KnowraAbel–Ruffini theoremLinked fromLinked fromThe 7 pages that link to Abel–Ruffini theorem, each with the reason it gives.All 7Broader topic 1Related 2Compared with 4Quadratic equationCompared with: The quadratic formula belongs to the lower-degree solvability that fails in general beyond quartics.Évariste GaloisCompared with: It frames the impossibility question that Galois theory explains structurally.Niels Henrik AbelBroader topic: Abel supplied the decisive proof that the general quintic is not solvable by radicals.Galois theoryRelated: Its explanation follows from the nonsolvability of the generic quintic's Galois group.Cubic equationCompared with: It marks the boundary beyond cubic and quartic equations for universal radical formulas.Solvability by radicalsRelated: It establishes that radical solvability fails for the general quintic and higher degrees.Algebraic functionCompared with: Algebraic functions exist beyond those expressible by nested radicals.