Thanks for the articles. I was looking at a paper a couple of days ago (Computational Economics by Paul Humphreys) and it mentioned P vs. NP

In the paper it said that "unless P = NP, any problem that is NP has instances that will resist any realistic attempt at an exact computational solution"

Whether the proof presented is correct, I don't know... but either way I think it is interesting that someone took the effort to tackle this very hard problem.

I wouldn't count on it. Several important mathematicians already have expressed heavy doubts that it will hold any water. Of course, there's the possibility that everyone so far (including Tao, Aarson, etc) is wrong in their judgment, but very unlikely. But there's the more likely possibility that his (hopefully novel) approach shines new light on complexity theory. That's more what mathematicians will be hoping for while reading his paper. That's what makes Millennium prize problems important -- they open doors to future advancement.

I glanced through it a few days ago (though this seem revised). Seems to use a lot of areas of math. I haven't invested much time in trying to understand or critique it (I'm no expert in this area, so I'd rather it get refereed first).

But, I'm rooting against him, because if P=NP that would be so much more interesting. Then again, 2 millennium problems in the first decade would be nice.

Can't compute exactly how a complex protein will fold? Within decades folding proteins may perhaps be used to compute even more complex problems.

The paper itself is way over my head.