Plimpton 322 and Babylonian exact sexagesimal trigonometry

Last week on Aug 24 Daniel Mansfield and I published the paper “Plimpton 322 is Babylonian exact sexagesimal trigonometry” in Historia Mathematica online. The paper has had a huge media response, partly due to the excellent press release created for us by Deb Smith from the Faculty of Science, UNSW Sydney, and partly by the lovely video put together by Brad Hall at UNSWTV with Daniel presenting an overview of our discovery that Plimpton 322 (P322), the world’s most famous Old Babylonian (OB) clay tablet, is actually the world’s first trigonometric table, and also the world’s most exact trigonometric table!!


These are remarkable claims that are sure to raise eyebrows not just in the historical community, but also in the mathematical one. How can an unknown scribe, writing almost 4000 years ago with a cuneiform wedge on a small clay tablet, possibly have understood trigonometry not only before anyone else, but in a fashion quite different from anything since (at least, everything before my book on Rational Trigonometry published in 2005)?

Could it really be that this ancient form of ratio-based trigonometry, which completely avoids all mention of angles, actually contains a more profound understanding of this fundamental subject than all those hundreds of subsequent tables? Might it be that we are on the verge of a major shift in our understanding of how to teach trigonometry to high school students by incorporating this new/ very old understanding? And could it be that the powerful sexagesimal system that the ancient Sumerians first devised and that is essential to the understanding of P322 holds powerful advantages for modern computing?

And of course: do we need to seriously re-evaluate the role of OB mathematics in the history of the subject? How many other important mathematics that is currently credited to the Greeks actually is due to the much earlier cultures of the Sumerians/Akkadians/Babylonians and/or the Egyptians?

These are fascinating questions that we hope will be among those discussed as the result of our work. But we do hope that people debate these and other important issues after at least having looked at our paper in some detail. Unfortunately some serious historical academics, as well as at least one science journalist, have leapt to negative conclusions without giving our paper a serious reading.

Eleanor and Evelyn: here is the link to the paper again — please have a go at  digesting our arguments, which we have spent two years carefully crafting, and which we are confident will change your orientation to this tablet: Plimpton 322 is far more than a teaching aid for teachers to cook up quadratic problems for their students. It is a work of undisputed genius which required a deep understanding of the trigonometry of a right triangle, and took a huge amount of effort to compile.

Anyway, I anticipate quite a few more posts on this fascinating development.

2 thoughts on “Plimpton 322 and Babylonian exact sexagesimal trigonometry

  1. Tom W.

    Fascinated and eager to read more on this from you! I’m have expecting to see Rational Trig emerge from this, I know there’s a link in there somewhere!


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