phlip wrote: Suffice it to say P is the set of all puzzles which are easy to solve (for a very specific and broad definition of "easy")... NP is the set of all puzzles that, when you're given an answer, it's easy to check whether the answer is correct. Like Sudoku for instance... if I give you the answer to a Sudoku puzzle, it's pretty simple to check if it's right... just make sure it follows all the rules, of each number appearing once, etc. But if I give you a partially-filled in grid and ask you "is it possible to solve this?", that's a harder question to answer. The question is whether it's hard enough, given the aforementioned specific-but-broad definition of "easy". That is, is P=NP... is every problem which is easy to check also easy to solve? Or are there some problems which are easy to check but hard to solve? It's generally presumed that P ≠ NP, but it's never been proven.
Oh. Hmm. Well, going from this line in the Wikipedia entry "In a 2002 poll of 100 researchers, 61 believed the answer is no, 9 believed the answer is yes, 22 were unsure, and 8 believed the question may be independent of the currently accepted axioms, and so impossible to prove or disprove", I'd go with the last 8, but simply because such a simple equation can't possibly account for all the variables.
But then, this is why I stay as far as possible from math with letters in it; after one too many exchanges of "why does it equal that?" "because it does, you are intended to know that type of equation and assume that value," I realized that math was as logical and straightforward for me as economics or sociology.
Aherm. Back to the point, P and NP both have nearly infinite variables, so formulating a rock solid equation is impossible. You mathy people will just have to accept that there are just some things that you aren't going to get, because they just aren't there.