) is different from f(x), because

f(x) = 5a_1(x) + 5

so f(x) cannot be like a fraction, so anyone arguing with this approach now need f(x) and g(x) to be distinct in this special way.

But I noticed that you can just move a factor of 2 around with

175x^2 - 15x + 2 = (f(x)/2 + 1)*(2*g(x) + 2)

and re-do the same analysis and get the same answer, which now would force f(x)/2 to be like a fraction, with some factor of 7 in the denominator, so don't let that 2 in the denominator throw you off.

Now that should end all debate as it's clear that the 2 can be moved around as described, but you can look in recent threads to see posters still arguing about it, and me talking about protecting leading mathematicians from the impact of the result.

So how could something this trivial looking be so big?

Well, mathematicians over a hundred years ago when algebraic integers were discovered, thought that what was true with algebraic integers was true in general, so to them 7 is NOT a factor of a_2(x), and somehow the 7 is getting split up, and they built mathematical ideas they thought were proofs on the flawed belief.

May not seem like a big deal, but that was over a hundred years ago.

Math people built on what came before, so the error has had over a hundred years to snowball, so now it shadows much of number theory, and is more than big enough to take away the techniques used by Andrew Wiles in his attempt to prove Taniyama-Shimura.

Math is a special discipline in that even seemingly small mistakes can take everything away.

So the arguing is over denying the basic math you see in this post to deny the huge impact over a lot of famous mathematical works, and famous mathematical people.

It would be unfair to just let this sock people like Wiles at random, as at first the impact could be very huge, while time would help to heal the wounds, so leading mathematicians need to be around people who care about them and understand what is going on in the early phases, so that they get through the hardest period ok.

Understand now?

I know it's a lot but in the modern age with so many incredible things happening. I'd hope that some of you can just follow the math, realize the implications, and understand that all of this is for real.

[A reply to someone who asked James to provide a reference for this claim: “what is true with algebraic integers is true in general”.]

Ok, maybe I'm wrong. I've been told this by posters on math newsgroups, so let's check.

For the sake of argument, consider the result that whether or not an algebraic integer has some number as a factor in the ring of algebraic integers means nothing important mathematically.

Just like it doesn't matter that 2 is not a factor of 6 with evens because we know it is a factor of 6 as 6 = 2*3. So let's say that now, for the sake of argument, it is clear that the ring of algebraic integers and results in that ring don't matter.

Would that impact any arguments accepted as proofs in the mathematical field?

## JSH: One mystery remains

I want to know why any of you would think that I am wrong at this point.

This is very important.

Why would any of you given what has happened from the publication in the math journal, to my having this neat prime counting function find, to a very simple explanation with a second proof that removes any mathematical doubt about my research, think I'm wrong?

Or if you don't think any of that is true, why not?

Why do you think people argue with me all the time when it's usually the same people replying to similar arguments over a period of literally years?

How do you explain all of that thinking I am wrong?

What do you think is actually going on here?

Your answers are very important.

I need to know how you are thinking here.

[A reply to someone who said that if James has the intention of convincing anyone that he knows what he is doing, then he must challenge himself to learn the language of proofs.]

Groupthink.

One of the most important events for me was getting to talk to a leading mathematician at my alma mater Vanderbilt University where I could hash it all out on the chalkboard, which was done at his request.

I drove over four hours from Atlanta at his request so that I could explain it in person—on the chalkboard.

Only took a couple of hours and we were in agreement on all of the major points, but inexplicably to me, he just went home and sent me an email later about how much he had enjoyed the conversation!

In reply I went off on him, and yup, I guess I ranted a bit as I could not comprehend how I could explain every point, get agreement on the math, and him just go on about his business like nothing.

Oh yeah, he did say I lacked "polish" which goes back to that learn the lingo thing, but when a mathematician can understand what I'm saying and follow the math, then "polish" is really just about style, now isn't it?

And why in the modern math world is style so much more important than anything else, even proof?

Or even publication?

So AFTER I had that drive to Nashville and that conversation, and the long drive back home wondering what in the hell had happened that I could explain, get agreement and then nothing, I kept at sending my paper to journals and SWJPAM published!!!

I thought it was finally over.

But the sci.math newsgroup erupted, as publication meant NOTHING to them.

NOTHING.

Publication in a peer reviewed math journal meant absolutely NOTHING to sci.math'ers.

There is no way to convince you people, as groupthink rules you.

Nothing means anything to you, not stepped through proof, not publication, not knowing that the hammer is about to fall as I have nice simple explanations and am back to writing papers.

