Several points on the question of whether the proof is likely to be correct: * As far as I know this paper wasn't circulated for informal peer review before be

Several points on the question of whether the proof is likely to be correct: * As far as I know this paper wasn't circulated for informal peer review before being made public; I heard no talk on the grapevine. (Edit: apparently it was circulated and someone other than the author made it public.) * Therefore a proper assessment is going to take a while. Until then we can only speculate :-) * While the crank attempts at P =? NP are statistically much more common (http://news.ycombinator.com/item?id=347295 http://news.ycombinator.com/item?id=347295), this isn't one of them. The author is a legit computer scientist: http://www.hpl.hp.com/personal/Vinay_Deolalikar/ http://www.hpl.hp.com/personal/Vinay_Deolalikar/ * On the other hand he hasn't published much on complexity theory and isn't known in that community. Which is weird but not necessarily a red flag. * Looking at his papers, it's possible he's been working on this for about 5+ years -- he has two threads of research, basic and industrial, and the former line of publications dried up around 2004. * On the other hand I don't think anyone knew he was working on this. The only known serious effort was by Ketan Mulmuley at U Chicago. * It has been known that the straightforward combinatorial approaches to P =? NP aren't going to work, and therefore something out of left field was required (http://web.cs.wpi.edu/~gsarkozy/3133/p78-fortnow.pdf http://web.cs.wpi.edu/~gsarkozy/3133/p78-fortnow.pdf). Mulmuley's plan of attack involved algebraic geometry. * This paper uses statistical physics. This approach doesn't seem to have been talked about much in the community; I found only one blog comment http://rjlipton.wordpress.com/2009/04/27/how-to-solve-pnp/#comment-1260 http://rjlipton.wordpress.com/2009/04/27/how-to-solve-pnp/#c... which mentions the survey propagation algorithm. (Deolalikar's paper also talks about it tangentially.) * If the statistical physics method used here is powerful enough to resolve P != NP, then there's a good chance it is powerful enough to have led to many smaller results before the author was able to nail the big one. It's a little weird we haven't heard anything about that earlier. * Finally, since the author is using physics-based methods, there's the possibility that he is using something that's a "theorem" in physics even though it is technically only a conjecture and hasn't actually been proven. Physicists are notorious for brushing technicalities under the rug. It would be very unlikely that the author didn't realize that, but still worth mentioning. * If that is indeed what happened here, but the rest of the proof holds up, then we would be left with a reduction from P != NP to a physics conjecture, which could be very interesting but not ground breaking. Conclusion: overall, it certainly looks superficially legit. But in non peer reviewed solutions of open problems there's always a high chance that there's a bug, which might or might not be fixable. Even Andrew Wiles's first attempt at FLT had one. So I wouldn't get too excited yet.