I can't explain the article but I can explain P vs NP (it's been a few years though so please forgive any mistakes). P and NP are two classes of problems. P is

I can't explain the article but I can explain P vs NP (it's been a few years though so please forgive any mistakes). P and NP are two classes of problems. P is simply problems with an input n that can be solved in n^c time for some value of c. So sorting n items is in class P, because it's bounded by n log n, (which will be smaller than n^2 for example). NP is a harder concept to grasp, the N actually stands for Non-deterministic. My college teacher explained it like this: imagine you could send out as many clones as you wanted to, and if any clone solves the problem, then the problem is solved. The way this gets explained a lot is that NP is the class of problems that can be verified in Polynomial time. One place NP really matters is security. Think of a password, a longer password makes it exponentially harder to brute force, but it's only linearly longer to check. If P=NP, then this would mean certain password type problems could be cracked in polynomial time. Now this might still be a large polynomial, maybe it would be n^1029281, but this would still excite scientists, partly because once something is polynomial time it opens the door to get exponent smaller. One example of this is matrix multiplication, where the exponent has gone from 3 to under 2.4 over the years (http://en.wikipedia.org/wiki/File:Bound_on_matrix_multiplication_omega_over_time.svg http://en.wikipedia.org/wiki/File:Bound_on_matrix_multiplica...). Note that some of these problems that have to do with security have been thoroughly studied and no one believes there is an "easy" (polynomial) way to crack these types of security, which implies P != NP, we just can't completely prove it. Another interesting thing is that if any problem in the NP "complete" class of problems can be solved in Polynomial time, there are ways to map the problems between each other and thus all of them could be solved in Polynomial time. The "core" problem I've seen listed is the Boolean Satisfiability problem, given a boolean formula with n clauses, can you find variables to satisfy those clauses. All NP complete problems are variations of this problem, essentially different phrasings of it.