Wikipedia has a list[1] of statements which are not provable in (or rather independent of) ZFC. IMO the most weird thing is the following, intertwining consist

Wikipedia has a list[1] of statements which are not provable in (or rather independent of) ZFC. IMO the most weird thing is the following, intertwining consistency of ZFC with Diophantine equations[2]: > One can write down a concrete polynomial p ∈ Z[x1, ..., x9] such that the statement "there are integers m1, ..., m9 with p(m1, ..., m9) = 0" can neither be proven nor disproven in ZFC (assuming ZFC is consistent). [...] the polynomial is constructed so that it has an integer root if and only if ZFC is inconsistent. [1] https://en.wikipedia.org/wiki/List_of_statements_independent_of_ZFC https://en.wikipedia.org/wiki/List_of_statements_independent... [2] https://en.wikipedia.org/wiki/List_of_statements_independent_of_ZFC#Number_theory https://en.wikipedia.org/wiki/List_of_statements_independent...