Quintic equations are polynomial equations with one variable, customarily denoted by x, which is never raised to a power greater than the fifth. Symbolically, such an equation can be written as follows: ax⁵ + bx⁴ + cx³ + dxdx² + ex + f = 0. The problem of solving polynomial equations in general, and quintic equations in particular, has been a central theme in from antiquity to the present.

Babylonian mathematicians already knew how to solve quadratic equations (with no power of x greater than 2). In the early 1500s, Italian mathematicians discovered how to solve cubic equations (with no power of x greater than 3) and quartic equations (with no power greater than 4). In each case, the solution could be found with nothing more than the elementary operations of addition, subtraction, multiplication and division, plus the special operations of taking square roots or cube roots. This discovery suggested that a general method for...