A 3,800-year-old Egyptian scroll poses algebra with no algebra
The Berlin Papyrus, written around 1800 BCE, poses this: the areas of two squares together equal 100 square cubits, and the side of one square is three-quarters the side of the other. How long is each side?
Reveal the answer
8 and 6. If the larger side is x, the smaller is (3/4)x, so x² + (9/16)x² = 100, giving x² = 64 and x = 8, with the other side equal to 6 (and indeed 8² + 6² = 100). It's one of the earliest known examples of solving what we'd now call a quadratic equation, centuries before algebraic notation existed.
— Unknown ancient Egyptian scribe, Berlin Papyrus 6619 — c. 1800 BCE