A graduate student at UCSB claims to have proven the Four Color Theorem in four pages and without any computer program. I read his write-up of it quite thoroughly and failed to find anything wrong. (Well, I don’t believe his proof of one of his lemmas, but he doesn’t even use that lemma in full generality but only a special case which is very obvious and easy to prove.) However, I don’t know what it has to do with the Four Color Theorem. He claims that it was shown to be equivalent to something else two years ago and he proved the something else, so now I’ll have to ask him for a reference on that if I see him next week. Understandably, the math department was talking about nothing else all afternoon.

\begin{edit} Now I know what the paper has to do with the Four Color Theorem after reading this AMS article. (You might need an AMS account to read it.) \end{edit}

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## About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.

Wow. My USAMO proof of #4 was longer than that…hehe…

I’m completely dumbfounded…is there a copy of his paper online? There’s a 12 page proof of this theorem (Cohit) w/o use of Coq, but even that’s still under dispute…

I don’t think so. He found out that it’s wrong. Lots of people (myself included) somehow completely managed to miss it.

Oh, that’s too bad. Otherwise, it would have been brilliant.

–random AoPS member

So then the flaw is irreperable?

Yes, I think so.