##### The earliest known mathematical exercise

*Artifact*: Clay tablet

*Provenience*: Uruk, modern Warka

*Period*: Uruk IV (ca. 3350-3200 BC)

*Current location*: University of Heidelberg, Heidelberg (W 19408,76+)

*Text genre, language*: School text, mathematical exercise; undetermined

CDLI page

*Description*: Peter Damerow and Bob Englund in Heidelberg.

Holding on to the grab rail of his somewhat dated Golf GT on our way to Heidelberg in the spring of 1985, I asked Peter why he felt he had to drive at such fearful speeds on the autobahn. His answer was a lesson in the obvious: “So kommt man schneller an!” (That way, you get there faster!). That fleet trip to collate texts in preparation of our chapter on the numerical sign systems of the archaic texts from Uruk (*ATU* 2, 117-166) resulted in many corrections in our preliminary study of the numerical notations on these texts from the latter half of the 4th millennium—although the unlimited access to the full collection graciously afforded us by Karl-Heinz Deller tested even Peter’s resolve to work his usual 16-hour days. Surely the most memorable moment was his discovery of the text in the figure above, W(arka) 19408,76, dating to ca. 3350 BC. I knew that, when the room grew quiet, Peter was calculating, and in this case it was no different. As he explained, the text from the earliest stage of writing contained several varied multiplicands representing field lengths and widths, leading in exercises on obverse and reverse to the same result of an irregularly large, but very rounded surface measure notation of 10 szar2, or ca. 40 km2. This earliest known school text in mathematics demonstrated the playful arrangement scribes of the 34th century BC had made with their new medium of expression. (Robert K. Englund,
UCLA)

*Edition(s)*: Englund, Robert K. & Nissen, Hans J., *ATU* 7 (Berlin 2001) pl. 14, W 19408,76+; *ATU* 2, plate 59; Nissen, Hans J., Damerow, Peter & Englund, Robert K., *Frühe Schrift und Techniken der Wirtschaftsverwaltung im alten Vorderen Orient* (Berlin 1990) 98, no. 12.3; discussed by J. Friberg, *AfO* 44/45 (1997/98) 10; R. Englund in J. Bauer, R. Englund and M. Krebernik, *OBO* 160/1 (Freiburg Switzerland 1998) 210 fig. 85.