But he systematically set out word-­form linear and quadratic equations, with algorithmic methods for solving them — that is, for finding the "unknown numbers," our modern x 's and y 's.

Babylonians, in particular, would solve simultaneous equations to find the roots of a quadratic. Egyptians, Grecians, Indians, and Chinese peoples used graphical methods to solve the equations.

Many former algebra students have painful memories of struggling to memorize the quadratic formula. A new way to derive it, overlooked for 4,000 years, is so simple it eliminates the need.