The Letter That Changed Everything

Using a letter to stand for an unknown number feels obvious now, but it took thousands of years to reach. The Babylonians (2000 BC) solved quadratic equations by recipe: "take half the coefficient, square it, add the constant," yet never used symbols. Diophantus (250 AD) introduced abbreviations, and full symbolic algebra arrived only in the 1500s-1600s.

The power of variables is compression. "For any rectangle, the area equals the length times the width" is a full sentence in English, but just A = lw in algebra. That compression lets you rearrange the relationship mechanically: w = A/l, and l = A/w.