Trigonometry Discovered on a 3700-Year-Old Ancient Babylonian Tablet

One pre­sump­tion of tele­vi­sion shows like Ancient Aliens and books like Char­i­ots of the Gods is that ancient people—particularly non-west­ern people—couldn’t pos­si­bly have con­struct­ed the elab­o­rate infra­struc­ture and mon­u­men­tal archi­tec­ture and stat­u­ary they did with­out the help of extra-ter­res­tri­als. The idea is intrigu­ing, giv­ing us the huge­ly ambi­tious sci-fi fan­tasies woven into Rid­ley Scott’s revived Alien fran­chise. It is also insult­ing in its lev­el of dis­be­lief about the capa­bil­i­ties of ancient Egyp­tians, Mesopotami­ans, South Amer­i­cans, South Sea Islanders, etc.

We assume the Greeks per­fect­ed geom­e­try, for exam­ple, and refer to the Pythagore­an the­o­rem, although this prin­ci­ple was prob­a­bly well-known to ancient Indi­ans. Since at least the 1940s, math­e­mati­cians have also known that the “Pythagore­an triples”—inte­ger solu­tions to the theorem—appeared 1000 years before Pythago­ras on a Baby­lon­ian tablet called Plimp­ton 322. Dat­ing back to some­time between 1822 and 1762 B.C. and dis­cov­ered in south­ern Iraq in the ear­ly 1900s, the tablet has recent­ly been re-exam­ined by math­e­mati­cians Daniel Mans­field and Nor­man Wild­berg­er of Australia’s Uni­ver­si­ty of New South Wales and found to con­tain even more ancient math­e­mat­i­cal wis­dom, “a trigono­met­ric table, which is 3,000 years ahead of its time.”

In a paper pub­lished in His­to­ria Math­e­mat­i­ca the two con­clude that Plimp­ton 322’s Baby­lon­ian cre­ators detailed a “nov­el kind of trigonom­e­try,” 1000 years before Pythago­ras and Greek astronomer Hip­parchus, who has typ­i­cal­ly received cred­it for trigonometry’s dis­cov­ery. In the video above, Mans­field intro­duces the unique prop­er­ties of this “sci­en­tif­ic mar­vel of the ancient world,” an enig­ma that has “puz­zled math­e­mati­cians,” he writes in his arti­cle, “for more than 70 years.” Mans­field is con­fi­dent that his research will fun­da­men­tal­ly change the way we under­stand sci­en­tif­ic his­to­ry. He may be over­ly opti­mistic about the cul­tur­al forces that shape his­tor­i­cal nar­ra­tives, and he is not with­out his schol­ar­ly crit­ics either.

Eleanor Rob­son, an expert on Mesopotamia at Uni­ver­si­ty Col­lege Lon­don has not pub­lished a for­mal cri­tique, but she did take to Twit­ter to reg­is­ter her dis­sent, writ­ing, “for any his­tor­i­cal doc­u­ment, you need to be able to read the lan­guage & know the his­tor­i­cal con­text to make sense of it. Maths is no excep­tion.” The trigonom­e­try hypoth­e­sis, she writes in a fol­low-up tweet, is “tedious­ly wrong.” Mans­field and Wild­berg­er may not be experts in ancient Mesopotami­an lan­guage and cul­ture, it’s true, but Rob­son is also not a math­e­mati­cian. “The strongest argu­ment” in the Aus­tralian researchers’ favor, writes Ken­neth Chang at The New York Times, is that “the table works for trigo­nom­ic cal­cu­la­tions.” As Mans­field says, “you don’t make a trigo­nom­ic table by acci­dent.”

Plimp­ton 322 uses ratios rather than angles and cir­cles. “But when you arrange it such a way so that you can use any known ratio of a tri­an­gle to find the oth­er side of a tri­an­gle,” says Mans­field, “then it becomes trigonom­e­try. That’s what we can use this frag­ment for.” As for what the ancient Baby­lo­ni­ans used it for, we can only spec­u­late. Rob­son and oth­ers have pro­posed that the tablet was a teach­ing guide. Mans­field believes “Plimp­ton 322 was a pow­er­ful tool that could have been used for sur­vey­ing fields or mak­ing archi­tec­tur­al cal­cu­la­tions to build palaces, tem­ples or step pyra­mids.”

What­ev­er its ancient use, Mans­field thinks the tablet “has great rel­e­vance for our mod­ern world… prac­ti­cal appli­ca­tions in sur­vey­ing, com­put­er graph­ics and edu­ca­tion.” Giv­en the pos­si­bil­i­ties, Plimp­ton 322 might serve as “a rare exam­ple of the ancient world teach­ing us some­thing new,” should we choose to learn it. That knowl­edge prob­a­bly did not orig­i­nate in out­er space.

Relat­ed Con­tent:

How the Ancient Greeks Shaped Mod­ern Math­e­mat­ics: A Short, Ani­mat­ed Intro­duc­tion

Ancient Maps that Changed the World: See World Maps from Ancient Greece, Baby­lon, Rome, and the Islam­ic World

Hear The Epic of Gil­gamesh Read in the Orig­i­nal Akka­di­an and Enjoy the Sounds of Mesopotamia

Josh Jones is a writer and musi­cian based in Durham, NC. Fol­low him at @jdmagness

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  • Jim says:

    Our soci­ety today can­not have a con­ver­sa­tion with­out get­ting extreme­ly polit­i­cal­ly cor­rect. This only accom­plish­es shut­ting down dia­logue and sup­press­ing infor­ma­tion.

  • Garry says:

    Him, How is trigonom­e­try extreme­ly polit­i­cal­ly cor­rect? And what’s wrong with hav­ing respect for fel­low human beings any­way? It actu­al­ly enables all peo­ple to com­mu­ni­cate and work togeth­er ami­ca­bly and roduc­tive­ly which has to be bet­ter than the alter­na­tive.

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