In Godel’s incompleteness theorem, his two statements relate to “non-trivial formal system”, but how are these determined? Is 1+1=2 one of these? What about P vs NP?
There is no general answer to that, but the incompleteness theorem states that any system that contains at least Robinson arithmetics, a weaker form of Peano arithmetics (natural numbers with addition and multiplication) is complex enough. Natural numbers with addition only, however, is complete and consistent. Also this does not mean that a system not containing Robinson arithmetics would not be complex enough.