Originally Posted by
Mario F.
P vs NP is deeply integrated into our understanding of mathematics. Even if we pretend to have solved it for our present knowledge, we can't claim it. We know the problem is still unsolved. P vs NP domain is the entire domain of problem solving techniques, including those we don't know about yet or those we haven't invented yet.
We are in a constant search for new and better mathematics. But heck, in order to finally put P vs NP to rest we need to reach a plateau of mathematical understanding in which we just know there is nothing new to invent in this area. Highly unlikely.
As we have been shown since as far back as ancient times, algebra isn't enough to deal with the largest sets of numbers. Although it has been refined and expanded through the ages, it also helped expose an hidden mathematical universe we have yet to tap into. We will eventually develop new axioms. New fields of mathematics will eventually one day be able to explore everything, from irrationals and hyperreals to transcendentals, in more formal ways. But what new unreachable secrets will they reveal?
Seems likely we will always think we live in a NP universe with P always tagging behind as we progress and evolve. If and when we reach the answer one day, our intellects may be too evolved to even consider P vs NP more than an ancient curiosity of our more single minded ancestors.