Babylonian astronomers used proto-calculus to track Jupiter

Five clay tablets in the British Museum, written in Babylon between 350 and 50 BCE, sat largely unread until scholar Mathieu Ossendrijver decoded their geometry in 2016. They contain instructions for predicting the position of Jupiter after it first appears in the night sky.

The method is genuinely abstract. The scribes took Jupiter’s velocity on day 1 and its slower velocity on day 60 as the two parallel sides of a trapezoid, with time running along its length. The area of that figure then equals the total distance the planet travels in those 60 days — the same link between speed, time, and distance that underlies modern integral calculus. They went a step further, halving the trapezoid into two equal areas to find the exact moment Jupiter had covered half its distance.

The figure exists in an abstract mathematical space — velocity drawn against time — a way of thinking historians had credited to 14th-century Europe.

That credit belonged to the Oxford and Paris scholars of the 1300s — the Merton “mean-speed” theorem and Nicole Oresme’s graphs of motion. The Babylonian tablets predate them by some 1,400 years.

The breakthrough hinged on a single object. Four of the tablets had been catalogued for over a century but misread, their purpose obscure. Only when Ossendrijver examined a fifth, unprovenanced tablet did the missing piece appear, linking the others and revealing what the trapezoid was really for — and reshaping our picture of how ancient science actually worked.