This repository contains code for demonstrating Arnold's topological proof of the Abel-Ruffini theorem that there is no general solution in radicals to polynomial equations of degree five or higher. quadratic.html contains a demo page for showing that an algebraic formula (i.e. a formula relying only on addition, subtraction, multiplication division, raising to integer powers, and the extraction of integer roots) with no radicals cannot be the quadratic formula. Similarly, cubic.html contains a demo page for showing that an algebraic formula with at most one nested radical cannot be the cubic formula, and quartic.html contains a demo page for showing that an algebraic formula with at most two nested radicals cannot be the quartic formula. (Although note that the quartic formula has not just three, but four nested radicals!) Finally, quintic.html contains a demo page for showing that an algebraic formula with any number of nested radicals (i.e., any algebraic formula) cannot be the quintic formula, which is the Abel-Ruffini theorem. Also, this repository contains some functions for working with complex polynomials, their roots, and continuously moving those roots. Tests are in tests.html.