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(firstname.lastname@example.org).
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 an outstanding scholar of African
Intellectual history, in general, and
Ancient Egyptian Mathematics, in particular.