Before anyone gets too excited, I would caution that there there is a long history of failed attempts at this problem, and an equally long history of premature announcements. On the surface, here is what is encouraging about this one:
- The author is a theory professional and not an amateur or a crank
- The author frames this as a possible proof where he's seeking feedback on the method, rather than declaring a solution up front
- The author builds on existing theory in a formerly mainstream approach that has been shown to have problems (circuit lower bounds)
- Looks like a serious and well-considered proof effort
Here is why HN should hold off on any excitement:
- This style of proof was found to be unworkable in the past. In particular, approaches to proving circuit lower bounds in this manner were shown by Razborov and Rudich to be "natural proofs" in the 1990s, which is a category of proof strategy that cannot demonstrate P/NP. It's not explained why this strategy does not succumb to the same problem -- though the author surely has some reasoning around it. (see point 6 of Scott Aaronson's "8 signs a proposed P/NP proof is wrong": http://www.scottaaronson.com/blog/?p=458. You might also see this comment from /r/math: http://www.reddit.com/r/compsci/comments/14mqqt/anyone_have_...)
).
- There is a very good community framework for evaluating proposed solutions when the author's ready. Possibly the author has already submitted the work to a journal, but it's not clear that he's confident enough yet to invite more active discussion on his effort from the theory community. I can't find any discussion of it online. It's likely he's pursuing these on his own, and conceivably flaws have been found since the summer.
- The author does not declare this as a completed solution in the same way that Deolikar did two years ago. In that case, his announcement led to an analysis by the theory community online that led to discovery of core errors. We can wait here 'til the author gives a bit more information.
- This proof joins dozens of other announced solutions to P/NP in both directions (see, for example, http://www.win.tue.nl/~gwoegi/P-versus-NP.htm) which emerge quite regularly, and close attention paid to each will leave no time for original research :)