07734 .....

Hi, I'm Frank, from New York.

I like math and I'm not dead yet.

I'm not sure, but I think I might have an easily understandable (relatively, anyway) 4-color proof. You can have a look at it in the topology section...I'm offering $5 to the first person who can point out a logical error in it (details in the post & first reply).

So far, it's cross-posted to this forum (in the Topology section) and the Sciences section of the Mensa Community website forum. It has one reply in the Mensa Community web site forum from Scott Bowden, who had time to give it a 5 minute lookover. He says the approach looks promising, which I find encouraging, although he also did state that he won't have the time to look at it in detail for a while...

I've already found two typos and a couple of errors in one of the diagrams. These showed up as errors, but nothing that compromises the validity of the proof... one of the typos is corrected in the proof itself, with a reply post recording what it previously said, and the second is corrected in a reply post, because edit opportunities for the proof had expired. Since I realized with the second that it technically would have been considered a non-typo from the previous rules, I revised the rules to close the loophole. (The first typo left out some words, the second left out two characters: "-1".

The errors in the diagram were not important to the proof. The first one that I found was insignificantly small and actually entirely irrelevant to the proof, so I left it alone (it was minor mistake in the node version...). However, when I noticed the other error in the same diagram that related to something I had mentioned in the proof, I decided to fix it and post the correction. (The second error was a mistake in the first step of the diagram. Since all of the future steps and the node version were based on that step, it necessitated a major redrawing. This was a non-trivial error with respect to the diagram's sequence; had the diagram's specifics been essential to the proof and someone else found and posted the error, the finder/poster would have been entitled to the prize, and I would be back at the drawing board.)

Since it is neither possible nor practical to continually update the proof in the postings, I will (probably sometime after next week) build a page on yahoo or youtube or my space or something where I can continually update the proof to perfection. My guess is that there are probably a few more typos and trivial errors, but I don't think there are any significant logical errors in the proof, which is what I'm offering the $5 in an effort to find. (More details in the post and my replies to it.)