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around 2600–2500 BCE

Sumerian Earliest Known Math Table

World's oldest reliably dated mathematical table

Sumerian tablet VAT 12593, held by the Vorderasiatisches Museum in Berlin, was created around 2600 BCE, making it the earliest known mathematical table that has been reliably dated.

Sumerian Earliest Known Math Table

This tablet was created around 2600 BCE in the Sumerian city of Shuruppak. The first two of a total of three columns give length measurements from 3.6 kilometers to 360 meters in descending units of 360 meters, while the final column gives their products as area measures. The sequence continues on the reverse, and probably ended at 1 rod (~6 meters).

Artifact dimensions

14.5 cm × 13.0 cm × 3.2 cm (0.88 kg)

Original artifact location

Shuruppak (historical name), Afak, Al-Qadisiyah, Iraq (current name)

Current artifact location

Vorderasiatisches Museum, Berlin

Catalog number

VAT 12593


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Interactive Content

Computational Explanation

Additional Reading

  • Chrisomalis, S. "Mesopotamian Systems." Ch. 7 in Numerical Notation: A Comparative History. Cambridge, England: Cambridge University Press, pp. 228–258, 2010.
  • Deimel, A. No. 82 in Die Inschriften von Fara, II: Schultexte aus Fara. Wissenschaftliche Veröffentlichungen der Deutschen Orient Gesellschaft, No. 43. Leipzig, Germany: J. C. Hinrichs, 1923.
  • George, A. R. Babylonian Topographical Texts. Orientalia Lovaniensia Analecta 40. Leuven: Peters, p. 119, 1993.
  • Neugebauer, O. and Sachs, A. (Ed.). "Metrology." Ch. 1, § 4 in Mathematical Cuneiform Texts. New Haven, CT: American Oriental Society and the American Schools of Oriental Research, pp. 4–10, 1945.
  • Nilson, H.; Damerow, P.; and Englund, R. K. Fig. 119 in Archaic Bookkeeping. Chicago, IL: University of Chicago Press, 1993.
  • Nissen, H. J. P.; Damerow, P.; and Englund, R. K. Archaic Bookkeeping: Early Writing and Techniques of Economical Administration in the Ancient Near East. Chicago: University of Chicago Press, pp. 30–33, 1993.
  • Powell, M. A. "Mathematik." In Reallexikon der Assyriologoe und vorderasiatischen Archäologie, Vol. 7 (Ed. D. O. Edzard). Berlin/New York: de Gruyter, pp. 457–530, 1990.
  • Robson, E. "Tables and Tabular Formatting in Sumer, Babylonia, and Assyria, 2500 BCE–50 CE." Ch. 1 in The History of Mathematical Tables: From Sumer to Spreadsheets (Ed. M Campbell-Kelly, M. Croarken, R. Flood and E. Robson). Oxford, England: Oxford University Press, Fig. 1.3 and pp. 27–31, 2007.
  • Robson, E. "Mesopotamian Mathematics." Ch. 2 in The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (Ed. V. J. Katz). Princeton, NJ: Princeton University Press, pp. 70–75, 2007.