Even knowing that the hammer will fall this time, and that you can't get away again with bushwhacking a journal to get a paper censored, you people blissfully chant nonsense, as if the real world doesn't exist.

But it does. And in the real world, publication does mean something. Proof does matter, and though it can take a while to convince people, once they are convinced, they act.

[A reply to someone who said that the fact that James' paper was accepted shows that the journal's reviewing was inadequate.]

Well either this newsgroup will get down on its knees and beg for forgiveness for destroying that journal or sci.math will cease to exist.

Some of you Usenetters forget that you get to post for free because a lot of other people are paying the bills.

Seems to me that sci.math is giving a lot of reason to re-think the current system.

Gotcha.

You people just don't think far enough ahead.

Part of the endgame is not only the end of sci.math but changing all of Usenet.

Free is not always good.

This is very important.

Why would any of you given what has happened from the publication in the math journal, to my having this neat prime counting function find, to a very simple explanation with a second proof that removes any mathematical doubt about my research, think I'm wrong?

Or if you don't think any of that is true, why not?

Why do you think people argue with me all the time when it's usually the same people replying to similar arguments over a period of literally years?

How do you explain all of that thinking I am wrong?

What do you think is actually going on here?

Your answers are very important.

I need to know how you are thinking here.

[A reply to someone who said that if James has the intention of convincing anyone that he knows what he is doing, then he must challenge himself to learn the language of proofs.]

Groupthink.

One of the most important events for me was getting to talk to a leading mathematician at my alma mater Vanderbilt University where I could hash it all out on the chalkboard, which was done at his request.

I drove over four hours from Atlanta at his request so that I could explain it in person—on the chalkboard.

Only took a couple of hours and we were in agreement on all of the major points, but inexplicably to me, he just went home and sent me an email later about how much he had enjoyed the conversation!

In reply I went off on him, and yup, I guess I ranted a bit as I could not comprehend how I could explain every point, get agreement on the math, and him just go on about his business like nothing.

Oh yeah, he did say I lacked "polish" which goes back to that learn the lingo thing, but when a mathematician can understand what I'm saying and follow the math, then "polish" is really just about style, now isn't it?

And why in the modern math world is style so much more important than anything else, even proof?

Or even publication?

So AFTER I had that drive to Nashville and that conversation, and the long drive back home wondering what in the hell had happened that I could explain, get agreement and then nothing, I kept at sending my paper to journals and SWJPAM published!!!

I thought it was finally over.

But the sci.math newsgroup erupted, as publication meant NOTHING to them.

NOTHING.

Publication in a peer reviewed math journal meant absolutely NOTHING to sci.math'ers.

There is no way to convince you people, as groupthink rules you.

Nothing means anything to you, not stepped through proof, not publication, not knowing that the hammer is about to fall as I have nice simple explanations and am back to writing papers.

Even knowing that the hammer will fall this time, and that you can't get away again with bushwhacking a journal to get a paper censored, you people blissfully chant nonsense, as if the real world doesn't exist.

But it does. And in the real world, publication does mean something. Proof does matter, and though it can take a while to convince people, once they are convinced, they act.

[A reply to someone who said that the fact that James' paper was accepted shows that the journal's reviewing was inadequate.]

Well either this newsgroup will get down on its knees and beg for forgiveness for destroying that journal or sci.math will cease to exist.

Some of you Usenetters forget that you get to post for free because a lot of other people are paying the bills.

Seems to me that sci.math is giving a lot of reason to re-think the current system.

Gotcha.

You people just don't think far enough ahead.

Part of the endgame is not only the end of sci.math but changing all of Usenet.

Free is not always good.

## JSH: Simpler explanation important as to motive

So I figured out a little while back that I could start differently to prove my non-polynomial factorization result:

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

I went to quadratics for simplicity, and start with a very simple looking factorization.

BUT posters still kept objecting claiming that g(x) was somehow a fraction to handle the part in the method where I multiply it by 7, to keep claiming that old ideas were ok, despite the reality that 7 is not a factor in the ring of algebraic integers.

And then I realized that the 2 could be moved so I switched to

175x^2 - 15x + 2 = (g'(x) + 1)*(f'(x) + 2)

where

g'(x) = f(x)/2 and f'(x) = 2g(x)

and you get the same result, of course, where intriguingly the reason you can divide one factor by 2 while multiplying the other and still get algebraic integers is that the 175x^2 - 15x + 2 is always even when x is an integer.

Now that takes away the ability to claim that g(x) can be dramatically different from f(x) and ends any room whatsoever for even the appearance of a rational objection.

Yet there are posters still objecting, and posters still insulting me.

