Harristotelian Logic

I've now successfully used tautological spaces against only two problems. Where the latest which lead me to an alternate solution for binary quadratic Diophantine equations is rather spectacular for quite a few reasons because of the history around the problem.

Obviously, I can contemplate other areas of mathematics on which to use tautological spaces.

But I also know about their limitations as the second problem I tried to use tautological spaces on, and failed with them, was the factoring problem, so they are not infallible, just unimaginably powerful.

I've been watching the television show "House" a lot lately. I've kind of become addicted to it which has impacted how I post, as in, I'm more insulting, and it feels good. But like Dr. House, my insults are for a purpose, or I think they are, though they may simply mean I'm juvenile?

In any event, the show has given me a different perspective on the problem space.

So what do we know?

This notion of using identities in such a clever way clobbered the hell out of binary quadratic Diophantines in a way so devastating it mostly shut up even the angry idiots. But not a lot has changed.There's no reason to suspect much will change, so we can move on. And when I say we, I mean me, and my team of those people who bizarrely for reasons that puzzle many, and probably themselves, help me.

So yes, I admit it. There are people who help me evaluate ideas and I mostly insult them. Like Dr. House.

So I have a paradigm around which to fit my behavior and I am watching more and more episodes of the TV show to refine my behavior, and improve my insults.

Hilbert came up with some problems. I can clobber quite a few of them but wonder if I care. Russell thought to formalize a few things, put some logic into it, but came up short, but I think a few simple ideas bridge things in a way he didn't imagine.

But at the end of the day, does anybody really care? I know I find it hard to care.

So what other problems for those who are silly enough to care might be amenable to tautological spaces in their new and raw form, which is new and raw as I just invented the concept, or discovered it, whatever, a few years ago?

(No one say Collatz. It's verboten.)

Of course I HAVE solved problems without using tautological spaces! But that's too advanced for this initial post.

I'm thinking about cleaning out some crap left over from the old geezers who used to do math before they keeled over and died, like Russell and Hilbert.

Still I'm kind of picky, so the idiots among you need not apply. Ok, anyone can of course as usual reply as if I try to put that kind of criteria on then no one is qualified but me to talk to myself and I do enough of that already.

My suspicion is that you will fail me.

That is good.

It just means I'm more brilliant than I previously thought.

So what is the state of the art of mathematics?

In flux. The old ways have failed. I've collapsed 2000 years of old ideas about some simple binary whatevers into a page or two of rather potent theory. Mathematics can be revolutionized like the sciences.

You CAN push out the old professors hogging up the works by outdoing them, re-inventing, discovering, starting from scratch, or not, if you're not smart enough.

Get started. Or not. I'll insult you either way you go. Or not.