Babylonian tablet from 3,700 years ago reveals that Pythagoras did not discover the theorem that bears his name

An unknown Babylonian mathematician defeated  Pythagoras  by discovering trigonometry more than 1,000 years before the Greek scholar, according to experts who are studying the piece. That Babylonian genius recorded the famous theorem usually associated with the name of  Pythagoras , along with other trigonometric tables, on a ceramic tablet now known as Plimpton 322.  Scientists  have further commented that the contents of this 3,700-year-old tablet surpass even our modern knowledge. .

As  The Guardian reports, researchers at the Sydney-based University of New South Wales have indicated that these four columns and 15 lines of cuneiform script “represent the oldest and most accurate operational trigonometric table, a working tool that could have been used in topography and calculation when building  temples ,  palaces  and  pyramids .”

The 3,700-year-old Plimpton 322 Babylonian tablet at the Columbia University Rare Book and Manuscript Library in New York. ( UNSW/Andrew Kelly )

Dr. Daniel Mansfield, from the University of New South Wales, explains about the finding :

Our investigation reveals that Plimpton 322 [tablet] describes the shapes of right triangles using a novel type of trigonometry based on proportions, not angles and circles. It constitutes a fascinating mathematical work that demonstrates an undoubted genius […] The tablet not only includes the oldest trigonometric table in the world; it is also the only completely accurate trigonometric table, taking into account the very different Babylonian approach to arithmetic and geometry.

It is not new that Pythagoras was not the first to realize that the square on the longest side of a right triangle is equal to the sum of the squares on the two remaining sides. The true mystery of the tablet is why the scribes went to the effort to obtain and record the numbers on the piece.

Spherical trigonometry: three right angles within a triangle drawn on a sphere ( Public Domain )

Luis Teia wrote about the possible purpose of the Plimpton 322 tablet  in a previous Ancient Origins article :

Contrary to what one might imagine, the reason for the tablet was not interest in a number theory question, but rather the need to find data for a ‘solvable’ mathematical problem. It is even believed that this tablet was a help for teachers when posing and solving problems related to right triangles. This fact evokes a scenario not unlike today’s classrooms.

Translated copy of the Babylonian ceramic tablet Plimpton 322.  ( Luis Teia )

Dr. Mansfield commented  in a video about the research results  that the base 60 system allowed the Babylonians to obtain more precise results than today using base 10. The different method used by the Babylonians when studying arithmetic and geometry could have “possible practical applications in surveying, computer graphics, and education.”

The tablet is believed  to have been created in the ancient Sumerian city of Larsa sometime between 1822 B.C. C. and 1762 a. c.; but Plimpton 322 gets its name from a New York publisher named George Plimpton, who donated the piece to Columbia University in the 1930s. Researchers have been enamored of the enigmatic tablet ever since. As Dr. Mansfield explains , “Plimpton 322 has baffled mathematicians for more than 70 years, ever since it was discovered to contain a special pattern of numbers known as Pythagorean triples.”

Dr. Mansfield and University of New South Wales Associate Professor Dr. Norman Wildberger have published the findings of their research in the journal  Historia Mathematica .

Dr. Wildberger explained  on Phys.org  that we still have a lot to learn from our ancient ancestors: