P != NP question

Question

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

Answer 1

Let's assume I am handed a solution to a "hard" problem by a magician, and I can easily verify if this solution is correct or not. BUT, can I compute this solution myself easily? (polynomial time)

This is exactly the question.