Beatrice Lumpkin    
Mathematics in Ancient 
Egypt by 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 Intra
departmental 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(mbooks@btconnect.com).

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.