Proto-Geometry Found in Babylonian Tablet, a Thousand Years Older than Pythagoras

TUCKED AWAY in a seemingly forgotten corner of the Istanbul Archaeology Museum, Daniel Mansfield found what may solve one of ancient math’s biggest questions.

First exhumed in 1894 from what is now Baghdad, the circular tablet — broken at the center with small perpendicular indentations across it — was feared lost to antiquity. But in 2018, a photo of the tablet showed up in Mansfield’s inbox.

Mansfield, a senior lecturer of mathematics at the University of New South Wales Sydney, had suspected the tablet was real. He came across records of its excavation and began the hunt. Word got around about what he was looking for, and then the email came. He knew what he had to do: travel to Turkey and examine it at the museum.

Hidden within this tablet is not only the oldest known display of applied geometry but a new ancient understanding of triangles. It could rewrite what we know about the history of mathematics, Mansfield argues.

These findings were published Wednesday in the journal Foundations of Science.

It’s generally thought that trigonometry — a subset of geometry and what’s displayed on the tablet in a crude sense — was developed by ancient Greeks like the philosopher Pythagoras. However, analysis of the tablet suggests it was created 1,000 years before Pythagoras was born.

Babylonian mathematics, which already holds a place of renown in the pantheon of ancient math, might’ve been more sophisticated than historians have given it credit for.

“The way we understand trigonometry harks back to ancient Greek astronomers,” Mansfield tells Inverse. “I like to think of the Babylonian understanding of right triangles as an unexpected prequel, which really is an independent story because the Babylonians weren’t using it to measure the stars, they were using it to measure the ground.”