(Disclaimer: I don't have the solution). When I think about the reason factorization is hard, I know it must be something about our failure to link the discrete and the continuous maths. When we want iterate over the search space somehow, we have to do it in discrete steps. Like 3, 5, 7, 11, etc. The thing is, if we could search it in a continuous math way it would be solvable, since it'd be easy to gather enough information to find the answer, like how easy it is to find the vertex of a parabola if you have enough points. So maybe if there was some object outside of number theory the problem could be mapped to then we could do something apart from iterating.