Sunday, May 13, 2007
Algebraic residues, dead math journal & fraud
Back in December of 1999 I came up with the idea of using identities that I call tautological spaces against the problem of Fermat's Last Theorem, as I'd run out of ways to manipulate the base equations, and was desperate.
So I realized, eventually—as even after the initial idea it took me a few years to get the right approach—that I could use
x^2 + y^2 +vz^2 = x^2 + y^2 + vz^2
where I'd write that as x^2 + y^2 + vz^2 = 0(mod x^2 + y^2 + vz^2), and I could do various algebraic manipulations and eventually subtract out
x^p + y^p = z^p
and analyze the algebraic residue, as remember, I subtracted from an IDENTITY, so all the properties of what was left that were of interest would come from the FLT equation itself, as there could be no other input, since the identity is always true—which is why I call it a tautological space.
So the brilliance of this approach is in recognizing that by using an identity I could get to an algebraic residue, where I could analyze that residue with a free variable that I could make whatever I wanted, and using this approach I could first force an integer requirement for x, y and z by picking a prime factor f, of x, and using
v = -1 (mod f)
where I figured out quickly that I needed v = -1 + mf^{2j}, where m is a non-zero integer, and j is a natural number, as then I could make
x^2 + y^2 + (-1 + mf^{2j)z^2 = 0 mod f^n
where n is an arbitrary counting number, so I had a way to get the mathematics focused on x, y and z being integers!!! And it REQUIRED using my free variable v, which I only had because I was working on an algebraic residue, as if x, y and z are not all integers, then you cannot get
x^2 + y^2 + (-1 + mf^{2j)z^2 = 0 mod f^n
and given that handle I could go all the way to the complete proof of Fermat's Last Theorem, and after celebrating a bit, I began talking it out on the sci.math newsgroup, where I really believed that I'd finally be welcomed for succeeding after so many failures, but little did I know that YEARS would pass, and along the way I'd learn a lot more about math society, and a mathematical journal would even die, quietly.
So I had, after years of searching, a dramatic and simple proof of Fermat's Last Theorem found by this new technique of analyzing the algebraic residue found from subtracting from a tautology and I'm expecting cheers from mathematicians but I ended up in more heated arguments!!!
Finally trying to be smart about the situation, I pulled out one piece of the full proof, and wrote a paper, and started sending it to math journals.
An early draft went to Barry Mazur at Harvard as I sought commentary and he actually replied, wishing me luck and asking about one section. I answered him but heard nothing further.
I sent a draft to Andrew Granville for publication in the New York Journal of Mathematics, and he claimed it was out of his area and referred it to the chief editor who replied back to me that the paper was too small for the journal!!!
Looking to bank on my status as an alumnus of Vanderbilt University I got hopeful when I saw a professor from my school's math department was an editor of a journal and sent it to him, a Ralph McKenzie. He claimed to not understand it, so I forwarded him Mazur's email. After that he suggested that next time I was in Nashville I should explain it all out on the chalkboard.
So I planned a trip!!! I told him I was driving up, and set up a time, and I drove back to my alma mater for the first time in over ten years, and met with my old physics adviser as well as with Professor McKenzie with whom I talked for several hours, and explained my paper.
Nothing came of that so I sent the paper to the Southwest Journal of Pure and Applied Mathematics (SWJPAM), and they accepted it for review, and eventually published it.
See: http://www.emis.de/journals/SWJPAM/
and
http://www.emis.de/journals/SWJPAM/vol2-03.html
But if you check those links you can see that the second says my paper was withdrawn, while the first talks about SWJPAM no longer being in operation.
What happened is that after my paper was published and I received more than one congratulatory email from the editors of SWJPAM, some person posted to the sci.math newsgroup that I was published, and the hate and fury that spewed out from that newsgroup was intense. They not only berated SWJPAM and its editors, maligning them repeatedly, but talked down the entire journal process, claiming that mathematical journals often publish in error.
Then some of them got the brilliant idea of emailing the editors claiming problems with my paper.
Their claims were ones I'd heard before before I ever sent the paper, which were easily resolved, but they have lied repeatedly about the mathematics in this area, and show no conscience nor regard for the truth.
I noted the posts conspiring to assault my paper by email and simply assumed that the formal peer review process would work, and if anything I'd just be questioned by the SWJPAM editors if they bothered to worry about emails from strange people asserting error.
