I think it's reasonably clear at this point that an elementary proof that P != NP is unlikely to exist; in all likelihood such a proof would have to traverse ma

I think it's reasonably clear at this point that an elementary proof that P != NP is unlikely to exist; in all likelihood such a proof would have to traverse many other fields of mathematics to get back to the main result, and would almost certainly hinge on areas of mathematics that have proven difficult to formalize so far.