Mathematics in Ancient Egypt

Beatrice Lumpkin

The chance preservation of artifacts from Ancient Egypt has provided us with a number of mathematical papyri that may or may not be a fair representation of A. E. mathematics. I feel fortunate to have been alerted to a reference to "an Egyptian zero" while discussing AE mathematics with Egyptologist Frank Yurco in Chicago. This reference was based not on a mathematical papyrus, but on balance sheets in papyrus Bulaq 18, a bookkeeping record written 3700 years ago and translated to German in the 1920's. A. Spalinger has provided a discussion and translation in English: "Notes on the Day Summary Account of P. Bulaq 18 and the Intradepartmental Transfers," in Studien Zur Altaegyptischen Kultur 12, 1985.

There was also a zero reference level marked on construction lines used as early as 2700 BCE. These lines, still visible at Old Kingdom pyramids and tombs, show the beginning of metricizing space, using concepts that do not appear in the mathematical papyri. These subjects are discussed in my article, B. Lumpkin. "Mathematics Used in Egyptian Construction and Bookkeeping," in The Mathematical Intelligencer, vol. 24, no. 2, 2002, 20-25. A further discussion, largely based on Lepsius' work newly translated to English, will appear next year: Beatrice Lumpkin, "Ancient Egyptian Mathematics and Forerunners: Some Hints from Work Sites," in: A Delta-man in Yebu, ed. A.K. Eyma and C. Bennett, Occasional Volume of the Egyptologists' Electronic Forum, no.1 (2003, forthcoming). The translation of Lepsius, side by side with the original German, is titled Richard Lepsius, The Ancient Egyptian Cubit and Its Subdivision (1865) translated by J. Degreef and edited by Michael St. John. It is available from the publishers, The Museum Bookshop Ltd., 36 Great Russell Street, London WC1B 3QT( The article for the EEF volume has been enriched by footnotes added by editor A.K. Eyma. These footnotes supply an extensive list of linguistic references for the Egyptian word nfr, a word that had many uses. Usages of mathematical interest include representation of a zero remainder in a bookkeeping papyrus and using a zero reference point on construction lines. *This information was first published in the Archives of the Historia Matematica Discussion Group, October 2002. Beatrice Lumpkin is a scholar of African Intellectual history, in general, and Ancient Egyptian Mathematics, in particular.