Wednesday, September 15, 1999


JSH: Finish line; re:FLT Proof

Four and a half years. I'm amazed that I went the distance.

In the Army they tell you never to stop moving. That is, a lot of people going through Basic Training aren't really in shape to run for four or five miles, or even two. Of course, you do run every single day. What the drill sergeants tell you is, walk if you have to, but never, never stop. You have to go the distance anyway, so stopping just means it'll take that much longer and it still hurts when you start up again.

The nice thing about finishing a long run is you get to relax and watch everyone else come in. It's an amazing feeling when the pressure finally comes off.

That's the way I feel now.

What I'll be doing over the next few days is watching to see who figures out that I have a proof first. I'm curious about that person. I'll also be recovering my emotional breath and trying to really relax completely for the first time in years.

I'll put the clock at 4 p.m. EST today for when I really had everything ironed out. I mean, that's when I realized one last little error at the end of my proof. I figured out how the entire proof should work at about 7:20 p.m. EST yesterday.

Truly finishing is a guarantee for me that it'll be known almost instantaneously. That is, amazingly enough, it will take only a day or so (if that) before you know from other sources that I'm telling the truth.

After all, I gave up believing that I'd convince anyone that I had a proof with these posts years ago. Only the math itself can ultimately convince, as it recently convinced me. And convince it shall.

I'm not even going to give a link to the proof site. There are plenty of posts around with links.

Sunday, September 12, 1999


JSH: Other research

Now I will finally get an answer to a question that I've wondered about for a long time. The answer will come with the first person who figured out the simple proof of FLT. I was lucky in getting the answer without any supportive help (that is, the help I've received up until now has been critical help from people shooting down bad ideas or wrong assumptions).

Since I now have the right answer and seem to have beaten everyone else, the length of time before the correct answer becomes generally known is of scientific interest. There's also the question of just what's going on when someone discovers something like this. Most of my attempts are public record.

It's undoubtably true that every discoverer goes down many wrong paths. They just don't typically leave that information out for public view. Gauss was notorious for sitting on things until he was certain, to the extent that some say mathematics was behind by 50 years because of that, since he had important results that took others 50 years to prove. I read about that and thought it was a waste. What did he really have to lose? A few mistakes here and there wouldn't have affected his stature.

In any event, I keep talking about time limits. The reason is that any time anything new is added to the noosphere (all human thought on the planet) it rapidly propagates, especially today in our "Information Age". Therefore, I think it reasonable to assume that something like this should take about half a day. Of course, yesterday I said it'd take about a day, but then I didn't have a simple proof, so I was racing with that deadline to be sure I wasn't "scooped".

Then there's the other stuff about group processes. I don't think that anything really new was revealed by my experiences on the newsgroup, but I might be too close to see it right now. I do think it important to realize that it does mix things up a lot for someone outside the discipline to come in with their ideas.

Groups can become too homogeneous when it comes to ideas as everyone accepts too much as being true when it's really just believed. Outsiders have the benefit of not caring too much about what the people in the newsgroup think of them and of not having been indoctrinated with all the beliefs.

As solutions to the problems humanity faces become more critical to its continued survival, it will become just as critical that good ideas aren't found just because people are too worried about artifical boundaries.

After all, if a big enough problem comes along that humanity can't solve in time, it loses. And losing could very well mean extinction.

Most species in the history of this planet have lasted about a million years. Wouldn't it be pitiful if one of the most successful in so many ways, was one of the least in the game of time.

Saturday, September 11, 1999


JSH: That was fun! What's next? Goldbach?

Man, all that effort and it was just following through to a result obvious in hindsight.

I'm a little disappointed it didn't take any brilliance or anything. Oh well, I'm just glad I'm done.

Well, at least I didn't lose that $500. I just couldn't take that. And now I'm covered completely. The proof is for p>=5.

I'd be shocked if any of you kept up through all the changes. I'd be impressed if any of you just jumped to the obvious ending and skipped all the drama.

But hey, the drama was all of the fun.

I'm kinda tired, so that's it for a bit. I've updated the webpage as usual and I gotta say, I feel just a little bit letdown. But I'll get over it.

So, what now? I don't know if I want to do math problems anymore. I do have some ideas about that Goldbach thing. However, I'd just as soon someone else had the fun and went ahead and solved it. I mean, doing the famous math problem thing was fun and all, but I don't like to do the same thing twice.

Well, I have some ideas...and a whole world to play with.

Been fun! Y'all take care and don't take yourselves too seriously now. Of course, that's going to be hard to do anyway after all of this :-)


JSH: Why I win.

I thought I'd add a bit more of the math side in this post. Some of you are about to have one of those "aha" experiences. Many of you will undoubtably still not have a clue and I hope it's all of you who've been endlessly criticizing me.

My "f polynomial" has an exponent of p(p-1). I treat it as having an exponent of (p-1) and look at roots to the p exponent.

What I've demonstrated in my current proof is the method for reducing this polynomial to one that has (p-1)/2 roots.

These roots are the two number combinations of the f^p roots.

For instance, with p=5, I get a polynomial with roots ab,cd

where ab are the reals and cd are the nonreals (a convention I've been using all along).

All well and fine for p=5, but for p>5 there are more than (p-3)/2 nonreal two number combinations (some of you are getting that "aha").

Since the calculations I use don't determine which of those I'm using, it shows that they are all equal. That is, the sums are equal. Ok, it's easier to show with an example.

e.g. for p=7, I start with a polynomial having 6 roots and reduce to one with 3, so I must have

cd + ef = ce + df = de + cf

(Now the lightbulbs should be really going off.)

With this alone I can produce a contradiction with p=7 because it forces

sqr(u^2 + y^2) to be an integer, but I needed something better for the general case, so I went to a modular relation.

The form of the modulus for the first coefficient of the reduced polynomial is easy to figure out. I'll think about explaining it, so that the necessary "rigor" is on my webpage.

It's been tons of fun folks. I think this has to be the greatest adventure of my entire life. And, I never would have guessed that it'd all end this way though.

I'm deeply appreciative of all the help.

I promise to be as forgiving as I can of the endless criticism over the past three plus years (can you imagine?) that I've received from a loud minority of you, but I won't forget.

Wednesday, September 08, 1999


JSH: TONITE!!! It all ends.

All the back-and-forth about whether or not I have my own proof of FLT ends tonite. It's been me saying I have a proof and everybody else saying that I don't.

Well, I've simplified both webpages and made the arguments about as obvious as they're going to get.

What's in it for you?

If any one of you proves that I'm wrong, I'll be sending Don Taylor the $500 that I'd owe him because of our bet. Then, I'll curse my miserable existence and pout for a couple of days. Then I'll go to work and forget about it, while I consider how I'm going to break into Hollywood. Of course, after feeling the sting of the monetary loss and the loss to my pride, I will finally be able to drop this stupid notion of finding a simple proof of FLT.

Of course, if I'm right. I won't pout. I won't curse (well, I won't curse my existence). I won't go to work. And I'll wait for Hollywood to call (oh pooh, I never wait for anything).

The website for what should be the last time is

The sooner someone figures it all out the sooner I can go get drunk.


Dammit. Nothing happened. I got a few emails with simple questions and that's it.

My life is on hold here. Hmmm…I think I'll just figure it's correct and start calling news organizations. I think I'll start with TIME and CNN.

Since I know I'm right there's no reason to go to work either. I'll just sit here in my underwear and wait.

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