But the methods I use, which were checked by peer review by a math journal that used two reviewers, and where I have now find a second proof to take away any options for the appearance of rational disagreement, represent advancements on techniques for mathematical analysis.

So fighting them is fighting the progress of mathematics itself.

Yet the bulk of posters on this newsgroup remain uncaring while a few still get away with lying about the math and attacking the discoverer.

There is no way that can happen if you people actually cared about mathematics.

No way.

And importantly later I can show that clearly your motives were hostile when the question comes up about whether or not any of you were just confused or not sure about what you were doing.

You have to know exactly what you are doing, from Magidin, to Ullrich, to Hughes, to Rupert and the rest of you, where for Magidin and Ullrich, importantly, and people like them who are academics the most important consequence of your behavior here will be the end of your academic careers.

And no, Ullrich and Magidin, you do not have the option to stay quiet now and try to claim you just didn't pay attention. Your silence is an admission of guilt as well with math this simple.

And consequences—very important—will be making sure you never teach college students again.

There is no choice there at this point as the one question has been—are posters REALLY deliberately lying about important mathematics?

Confusion or not quite understanding was an explanation that I considered for years now as I've looked for simpler and simpler explanation of the primary results.

But with a math proof that removes all areas of confusion now out there, there is no room for that defense and now no doubt whatsoever that people like W. Dale Hall, Arturo Magidin, and David Ullrich are fighting mathematical results that are clear, obvious and supremely important.

W. Dale Hall and Magidin fought the results in emails and now by keeping quiet they can keep up the appearance that there is doubt, when if they were confused before, the simplest and most important thing to do now would be to apologize.

But I think they're waiting to see if anyone will realize the truth, and if it looks like no one will, they think they can just keep doing what they were doing.

So in case you were wondering, part of the reason for me to keep posting simpler and simpler explanations was to determine whether people were just confused or actually were deliberately acting against the discipline of mathematics.

If Magidin and Ullrich are deliberately attacking the discipline itself, then how can they be trusted with young minds?

175x^2 - 15x + 2 = (f(x) + 2)*(g(x) + 1)

I went to quadratics for simplicity, and start with a very simple looking factorization.

BUT posters still kept objecting claiming that g(x) was somehow a fraction to handle the part in the method where I multiply it by 7, to keep claiming that old ideas were ok, despite the reality that 7 is not a factor in the ring of algebraic integers.

And then I realized that the 2 could be moved so I switched to

175x^2 - 15x + 2 = (g'(x) + 1)*(f'(x) + 2)

where

g'(x) = f(x)/2 and f'(x) = 2g(x)

and you get the same result, of course, where intriguingly the reason you can divide one factor by 2 while multiplying the other and still get algebraic integers is that the 175x^2 - 15x + 2 is always even when x is an integer.

Now that takes away the ability to claim that g(x) can be dramatically different from f(x) and ends any room whatsoever for even the appearance of a rational objection.

Yet there are posters still objecting, and posters still insulting me.

But the methods I use, which were checked by peer review by a math journal that used two reviewers, and where I have now find a second proof to take away any options for the appearance of rational disagreement, represent advancements on techniques for mathematical analysis.

So fighting them is fighting the progress of mathematics itself.

Yet the bulk of posters on this newsgroup remain uncaring while a few still get away with lying about the math and attacking the discoverer.

There is no way that can happen if you people actually cared about mathematics.

No way.

And importantly later I can show that clearly your motives were hostile when the question comes up about whether or not any of you were just confused or not sure about what you were doing.

You have to know exactly what you are doing, from Magidin, to Ullrich, to Hughes, to Rupert and the rest of you, where for Magidin and Ullrich, importantly, and people like them who are academics the most important consequence of your behavior here will be the end of your academic careers.

And no, Ullrich and Magidin, you do not have the option to stay quiet now and try to claim you just didn't pay attention. Your silence is an admission of guilt as well with math this simple.

And consequences—very important—will be making sure you never teach college students again.

There is no choice there at this point as the one question has been—are posters REALLY deliberately lying about important mathematics?

Confusion or not quite understanding was an explanation that I considered for years now as I've looked for simpler and simpler explanation of the primary results.

But with a math proof that removes all areas of confusion now out there, there is no room for that defense and now no doubt whatsoever that people like W. Dale Hall, Arturo Magidin, and David Ullrich are fighting mathematical results that are clear, obvious and supremely important.

W. Dale Hall and Magidin fought the results in emails and now by keeping quiet they can keep up the appearance that there is doubt, when if they were confused before, the simplest and most important thing to do now would be to apologize.

But I think they're waiting to see if anyone will realize the truth, and if it looks like no one will, they think they can just keep doing what they were doing.

