Abstract: We will review the history of the solvability of polynomial equations by radicals, concentrating on the two Memoirs of Evariste Galois.  We will show how the first Memoir allows us to determine all equations of prime degree which are solvable by radicals, and the second Memoir similarly leads to the determination of all primitive equations which are solvable by radicals.  All these terms will be explained.

The talk will be meant for a general audience.  We will take a historical point of view, starting from the work of the Italians on the cubic and the quartic, mentioning the work of Abel and Galois’s First Memoir, and illustrating the whole theory with the toy case of extensions of prime degree.