Cuneiform tablets show the Babylonians’ advanced mathematical knowledge

The tablet key to undestand the ancient Babylonians' mathematical knowledge (Image courtesy Mathieu Ossendrijver / Science. All rights reserved)
The tablet key to undestand the ancient Babylonians’ mathematical knowledge (Image courtesy Mathieu Ossendrijver / Science. All rights reserved)

An article published in the journal “Science” describes the discovery of the ancient Babylonian mathematical knowledge. Putting together the translation of various cuneiform tablets, Mathieu Ossendrijver, professor of the History of Ancient Science at Humboldt University in Berlin, concluded that the Babylonians knew the basics of calculus over 14 centuries earlier than previously thought and they used it to calculate the motion of the planet Jupiter.

It was already known that the Babylonians had developed certain mathematical techniques and used them to calculate the motion of Sun, Moon and planets but until now it was thought that this was arithmetics at a level simpler than calculus. It was believed that the basis for this more advanced mathematics was laid in the 14th century in Europe and then developed by Newton and Leibniz in the 17th century. The discoveries made by Ossendrijver tell a different story.

Mathieu Ossendrijver has a doctorate in astrophysics and one in Assyriology specializing in Babylonian astronomy. In his work as a historian of ancient science he’s been studying for years the tablets of the British Museum’s vast collection, which spans centuries of history.

In particular, Mathieu Ossendrijver’s interest turned to a total of four tablets that contained geometrical techniques concerning instructions to construct trapezoidal figures. In two of these tablets there are references that sees about the planet Jupiter, which symbolized the Babylonian god Marduk, their main deity.

Unfortunately, the four tablets were only partial so the texts arrived to us incomplete. As a result, it was impossible to confirm all the references. The key came from a fifth tablet of which another Assyriologist, Hermann Hunge, in 2014 showed the photos to Mathieu Ossendrijver. It shows the same trapezoidal calculations but also describes the motion of the planet Jupiter.

Putting together all the information gathered from the five tablets, Mathieu Ossendrijver concluded that the mathematical techniques described used to calculate the motion of Jupiter are the same at the base of calculus. The astronomers and mathematicians who developed and used these techniques were also priests and their knowledge was kept within their caste. When their civilization collapsed and the knowledge of the cuneiform writing got lost, their knowledge was forgotten too.

Today we’re rediscovering knowledge of ancient peoples that had been lost for centuries and that of Babylonian mathematics is an example. This research brought together archeology, mathematics and astronomy to interpret ancient tablets showing the need to use different types of competence to understand the ingenuity of the ancients.

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