But instead the chief editor immediately pulled my paper from the already published edition, and informed me by email that publication was a mistake and that he was going on sabbatical to Greece!!!
So not only were the rules not being followed, but I'd get no opportunity to answer.
The original paper can be found at my Extreme Mathematics group on a page that I have devoted to this story:
http://groups.google.com/group/extrememathematics/web/non-polynomial-factorization-paper
The equations in that paper are algebraic residues, though I don't explain that in the paper,. as it's not relevant to the proof.
What I did was take a slight variation on the FLT equation for p=3, and took the algebraic residue.
So what you now know is that the techniques I've talked about, using identities, what I call tautological spaces, with equation to get an algebraic residue, has had key portions formally peer reviewed.
Oh yeah, so after that capitulation to the sci.math newsgroup posters—who broke the formal peer review system with a few emails—the editors of SWJPAM managed one more edition before they just quietly shut-down.
Their school Cameron University removed ALL mention of the journal from its webpages, and they just dropped all service of the math papers within it over its entire nine years plus of existence, as did ALL of their mirror servers except EMIS.
Thankfully EMIS kept the prior papers available, for what about all those mathematicians who got published through them for years?
See: http://www.emis.de/journals/SWJPAM/
I am thankful to those Germans who were thoughtful enough to keep the history and work the journal represented available, when even its own creators were ready to just toss it and all the effort represented by it.
Think about it, as if you think this story is just about me, consider how many others who had papers published were being left hanging without a word of explanation, just by publishing in an electronic journal which one day decided to commit seppuku.
You might be one of those authors, or you could be one in the future in a math society many of you may not understand as that dead math journal is about an inconvenient truth—mathematical proof that some powerful mathematicians would just as soon not be known and accepted.
It's about people who through their actions show they actually hate mathematics, no matter what their titles, and about how difficult it can be to get the truth known—even with absolute proof—when people just do not want it.
Years have passed and so far they have won, holding back the consequences of the mathematics, stopping human intellectual progress in this area, and keeping the use of algebraic residues—out of the world's textbooks.
[A reply to someone who wanted to know whether or not “Nothing came of that” was James' way of saying that professor McKenzie had told him that he was wrong.]
No. I explained it all in detail, answered various questions he raised, and at 4:30 pm exactly he went home—along with the rest of the Vanderbilt math department. It was like a freaking whistle went off. Then I got in my car and went home, wondering a bit about the situation as I'd managed to explain everything completely in person to a leading mathematician, and answer all objections and he inexplicably just went home.
Later he emailed me thanking me for the conversation, and suggesting some books I might read, and I went off on him in reply, which, um, ended things there.
But understand, after years of arguing with very rude and obnoxious people on sci.math, and years of searching for some valid mathematical ideas of my own, with real success and the ability to explain it all in detail, face-to-face with a professional mathematician, he could just listen, and walk away.
I just couldn't take it, and maybe have learned from arguing on Usenet to too easily turn to angry responses, so I did, and that ended the conversation with McKenzie!
But later I got published in SWJPAM anyway.
During that meeting he told me I lacked "polish" which I took to mean that I didn't show formal training in terms of how I presented the mathematics, not as to whether or not it was correct, and no, I don't have formal training as a mathematician as my degree is in physics.
I DO have formal training as a physicist.
He also asked me if I was independently wealthy or had a rich uncle, apparently wondering how I was supporting my mathematical efforts.
Of course none of that sat well with me. It was like he was checking to see if I had other resources that I might apply if he just blew me off, like if I were rich, I might have pursued other means.
I learned a lot about mathematicians that day.
It was later that my paper was published in SWJPAM. And I know now what I knew then, as I'd explained everything to a leading mathematician—my research is correct, and people get away with lying about it.
That dead math journal is reality. Yes, math society can lie about reality all it wants, but make no mistake, you are lesser people if you do.
I think of you as a society that only cares what people think.
You say otherwise, but people can lie about lying, and from years of experience with your society I know that you people don't care about mathematical proof, but only about what you can convince people.
As long as people believe you care about mathematical truth, the bulk of you feel satisfied which is why this story keeps playing out as it does.
As long as you can lie to the world and be believed you don't care if you are mathematically wrong, or you would care about algebraic residues, and you couldn't so easily dismiss that dead math journal.
