A new analysis of an ancient Babylonian tablet is forcing historians to rewrite the history of mathematics. The report (Plimpton 322: A Study of Rectangles), written by the Australian mathematician Daniel F. Mansfield, was published in the journal Foundations of Science on August 3rd, 2021. The tablet has been dated to the Old Babylonian period, which occurred around 3600-3800 years ago.
“This broken clay tablet dates from the Old Babylonian (OB) period (1900–1600 BCE) and contains a table of “Pythagorean triples” over a millennium before Pythagoras was born.”
Daniel F. Mansfield
The reason this find is important is because it moves the introduction of applied geometry more than a thousand years farther away from us in time, making it much more ancient than previously believed. It also shows that the Babylonians were practicing this type of math before the Greeks, namely Pythagoras (C6th BCE), the man after which the Pythagorean theorem was named. The difference between the Greek and Babylonian geometry is that the Greeks developed theirs by observing the night sky while the Babylonians were observing the land.
The featured image for this article is of Si.427. This Old Babylonian tablet dates to around 3700 BCE, which is about the same time as Plimpton 322. It shows that the Babylonians were using geometry for land surveying. This helped make sense of Plimpton 322 because it meant that the tablet could have a practical purpose instead of one meant purely for mathematics in a school room or other such setting. Here’s an image of Plimpton 322:
“Like earlier field plans, Si.427 retains the subdivision into rectangles, right trapezoids, and right triangles. But unlike earlier field plans it concerns the sale of private land and the measurements have been made with unusually high precision.”
Daniel F. Mansfield
Together, these two artifacts are challenging old notions about the origins of mathematics. Si.427 was discovered in Sippar in 1894 by Father Vincent Scheil during an archeological expedition. Today, it is displayed at the İstanbul Arkeoloji Müzeleri.
This discovery is only one small piece of the larger puzzle of history. What did the ancient Babylonians know? And when did they know it? Where did math originate? How much did one culture influence another? Are these artifacts authentic? Let me know what you think in the comments.
Sometimes I find plagiarism in news reports but this time around it seemed to me like everyone was on their A game. The original article was published on August 3rd, 2021. I have it listed as my first reference below. The news reports began coming out the following day at 11am.
The original publication was academic but I still recommend reading it. After reading that, I recommend Daniel’s more concise report that he published with The Conversation.
Sara Wells published a news report on this which covers all the basics and provides more details about the discovery. Vice picked up this story and published an article written by Becky Ferreira that goes into Daniel’s past interactions in this field of Old Babylonian mathematics.
Out of the 10 articles that I read about this, the four that I recommended above contain the earliest and novel information on the topic. Each of them provides links for further reading too.
 – Mansfield, D.F. Plimpton 322: A Study of Rectangles. Found Sci (2021). https://doi.org/10.1007/s10699-021-09806-0. Accessed 5 Aug. 2021.
 – Mansfield, D.F. How ancient Babylonian land surveyors developed a unique form of trigonometry — 1,000 years before the Greeks. 4 Aug. 2021 @ 4:08pm EDT. https://theconversation.com/how-ancient-babylonian-land-surveyors-developed-a-unique-form-of-trigonometry-1-000-years-before-the-greeks-163428. Accessed 5 Aug. 2021.
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