### Monday, March 20, 2006

## SF: Factoring and conic sections

When I first introduced my equations that follow from my non-polynomial factorization research I used equations that were hobbled in a special way:

k_1 y^2 = T

and y = n, which if you use that with

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

and

(2(v^2 - k_2)z + vy)^2 = ((1-4k_1)y^2+4T)v^2 + 4k_2(k_1y^2 - T)

and

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

you get equations provably—rather easily in fact—equivalent to what is commonly called Fermat's Factoring Method as you get rid of the hyperbola and instead have a quadratic.

Those of you who are experts on modern factoring techniques should know that all of those techniques inherit something from the Fermat factoring method, as quadratics in some way or another dominate current techniques, while the full equations I use rely on a hyperbola, unless you crush that out by using k_1 y^2 = T.

My research shows the potential of using any conic, not just parabolas, for factoring, but given the hundreds of years without that being shown, it's also clear that it's either extremely difficult to do, or impossible to do with previously known methods–what I call classical techniques.

You have to have that neat idea of using identities like

x+y+vz = x+y+vz

and then you have the world of conics opened up, and maybe there's some really snazzy way to use a circle or an ellipse, while I've shown how to use a hyperbola, where it's also neat that it's part of a hyperbloid.

That's how my research encompasses what came before and extends it.

And if you think that my ability to encompass previous factoring techniques, as provably I can, like my equations being able to reduce to the quadratic case, while extending to areas previously inaccessible is a hallmark of unimportant research, then you're just not being rational on the subject.

So why aren't people rational on the subject when it's my research?

I have two theories:

Here's one of my favorites from another research area–prime counting–as I sent my prime counting function to a mathematician at a college in Atlanta, and he rather forcefully proclaimed to me that it was impossible. Um, but, I'm sending him the equations that actually DO work, and he's saying that they're impossible?

You do the math.

Oh, and then there's that Cornell math grad student who worked through some of my research in his own words, until he got to the end and stated that the result seemed correct for INTEGERS when it followed more generally, and then he said he needed to research algebraic integers.

And yes, I've been in contact with him since then by email, when he's been somewhat upset at some things I've said, while seemingly comfortable with his own ignoring of a revolutionary proof, as I think he just figures that no one will ever believe me.

And, if mathematicians can just use cognitive dissonance, and simply quit being rational about my research, maybe no one will, for a while, unless someone develops that factoring research into something practical and puts you all out of jobs.

Then when people ask me about how all this happened, I'll remind them of that Cornell grad student—who will still be a grad student–and of Barry Mazur, and of that mathematician in Atlanta, and all the other mathematicians all over the world who managed to just not do what society should reasonably expect them to do, until a lot of other people paid the price.

k_1 y^2 = T

and y = n, which if you use that with

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

and

(2(v^2 - k_2)z + vy)^2 = ((1-4k_1)y^2+4T)v^2 + 4k_2(k_1y^2 - T)

and

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

you get equations provably—rather easily in fact—equivalent to what is commonly called Fermat's Factoring Method as you get rid of the hyperbola and instead have a quadratic.

Those of you who are experts on modern factoring techniques should know that all of those techniques inherit something from the Fermat factoring method, as quadratics in some way or another dominate current techniques, while the full equations I use rely on a hyperbola, unless you crush that out by using k_1 y^2 = T.

My research shows the potential of using any conic, not just parabolas, for factoring, but given the hundreds of years without that being shown, it's also clear that it's either extremely difficult to do, or impossible to do with previously known methods–what I call classical techniques.

You have to have that neat idea of using identities like

x+y+vz = x+y+vz

and then you have the world of conics opened up, and maybe there's some really snazzy way to use a circle or an ellipse, while I've shown how to use a hyperbola, where it's also neat that it's part of a hyperbloid.

That's how my research encompasses what came before and extends it.

And if you think that my ability to encompass previous factoring techniques, as provably I can, like my equations being able to reduce to the quadratic case, while extending to areas previously inaccessible is a hallmark of unimportant research, then you're just not being rational on the subject.

So why aren't people rational on the subject when it's my research?

I have two theories:

- My research is such a leap forward with such simple ideas that there's some kind of shock that researchers go into. It's almost like communications from another planet the leap is so huge.
- Looking around, researchers wait for someone else to move, and no one moves, so mostly there is quiet, while there are a few people who reply to me on Usenet, who if you read closely, don't actually make ANY sense at all.

Here's one of my favorites from another research area–prime counting–as I sent my prime counting function to a mathematician at a college in Atlanta, and he rather forcefully proclaimed to me that it was impossible. Um, but, I'm sending him the equations that actually DO work, and he's saying that they're impossible?

You do the math.

Oh, and then there's that Cornell math grad student who worked through some of my research in his own words, until he got to the end and stated that the result seemed correct for INTEGERS when it followed more generally, and then he said he needed to research algebraic integers.

And yes, I've been in contact with him since then by email, when he's been somewhat upset at some things I've said, while seemingly comfortable with his own ignoring of a revolutionary proof, as I think he just figures that no one will ever believe me.

And, if mathematicians can just use cognitive dissonance, and simply quit being rational about my research, maybe no one will, for a while, unless someone develops that factoring research into something practical and puts you all out of jobs.

Then when people ask me about how all this happened, I'll remind them of that Cornell grad student—who will still be a grad student–and of Barry Mazur, and of that mathematician in Atlanta, and all the other mathematicians all over the world who managed to just not do what society should reasonably expect them to do, until a lot of other people paid the price.