Harristotelian Logic

So now I've gone to showing what you can't do with just algebraic integers. I want to make another post to just these two newsgroups though to explain a little more about how politically things have worked out.

My original paper steps through quite nicely in a very rigorous way a path to understanding there is something wrong with the old ideas on algebraic integers, but it's abstruse and complicated.

It is a much more difficult argument in many ways as I use a degree three polynomial, and other stuff, while using a much more stylized language—and sci.math'ers went to town confusing people about the mathematics.

So I've had to simplify, moving to quadratics, and trying to explain in simple ways, but posters on sci.math repeatedly found ways to confuse, so I finally—years have passed now—came up with the notion of showing what you CANNOT do with the old ways of thinking.

So why was all that necessary?

After all, I've done much, much more than just argue about this on Usenet. Barry Mazur himself saw an early draft of my paper in this area and commented on it, so I know he read it. I sent it past Andrew Granville who passed on telling me the New York Journal of Mathematics wouldn't publish my paper, sending me to the chief editor who did pass on it.

And the paper, did, of course, get published in the now defunct Southwest Journal of Pure and Applied Mathematics, and some sci.math'ers sent some emails and convinced the chief editor to withdraw it.

What could be so huge? What is the big deal?

Well I found a small little problem with the idea that the ring of algebraic integers is big enough to cover all the numbers you need it to cover, when mathematicians thought it was.

So they have mathematical arguments that just get to the point of saying something like, and this cannot be this or that in the ring ofalgebraic integers, so this or that is true.

Well, I prove that is not sufficient, so that means that arguments thought to be proofs, are not.

How far back does this go?

Over a hundred years, all the way back to Dedekind.

How much impact?

Well, you can possibly toss textbooks in number theory into the trash going back, oh, about a hundred years back to Dedekind.

Whole swaths of the mathematical world are just wiped away, like flipping a switch.

Reams of papers just totally yanked away. Books, supposed accomplishments, the hopes and dreams of thousands of people who thought they had it right, but were wrong.

The mathematics here is in a way unimaginably cruel. It is about as cruel as you can get in a way because mathematics is so absolute, so hard.

So people fight the truth. Mathematicians turn away from mathematical proof—maybe even disgusted by it—and cling to just believing what they believe, and can look at social support as validation.

So as I've made my discoveries the mathematical world worldwide has shifted to being more of a social organization. Mathematicians are more about convincing each other than proving anything, as they shfit away from mathematical proof.

They have to, or face what for many of them could be considered, the end of the world.

By showing what you can't do with the old thinking I'm helping some of you understand that I am right, but you also need to understand that I've proven this result many ways over the years, and been heard by people at the top of math society.

It's not about mathematical proof at this point.

It's about a deep human need to just cry no!!!—at a reality deemed too cruel.

It is just so damn cruel and harsh to accept the truth here that a lot of people…just don't.