Ancient tablet turns history of mathematics on its head

A mathematician from the University of New South Wales has found the oldest known example of applied geometry, on a small piece of clay dug up in central Iraq. The circular tablet features a diagram drawn by a Babylonian surveyor about 1900-1600 BC. 

"It's the only known example of a cadastral document from the OB (Old Babylonian) period, which is a plan used by surveyors to define land boundaries," mathematician Daniel Mansfield said. "In this case, it tells us legal and geometric details about a field that's split after some of it was sold off." 

But what is significant about the drawing is the inclusion of Pythagorean triples, which are used to make accurate right angles. "The discovery and analysis of the tablet have important implications for the history of mathematics," Dr Mansfield said. 

"This is over a thousand years before Pythagoras was born." The discovery turns our understanding of the history of mathematics on its head. "It is generally accepted that trigonometry – the branch of maths that is concerned with the study of triangles – was developed by the ancient Greeks studying the night sky in the second century BCE," Dr Mansfield said. 

"But the Babylonians developed their own 'proto-trigonometry' to solve problems measuring the ground, not the sky." Despite this breakthrough only being announced today, the tablet in question, Si.427, was excavated in 1894 outside of Baghdad. 

"It was a real challenge to trace the tablet from these records and physically find it – the report said that the tablet had gone to the Imperial Museum of Constantinople, a place that obviously doesn't exist anymore," Dr Mansfield said. 

"Using that piece of information, I went on a quest to track it down, speaking to many people at Turkish government ministries and museums, until one day in mid-2018 a photo of Si.427 finally landed in my inbox." The tablet features writing in cuneiform, one of the earliest systems of writing. 

Before the invention of paper, parchment or papyrus, Babylonians would write on soft clay with a reed stylus. A mystery remains about a particular detail at the bottom of the tablet. The numbers "25,29'" is written at the bottom. 

"I can't figure out what these numbers mean – it's an absolute enigma," Dr Mansfield said. "I'm keen to discuss any leads with historians or mathematicians who might have a hunch as to what these numbers trying to tell us." 

Many Babylonian tablets that have survived to this day are documentations of mundane legal and business disputes. The first Babylonian dynasty took in much of the fertile land in Iraq, and dominated the region for several hundred years until Babylon itself was sacked by the Hittites. 

By Nick Pearson

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