Overview

The search for the solutions of polynomial equations continued throughout the eighteenth century. Within a period of a couple of years around 1770, mathematicians in a number of countries made almost simultaneous advances that led to new ways of approaching the problem. There was disappointment in that none of the advances led to a general solution of the higher-degree equations, but some specific equations could be solved in the aftermath of this work. More importantly, the new approaches provided the means for answering the question about the solvability of polynomial equations in general early in the next century.

Background

An equation is simply an expression in which the two sides are asserted to be equal, which may not involve anything more than numbers. Early on in the development of algebra, the equations of greatest interest were those in...