Sure, I'll try and present my considerations or reason for asking this deep question. Since I lack the skills, I'll just start out by saying that since logic has been progressing in a manner where one does not know whether that logic or a system of logic is universal, then assuming that logical monism is true, then one can think that it should be possible to find a hermetic/tautological language.

But, to really reduce what I have to say or rephrase it as a question, are the implications of Gödel's Incompleteness Theorems somehow restricting us or preventing us from arriving at an answer? Is it that because of his theorems, scientists don't believe that P=NP? I'm only saying this because it is thought that for P=NP to be proven it would have to be a formally complete and consistent complexity class.

There are numerous Youtube videos on P v. N-P. Best are from MIT. That's the place to start. A quick test: do you, gentle reader, know what N-P stands for?