Researchers at UNSW Sydney have finally unlocked the mystery of a 3,700-year-old Babylonian clay tablet, discovering that it is in fact the oldest—and most accurate—trigonometric table known to humanity.
The tablet, known as Plimpton 322, shows that the Babylonians, not the Greeks, were the true pioneers of trigonometry—the study of triangles. This remarkable find highlights the advanced mathematical knowledge of ancient Mesopotamia, long hidden in history.
Originally unearthed in the early 1900s in southern Iraq by archaeologist Edgar Banks—who partly inspired the fictional Indiana Jones—the tablet contains four columns and 15 rows of numbers written in cuneiform script, using the Babylonian base-60 (sexagesimal) number system.
“For over 70 years, scholars have known that Plimpton 322 contains a series of Pythagorean triples,” explains Dr. Daniel Mansfield from UNSW’s School of Mathematics and Statistics. “But its true purpose remained a mystery—why would ancient scribes go to such effort to generate and order these numbers?”
The breakthrough came when Dr. Mansfield and Associate Professor Norman Wildberger demonstrated that the tablet actually describes right-angled triangles using a unique form of trigonometry based on ratios rather than angles or circles. Their study, published in Historia Mathematica, shows that the Babylonians created not only the world’s oldest trigonometric table, but also the only one that is mathematically exact.
This challenges the long-held belief that the Greek astronomer Hipparchus (circa 120 BC) was the father of trigonometry. In fact, Plimpton 322 predates his work by more than a millennium.
“This discovery changes everything,” says Dr. Wildberger. “The Babylonian approach is simpler and more accurate than our modern trigonometry, and it could even transform the way mathematics is taught today.”
The tablet’s 15 rows outline a sequence of right-angled triangles with steadily decreasing slopes. The researchers argue that the original tablet likely had six columns and 38 rows. They also reconstructed how ancient scribes—working in base-60 rather than base-10—would have calculated the numbers.
Far from being a mere teaching tool, the tablet may have been used to design canals, palaces, temples, and step pyramids.
Dated between 1822 and 1762 BC and thought to have originated in the Sumerian city of Larsa, Plimpton 322 now resides in Columbia University’s Rare Book and Manuscript Library in New York.
At its core, the tablet is filled with Pythagorean triples—sets of whole numbers a, b, and c that satisfy the equation a² + b² = c². While the classic 3-4-5 triangle is well known, the values on Plimpton 322 are far larger and more complex, such as 119, 120, and 169.
This ancient artifact not only redefines the origins of trigonometry but also showcases the extraordinary mathematical brilliance of the Babylonians—centuries before Greece’s so-called “mathematical golden age.”
