  We present short elementary proofs of the well-known Ruffini-Abel-Galois
theorems on insolvability of algebraic equations in radicals. These proofs are
obtained from existing expositions by stripping away material not required for
the proofs (but presumably required elsewhere). In particular, we do not use
the terms `Galois group' and even `group'. However, our presentation is a good
way to learn (or to recall) a starting idea of Galois theory: the symmetry of a
polynomial of several variables is decreased when a radical is extracted. So
the note provides a bridge (by showing that there is no gap) between elementary
mathematics and Galois theory. The note is accessible to students familiar with
polynomials, complex numbers and permutations; so the note might be interesting
easy reading for professional mathematicians.
