The proof utilizes the theory of functions of a complex variable, specifically exploring Riemann surfaces and monodromy . Summary of Arnold's Topological Proof
When coefficients traverse certain loops, the roots of the polynomial undergo a non-trivial permutation. Abel's theorem in problems and solutions based ...
Groups are introduced naturally as "transformation groups" (e.g., symmetry groups of regular polyhedra like the dodecahedron) rather than starting with abstract definitions. The proof utilizes the theory of functions of