Von Zahlen und Zahlworten bei den Alten Ägyptern (Concerning the Numbers and Numerals of the Ancient Egyptians)

by Kurt Sethe

Amice Mary Calverley
Kurt Sethe (1869-1934)

Kurt Sethe (1869-1934), was one of the greatest Egyptologists of his time. His work on Egyptian mathematics is not as well known as his other works. Von Zahlen und Zahlworten bei den Alten Ägyptern (Concerning the Numbers and Numerals of the Ancient Egyptians), published at Strassburg in 1916 (147 pages with three folding plates at the rear) in the middle of the First World War, deserves wider circulation.

It is divided into four main sections:
(1) ‘The Numeral System of the Egyptians’
(2) ‘Cardinal Numbers’
(3) ‘Fractions’
and
(4) ‘Ordinal Numbers’.

This is a truly thorough and fundamental study of the subject from the basic sources, utilizing Sethe’s profound knowledge of the Egyptian language. Some persons may be puzzled by Sethe’s frequent references to ‘Cantor’ in his footnotes. They are not to the mathematician Georg Cantor (1845-1918), famous for his transfinite numbers, but to the historian of mathematics, Moritz Cantor (1829-1920), author of the monumental Geschichte der Mathematik (History of Mathematics, published 1880-1908) in four volumes, which has unfortunately never been translated into English. The two Cantors, being contemporary, are sometimes confused with one another, especially when references to them are simply to ‘Cantor’. The references to ‘Hultsch’ are to Friedrich Hultsch (1833-1906), the famous classical scholar and editor of Polybius, who was also an expert on ancient coins and metrology. It is important to bear in mind that the work by Sethe was published seven years prior to the publication of the mathematical Rhind Papyrus in English translation by T. Eric Peet (in 1923). Sethe’s knowledge of the Rhind Papyrus was thus drawn from the German translation by August Eisenlohr published in 1877 in two volumes. This does not by any means negate the importance of Sethe’s work, which is a massive scholarly achievement of which few scholars would have been capable, but one must continually bear in mind the need to take account of the updating of many of Sethe’s observations in the light of what came to be known subsequent to Sethe’s book of 1916, with Peet’s further extensive work on the Rhind Papyrus. In his 1923 book The Rhind Mathematical Papyrus, Peet cites Sethe in his own text, not only Sethe’s book, but also a journal article by him. The foundation’s copy of Peet’s original book is extensively  annotated with marginal notes and corrections by an unknown expert in Egyptian mathematics in the late 1920s, who has recorded on the title page that Sethe reviewed Peet’s book in 1925 in a German mathematical journal, the Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 33, pp. 139 ff.  The Foundation is pleased to make Sethe’s important work on Egyptian mathematics available in its entirety, from the Foundation’s own copy, as a pdf download, in order to facilitate a fuller and deeper understanding of the world of Egyptian mathematics. Further material will be posted on this subject on future occasions.

Download original German version as PDF