Not a 'pure' programming question, but since it is deeply involved in programming theory, I thought it best to ask here.
Regarding the P NP problem, this excerpt from http://en.wikipedia.org/wiki/P_versus_NP_problem : "In essence, the question P = NP? asks: Suppose that yes answers to a yes or no question can be verified quickly. Then, can the answers themselves also be computed quickly?"
I am left wondering, how is the speed of verifying an answer related to the speed of generating a solution?
Essentially, in the set of NP, or Nondeterministic Polynomial time, problems, the answer can be verified in polynomial time. The question is whether all such problems can be determined in polynomial time.
If P=NP is true, and such algorithms are discovered many problems that are hard to solve but easy to verify the solution, such as proofs, become as easy to solve as to verify.