So in case you were wondering, part of the reason for me to keep posting simpler and simpler explanations was to determine whether people were just confused or actually were deliberately acting against the discipline of mathematics.

If Magidin and Ullrich are deliberately attacking the discipline itself, then how can they be trusted with young minds?

## JSH: Stupidity bothers me

There is already my paper on the prime counting function at the Annals of Mathematics.

Now I have a new paper outlining this incredibly simple approach that removes even the hint of an objection.

Defying these very basic mathematical ideas with such huge implications is just a way to hurt other people besides me.

Some of you may have noticed that I've emphasized that repeatedly.

Well, I need to protect myself.

Think about it.

The clock is ticking. What you do not know about people you may have admired and deified does not change the reality of what may soon be going through their minds.

Maybe some of you like "Rupert" and "William Hughes" wish them to die.

Ok then, but I'm stating up front that what you are doing now is a path to something you now know is a possible occurrence, so you can't claim denial later.

If any one of them commits suicide, then you people will be facing a harsh reality in the real world, for the rest of your lives.

Now I have a new paper outlining this incredibly simple approach that removes even the hint of an objection.

Defying these very basic mathematical ideas with such huge implications is just a way to hurt other people besides me.

Some of you may have noticed that I've emphasized that repeatedly.

Well, I need to protect myself.

Think about it.

The clock is ticking. What you do not know about people you may have admired and deified does not change the reality of what may soon be going through their minds.

Maybe some of you like "Rupert" and "William Hughes" wish them to die.

Ok then, but I'm stating up front that what you are doing now is a path to something you now know is a possible occurrence, so you can't claim denial later.

If any one of them commits suicide, then you people will be facing a harsh reality in the real world, for the rest of your lives.

### Friday, December 08, 2006

## JSH: Remember context

I've said a lot of things over the years but remember I was working at a difficult task where for a long time there was little room to think I would succeed and later after I succeeded I was facing tremendous denial from others, lots of abuse on the newsgroups, and my own self-doubts.

Besides 'talking trash' is in some ways part of extreme mathematics.

Kind of like a tool to keep yourself psyched up, and a lot of my posts were meant to be entertaining or just to blow off steam.

So remember context. Don't read too seriously into past posts of mine, especially about consequences.

A subtle error in number theory from over a hundred years ago is just so far out there that there is no rule book.

We are all in new territory here today.

Besides 'talking trash' is in some ways part of extreme mathematics.

Kind of like a tool to keep yourself psyched up, and a lot of my posts were meant to be entertaining or just to blow off steam.

So remember context. Don't read too seriously into past posts of mine, especially about consequences.

A subtle error in number theory from over a hundred years ago is just so far out there that there is no rule book.

We are all in new territory here today.

## JSH: Two proofs equals a lot of denial

So I had to find two proofs of the same problem, where the second proof had to be obvious in such a way that there was no room for anyone to find even the hint of an objection.

That's a lot to ask someone, but then again, the proofs show that much of what many of you may have cherished as brilliant mathematics is just wrong.

The theory of ideals goes and Galois Theory as many of you have been taught it, isn't quite right.

That's a lot to absorb.

But the wrong answer is to decide that you can't handle that truth, and figure if I were right then mathematicians in charge would tell the truth—even if it meant they were not as brilliant as they thought, and even if for some of them it might mean losing positions of high prestige.

I think this situation leaves the door open for a lot of finger pointing at who is supposed to do the right thing.

So, should Andrew Wiles, if he were to find out about all of this, come forward and step up to the world and say, hey, there was this incredible mistake made in the math field over a hundred years ago, long before anyone alive today was born, and um, it just so happens because of this mistake that only was just noticed by some, um, amateur math guy that people were calling a crackpot, I didn't prove Taniyma-Shimura and much of the accomplishments I think I have in mathematics are crap?

You people are very cruel if you expect the people currently at the top in the field by a strong opinion of the majority to come forward and do something like that.

It's just not a human thing for you to do to them.

In many ways, it's NOT THEIR FAULT.

The mistake entered the field after Gauss, and it kind of snow-balled over the years.

The mistake is not your fault—hiding it would be.

Hiding it would be a very big mistake.

Especially trying to hide it knowing that I'm the person you would have to out-think, and beat down the line, indefinitely, knowing that the day I pushed it through against a math community in denial would be the day the world would see you not as people caught up in a remarkable situation difficult for anyone—but as cons and frauds.

I am asking you to protect people like Wiles, Ribet, Taylor and all those others who had so many reasons to believe they were brilliant and right, who will have to live with learning they were wrong, and I am asking you not to say it is their responsibility to tell the truth here.

