I heard that straight edge + compass can solve up to quadratic equations. I've also heard the Origami/Paper-folding can solve cubic equations. But can it solve higher-degree polynomial equations (e.g. quartic, quintic) in general? If not, is there a geometric construction framework that could solve these higher degree polynomial equations?
My intuition says that degree 5 and higher can't be solved because of the Abel-Ruffini theorem proving that no general formula exists for degree-5 and higher polynomial equations that only involves arithmetic and radicals.