What's Sumerian for "D-"? Suen-apil-Urim's first attempt at a math exercise (top) had to be repeated 4 days later (bottom).

Even Sumerians Had Homework

BALTIMORE--A four-millennium-old set of clay tablets has given a surprising new insight into ancient mathematics. The tablets, which scholars believe came from the Sumerian city of Larsa (in modern-day Iraq), show how long it took scribes to learn their multiplication tables. "It's a first for any scribal tradition," says Eleanor Robson, an intellectual historian at the University of Oxford, United Kingdom.

Modern historians already knew a lot about how Sumerian scribes learned their mathematics, even the order in which they learned their lessons. But one critical piece of information was missing: how long students spent mastering math.

According to Robson, who presented her findings here last week at the Joint Mathematics Meetings, that uncertainty may be over. She analyzed two tablets stored at Oxford's Ashmolean library and concluded that they are multiplication tables used by an aspiring Sumerian scribe named Suen-apil-Urim. Students created these tablets when memorizing multiplication tables "to show teachers that they've memorized the whole lot," Robson says. Suen-apil-Urim wrote down the product of 24 and various other numbers, but his first tablet, written on the 9th day of the harvest month (in late winter) had some errors, so he had to do it again 4 days later.

What makes these tablets especially valuable is that they are signed and dated. A third tablet written by Suen-apil-Urim, housed at Yale University, is a 4-times table, which comes somewhat later in the Sumerian math curriculum. Not only did the Yale tablet pin down the year the tablets were created (1815 B.C.), but also showed that it took 6 months for the scribes to progress from learning the 24-times tables to the 4-times tables. Given the progression of the curriculum, Robson concludes that it took about a year for Sumerian scribes to learn how to multiply.

"This is a very interesting clue and very important if the extrapolation is correct," says Steve Tinney, a Sumerologist at the University of Pennsylvania in Philadelphia. Although Suen-apil-Urim spent a year struggling to learn his times tables, he'd no doubt be pleased that his schoolwork has taught something to scholars nearly 40 centuries later.

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