Some one of you needs to step up here.

Don't leave this on "leading mathematicians" who are getting the full kick in the gut as if you can just blame them later if this thing drags out while students keep getting taught wrong stuff!!!

Those students deserve better. The world deserves better.

This story can still be rather remarkable and kind of neat with some people, yes, having to live through some extreme disappointment.

But you people do not want to live with the disappointment you would feel later for denying easy mathematical proofs that show one of the most dramatic events in the history of mathematics, opening the door to a surge in mathematical knowledge about the fundamental properties of numbers, and who knows what else we could figure out?

Mathematics is the "queen of the sciences" for good reason.

There may have been a block to mathematical knowledge we can no more comprehend than cavemen could comprehend integral calculus that was just removed.

Over a hundred years with a subtle mistake that JUST recently got found out, opening the door to huge increases and leaps in knowledge that could be beyond our imaginations.

Your choice.

Keep fighting the math or go with it.

But you know the answer here, if you fight the math, go against mathematical proof, no matter what happens, you lose.

[A reply to someone who said that he didn't understand why James keeps trying to educate the nay sayers.]

Well, idealism has its price.

There are of course other factors.

If any of you really knew my place in history, and really understood just how big these results are, would you dare talk to me?

No. You wouldn't. But now, thinking that I am wrong and incapable of getting my research accepted unless I convince some nobodies on Usenet, you do.

I know what the future holds. You clearly do not.

That's a lot to ask someone, but then again, the proofs show that much of what many of you may have cherished as brilliant mathematics is just wrong.

The theory of ideals goes and Galois Theory as many of you have been taught it, isn't quite right.

That's a lot to absorb.

But the wrong answer is to decide that you can't handle that truth, and figure if I were right then mathematicians in charge would tell the truth—even if it meant they were not as brilliant as they thought, and even if for some of them it might mean losing positions of high prestige.

I think this situation leaves the door open for a lot of finger pointing at who is supposed to do the right thing.

So, should Andrew Wiles, if he were to find out about all of this, come forward and step up to the world and say, hey, there was this incredible mistake made in the math field over a hundred years ago, long before anyone alive today was born, and um, it just so happens because of this mistake that only was just noticed by some, um, amateur math guy that people were calling a crackpot, I didn't prove Taniyma-Shimura and much of the accomplishments I think I have in mathematics are crap?

You people are very cruel if you expect the people currently at the top in the field by a strong opinion of the majority to come forward and do something like that.

It's just not a human thing for you to do to them.

In many ways, it's NOT THEIR FAULT.

The mistake entered the field after Gauss, and it kind of snow-balled over the years.

The mistake is not your fault—hiding it would be.

Hiding it would be a very big mistake.

Especially trying to hide it knowing that I'm the person you would have to out-think, and beat down the line, indefinitely, knowing that the day I pushed it through against a math community in denial would be the day the world would see you not as people caught up in a remarkable situation difficult for anyone—but as cons and frauds.

I am asking you to protect people like Wiles, Ribet, Taylor and all those others who had so many reasons to believe they were brilliant and right, who will have to live with learning they were wrong, and I am asking you not to say it is their responsibility to tell the truth here.

Some one of you needs to step up here.

Don't leave this on "leading mathematicians" who are getting the full kick in the gut as if you can just blame them later if this thing drags out while students keep getting taught wrong stuff!!!

Those students deserve better. The world deserves better.

This story can still be rather remarkable and kind of neat with some people, yes, having to live through some extreme disappointment.

But you people do not want to live with the disappointment you would feel later for denying easy mathematical proofs that show one of the most dramatic events in the history of mathematics, opening the door to a surge in mathematical knowledge about the fundamental properties of numbers, and who knows what else we could figure out?

Mathematics is the "queen of the sciences" for good reason.

There may have been a block to mathematical knowledge we can no more comprehend than cavemen could comprehend integral calculus that was just removed.

Over a hundred years with a subtle mistake that JUST recently got found out, opening the door to huge increases and leaps in knowledge that could be beyond our imaginations.

Your choice.

Keep fighting the math or go with it.

But you know the answer here, if you fight the math, go against mathematical proof, no matter what happens, you lose.

[A reply to someone who said that he didn't understand why James keeps trying to educate the nay sayers.]

Well, idealism has its price.

There are of course other factors.

If any of you really knew my place in history, and really understood just how big these results are, would you dare talk to me?

No. You wouldn't. But now, thinking that I am wrong and incapable of getting my research accepted unless I convince some nobodies on Usenet, you do.

I know what the future holds. You clearly do not.