You people are social. Your society is purely political as long as you can get away with it, and for you, the mathematics be damned.
So I realized, eventually—as even after the initial idea it took me a few years to get the right approach—that I could use
x^2 + y^2 +vz^2 = x^2 + y^2 + vz^2
where I'd write that as x^2 + y^2 + vz^2 = 0(mod x^2 + y^2 + vz^2), and I could do various algebraic manipulations and eventually subtract out
x^p + y^p = z^p
and analyze the algebraic residue, as remember, I subtracted from an IDENTITY, so all the properties of what was left that were of interest would come from the FLT equation itself, as there could be no other input, since the identity is always true—which is why I call it a tautological space.
So the brilliance of this approach is in recognizing that by using an identity I could get to an algebraic residue, where I could analyze that residue with a free variable that I could make whatever I wanted, and using this approach I could first force an integer requirement for x, y and z by picking a prime factor f, of x, and using
v = -1 (mod f)
where I figured out quickly that I needed v = -1 + mf^{2j}, where m is a non-zero integer, and j is a natural number, as then I could make
x^2 + y^2 + (-1 + mf^{2j)z^2 = 0 mod f^n
where n is an arbitrary counting number, so I had a way to get the mathematics focused on x, y and z being integers!!! And it REQUIRED using my free variable v, which I only had because I was working on an algebraic residue, as if x, y and z are not all integers, then you cannot get
x^2 + y^2 + (-1 + mf^{2j)z^2 = 0 mod f^n
and given that handle I could go all the way to the complete proof of Fermat's Last Theorem, and after celebrating a bit, I began talking it out on the sci.math newsgroup, where I really believed that I'd finally be welcomed for succeeding after so many failures, but little did I know that YEARS would pass, and along the way I'd learn a lot more about math society, and a mathematical journal would even die, quietly.
So I had, after years of searching, a dramatic and simple proof of Fermat's Last Theorem found by this new technique of analyzing the algebraic residue found from subtracting from a tautology and I'm expecting cheers from mathematicians but I ended up in more heated arguments!!!
Finally trying to be smart about the situation, I pulled out one piece of the full proof, and wrote a paper, and started sending it to math journals.
An early draft went to Barry Mazur at Harvard as I sought commentary and he actually replied, wishing me luck and asking about one section. I answered him but heard nothing further.
I sent a draft to Andrew Granville for publication in the New York Journal of Mathematics, and he claimed it was out of his area and referred it to the chief editor who replied back to me that the paper was too small for the journal!!!
Looking to bank on my status as an alumnus of Vanderbilt University I got hopeful when I saw a professor from my school's math department was an editor of a journal and sent it to him, a Ralph McKenzie. He claimed to not understand it, so I forwarded him Mazur's email. After that he suggested that next time I was in Nashville I should explain it all out on the chalkboard.
So I planned a trip!!! I told him I was driving up, and set up a time, and I drove back to my alma mater for the first time in over ten years, and met with my old physics adviser as well as with Professor McKenzie with whom I talked for several hours, and explained my paper.
Nothing came of that so I sent the paper to the Southwest Journal of Pure and Applied Mathematics (SWJPAM), and they accepted it for review, and eventually published it.
See: http://www.emis.de/journals/SWJPAM/
and
http://www.emis.de/journals/SWJPAM/vol2-03.html
But if you check those links you can see that the second says my paper was withdrawn, while the first talks about SWJPAM no longer being in operation.
What happened is that after my paper was published and I received more than one congratulatory email from the editors of SWJPAM, some person posted to the sci.math newsgroup that I was published, and the hate and fury that spewed out from that newsgroup was intense. They not only berated SWJPAM and its editors, maligning them repeatedly, but talked down the entire journal process, claiming that mathematical journals often publish in error.
Then some of them got the brilliant idea of emailing the editors claiming problems with my paper.
Their claims were ones I'd heard before before I ever sent the paper, which were easily resolved, but they have lied repeatedly about the mathematics in this area, and show no conscience nor regard for the truth.
I noted the posts conspiring to assault my paper by email and simply assumed that the formal peer review process would work, and if anything I'd just be questioned by the SWJPAM editors if they bothered to worry about emails from strange people asserting error.
But instead the chief editor immediately pulled my paper from the already published edition, and informed me by email that publication was a mistake and that he was going on sabbatical to Greece!!!
