Deciphered Ancient Tablet Reveals Babylonians’ Mastery Over Mathematics

Australian scientists have deal to crock up the codification of a cryptic 3,700 - twelvemonth - honest-to-goodness Babylonian clay tablet , revealing a degree of mathematical sophistication that pre - date the ancient Greeks by a thumping 1,500 yr .

This Babylonian tab , known as Plimpton 322 , is the globe ’s oldest — and most exact — trigonometric table , according toresearchpublished this week in Historia Mathematica . The University of New South Wales Sydney researchers who cracked the code say the tablet was in all probability used by numerical scribes to aim angles when design palaces , temple , footfall pyramids , and canals . This discovery shows that the ancient Babylonians — and not the Greeks — were the first to contemplate trigonometry , the mathematical study of triangles .

Plimpton 322 was chance on in the other 1900s in southerly Iraq by famed archeologist Edgar Banks , who would go on to be the aspiration for Indiana Jones . date to between 1822 and 1762 BC , the lozenge probably uprise in the ancient Sumerian city of Larsa . Analysis of the tablet showed that the ancient Babylonians knew about the Pythagorian Theorem long before the rise of ancient Greece , but the tablet ’s precise intent remained a mystery story .

One of the potent theories was that it was a teaching help for correspond quadratic problem , but newfangled research direct by UNSW scientists Daniel Mansfield and Norman Wildberger now confirm the marking on the pill as a trigonometry mesa .

After bear a historiographical depth psychology of the tablet ’s purported purpose , Mansfield and Wildberger take a closer feeling at the tablet and its inscriptions . Plimpton 322 features four columns and 15 rows of numbers written in the cuneiform playscript of the time . significantly , this text is write in a base-60 enumeration system , also known as a sexagesimal system ( think of it like the hour on an analog clock ) . Its 15 wrangle describe a sequence of 15 right - angle triangles , which are steady lessen in inclination . Also , the left over - paw edge of the pad is break , meaning parts of Plimpton 322 are miss .

Building on previous research , Mansfield and Wildberger were capable to show that two columns and 23 row are missing — the original pad hold six columns and 38 rows . The tablet contains a special figure of numbers known as Pythagorean three-base hit ( now an anachronism , given that Hellenic mathematician Pythagoras was digest about 1,300 year later ) . This suggests that Plimpton 322 delineate the shapes of right - slant triangles using a fresh form of trigonometry based on ratios , rather than Angle or traffic circle . Thus , scrivener could use the table to carry out the complex task of generating and classify the number on the tablet ; they could take one know ratio of the position of a ripe - angle triangle to square off the other two unknown ratios .

Argentina’s President Javier Milei (left) and Robert F. Kennedy Jr., holding a chainsaw in a photo posted to Kennedy’s X account on May 27. 2025.

“ It is a fascinating numerical work that demonstrates undoubted genius , ” exclaimed Mansfield in a instruction .

Crazily enough , Plimpton 322 is not just the oldest trim tabular array , the researchers say it ’s the most accurate trig mesa on record book , on chronicle of the ancient Babylonians ’ unique base-60 plan of attack to arithmetic and geometry ( try dividing 1 by 3 and you ’ll instantly run into the limitation of our base-10 organization ) . And as note , it ’s also rewrite history ; Greek astronomer Hipparchus , who experience around 120 BC , is normally considered the launch Church Father of trig . His “ board of chords ” on a circle was the one-time trim table , until now .

“ Plimpton 322 predates Hipparchus by more than 1,000 year , ” said Wildberger . “ It opens up new possibleness not just for modern mathematics research , but also for mathematics education . With Plimpton 322 we see a elementary , more accurate trigonometry that has clear advantages over our own . A gem - trove of Babylonian tablets survive , but only a fraction of them have been studied yet . The mathematical world is only waking up to the fact that this ancient but very advanced mathematical culture has much to teach us . ”

William Duplessie