From what I understand, Cook-Levin Theorem states that there is an bijection (or at least injection) between mathematical statements and maps. Moreover, the statement is true iff the corresponding map is 3-colourable. First of all, this itself seems pretty amazing. Does this imply if there exist a polynomial-time algorithm to check for 3-colourability of maps (with QC perhaps?), all mathematical statements can be proven in polynomial time? Even if no polynomial-time algorithms exist, can we say, use our best algorithm and computational power to bash the Goldbach Conjecture? Might take a long time but its been 280 years already and we still don't have a proof.
Secondly, I imagine the 3-colourability of maps are decidable, which would imply the truthfulness of every mathematical statement is decidable. Does that not contradict Gödel's Incompleteness (there exist true statements that cannot be proven)? As in, every statement that is true can be proven from Cook-Levin Theorem. That is, if statement A is true, then we can find a 3 colouration of the map corresponding to A, which by Cook-Levin Theorem proves A is true.
Full disclosure, I only have a general idea of the Cook-Levin Theorem and Gödel's Incompleteness so I might have missed something obvious.