So not only were the rules not being followed, but I'd get no opportunity to answer.
The original paper can be found at my Extreme Mathematics group on a page that I have devoted to this story:
http://groups.google.com/group/extrememathematics/web/non-polynomial-factorization-paper
The equations in that paper are algebraic residues, though I don't explain that in the paper,. as it's not relevant to the proof.
What I did was take a slight variation on the FLT equation for p=3, and took the algebraic residue.
So what you now know is that the techniques I've talked about, using identities, what I call tautological spaces, with equation to get an algebraic residue, has had key portions formally peer reviewed.
Oh yeah, so after that capitulation to the sci.math newsgroup posters—who broke the formal peer review system with a few emails—the editors of SWJPAM managed one more edition before they just quietly shut-down.
Their school Cameron University removed ALL mention of the journal from its webpages, and they just dropped all service of the math papers within it over its entire nine years plus of existence, as did ALL of their mirror servers except EMIS.
Thankfully EMIS kept the prior papers available, for what about all those mathematicians who got published through them for years?
See: http://www.emis.de/journals/SWJPAM/
I am thankful to those Germans who were thoughtful enough to keep the history and work the journal represented available, when even its own creators were ready to just toss it and all the effort represented by it.
Think about it, as if you think this story is just about me, consider how many others who had papers published were being left hanging without a word of explanation, just by publishing in an electronic journal which one day decided to commit seppuku.
You might be one of those authors, or you could be one in the future in a math society many of you may not understand as that dead math journal is about an inconvenient truth—mathematical proof that some powerful mathematicians would just as soon not be known and accepted.
It's about people who through their actions show they actually hate mathematics, no matter what their titles, and about how difficult it can be to get the truth known—even with absolute proof—when people just do not want it.
Years have passed and so far they have won, holding back the consequences of the mathematics, stopping human intellectual progress in this area, and keeping the use of algebraic residues—out of the world's textbooks.
[A reply to someone who wanted to know whether or not “Nothing came of that” was James' way of saying that professor McKenzie had told him that he was wrong.]
No. I explained it all in detail, answered various questions he raised, and at 4:30 pm exactly he went home—along with the rest of the Vanderbilt math department. It was like a freaking whistle went off. Then I got in my car and went home, wondering a bit about the situation as I'd managed to explain everything completely in person to a leading mathematician, and answer all objections and he inexplicably just went home.
Later he emailed me thanking me for the conversation, and suggesting some books I might read, and I went off on him in reply, which, um, ended things there.
But understand, after years of arguing with very rude and obnoxious people on sci.math, and years of searching for some valid mathematical ideas of my own, with real success and the ability to explain it all in detail, face-to-face with a professional mathematician, he could just listen, and walk away.
I just couldn't take it, and maybe have learned from arguing on Usenet to too easily turn to angry responses, so I did, and that ended the conversation with McKenzie!
But later I got published in SWJPAM anyway.
During that meeting he told me I lacked "polish" which I took to mean that I didn't show formal training in terms of how I presented the mathematics, not as to whether or not it was correct, and no, I don't have formal training as a mathematician as my degree is in physics.
I DO have formal training as a physicist.
He also asked me if I was independently wealthy or had a rich uncle, apparently wondering how I was supporting my mathematical efforts.
Of course none of that sat well with me. It was like he was checking to see if I had other resources that I might apply if he just blew me off, like if I were rich, I might have pursued other means.
I learned a lot about mathematicians that day.
It was later that my paper was published in SWJPAM. And I know now what I knew then, as I'd explained everything to a leading mathematician—my research is correct, and people get away with lying about it.
That dead math journal is reality. Yes, math society can lie about reality all it wants, but make no mistake, you are lesser people if you do.
I think of you as a society that only cares what people think.
You say otherwise, but people can lie about lying, and from years of experience with your society I know that you people don't care about mathematical proof, but only about what you can convince people.
As long as people believe you care about mathematical truth, the bulk of you feel satisfied which is why this story keeps playing out as it does.
As long as you can lie to the world and be believed you don't care if you are mathematically wrong, or you would care about algebraic residues, and you couldn't so easily dismiss that dead math journal.
You people are social. Your society is purely political as long as you can get away with it, and for you, the mathematics be damned.
# posted by James Harris @ 16:37 
