I was merely responding to your sentence: > The way I like to think about NP is: are there certain types of problems which we, as smart as we might be, cannot

I was merely responding to your sentence: > The way I like to think about NP is: are there certain types of problems which we, as smart as we might be, cannot easily solve, not because we aren't smart enough but because of the nature of the problem itself? If you read it one way, it sounds as if P=NP would allow us to solve every formal problem. It doesn't. One very interesting example: The concept of Kolmogorov Complexity. I'm not a CS theorist, so I can only give my layman interpretation, but if I understand it well it goes like this: given a particular string of bits, the Kolmogorov Complexity relates to the shortest possible program that can describe this string. In effect, that means: the ultimate compression. Well, the whole theory of KC says that you can't find this shortest possible program for every string. Not because it takes too much time to check very possible combination (P=?=NP) but because of the nature of the problem.