ABSTRACT
In the 16th century, formulas that express the solutions of a cubic equation and a quartic equation in terms of radicals were discovered. For 200 years, mathematicians wondered whether the same could be done for quintics. Around 1800 it was shown that this is impossible. In this chapter, we shall first see how to write the solutions of a cubic in terms of radicals. Then we shall prove that for an equation of degree 5 or greater, no such formulas exist in general. All fields are assumed to be of characteristic 0.
