Mathematics in the Time of the Pharaohs [Englisch] [Taschenbuch]

The Rhind, Moscow, and other important mathematical papyri decoded in every detail. A sweeping tour through the ancient Egyptian methods of calculation, parts of which are still used today in computer code! In his well-written account, Mr. Gillings makes it very clear that the common view on ancient Egyptian mathematics as 'rather primitive' is definitely to be revised. Provided with a few basic tools, the scribes of the epoch were able to carry out very complicated computations indeed, at times involving several different units. Their rough-and-ready estimate of pi was off by only 0.6 percent as compared to the correct value. The author presents a rich variety of calculated examples and explains the logic behind them. Earlier researchers in the field are commented.

Gillings attempted to bring together all the known hieratic mathematical texts. Even the Akhmim Wooden Tablet (AWT) was mentioned as a footnote. Though not analyzed in any section, the AWT and the hieratic math texts outline an exciting book. Taken together the Middle Kingdom math texts were read as one document, one text checking the another text for errors and omissions. In great part Gillings followed that rule.

Exceptions to the rule lie in the reporting of five texts, and aspects of other texts. The five under valued texts are the AWT, the Egyptian Mathematical Leather Roll, the Reisner Papyri, the Kahun Papyrus, and the RMP. All five texts were reported by Gillings with minor oversights becoming major oversights when oversights were placed in the larger context of scribal meta mathematics.

Concerning the EMLR, Gillings' oversight consisted of four of the 26 lines of texts, only reporting them as additive in scope, as were the other 22 lines. Actually a higher form of abstract arithmetic should have been discussed as potentially present.

The Reisner Papyri was discussed as containing quotients, which it does. Gillings' oversight was not mentioning the remainders that filled the scribal overseer notes from a construction site where daily worker digging rates were measured in units of 10. Hence all of the digging rates were divided by 10, and were reported by the scribe as quotient and remainder totals, a remainder arithmetic fact that escaped Gillings analysis. One scribal error was corrected by Gillings, properly listing a quotient and remainder; however, the proper modern name for the ancient arithmetic was not potentiallly commented upon by Gillings.

Finally, throughout the RMP quotients and remainders fill the document for almost every division and subtraction that Ahmes reported in his 84 problems. Yet, again, only quotients are mentioned, from time to time, with the remainder aspect of Egyptian fractions often being the major component, were not commented upon by Gillings. A clear example of Gillings' oversight is cited on page 250 "Horus-Eye fractions in terms of hin", where 29 divisions of a hekat, a volume unit, were divided by rational numbers in the range 1/64 to 64, with each answer written down as quotients and remainders. All of the two-part statements were created from the hekat unity, (64/64), being divided by a divisor n, or: (64/64)/n = Q/64 + (R5/n)*1/320, with Q the quotient and R the remainder. As a passing comment, Gillings also missed Ahmes' hin rule, 1/10 of the hekat, creating a one-part number by using 10/n hin, as listed 29 times in the table, the additive context in which Gillings incorrectly reported the totality of the table.

Returning the the Akhmim Wooden Tablet, the text reported in vivid terms a hekat unity (64/64) divided by 3, 7, 10, 11 and 13. The answers used binary quotients and scaled remainders, an abstract form of arithmetic used in the RMP 40 times. Georges Daressy first reported aspects of the AWT in 1906. Gillings cited none of Daressy' ground breaking work. Daressy's incomplete analysis OF THE AWT was finally corrected on the proof side, in 2002 by Hana Vymazalova, a Charles U., Prague, graduate student.

In summary, Gillings' main 1972 point: that Egyptian mathematics must be revisited and updated is true. 21st century math historians have taken up the 1972 challenge and completing the decoding of the hieratic texts as one body of knowledge. A Charles University grad student, Hana Vymazolva, and other young students are finding pieces of a large jig-saw puzzle. Humpty dumpty is being put back together again, thanks to the urgings of Gillings.