Mathematics in the time of the pharaohs By Richard J. Gillings. Cambridge, Mass. (M.I.T. Press), 1972. 297 p. US $25

AbstractThe author's treatment of many problems and some of his hypotheses are original and elegant. He does not limit himself to describing the content of his sources but tries to reveal the paths followed by the Egyptians as well as their ideas and methods. This leads him to interesting and on the whole covinncing reconstructions and results. For example, the author concludes that there must have existed extensive addition tables that have not survived.Although the materials available today seem insufficient to explain how the Egyptians happened to use the qlumsy binary method mu multiplication and division, Gillings' discussion throws light on the problem and poses questions for further research. Careful analysis of special tables and solutions of problems and the comparison of sources enable the author in large measure to reveal the methods and ideas of Egyptian mathematicians. How the Egyptians constructed their tables still remains an unsolved problem. Because divisions sometimes began by dividing by 3, Gillings concludes that tables for 3 must have existed and his reconstruction of such a table has great interstt. His Rule G for sums and differences of fractions is original and ingenious. He strsses the importance of EMLR. He argues that the Egyptians used the concepts of arithmetic and harmonic means. He gives an interesting explanation for the origin of the Egyptian formulas for squaring the circle, though its simplicity is clear only after the result is known.Although answers are not given to all questions, the book leads the reader to search for answers, to formulate new reconstructions, and to make new hypotheses. This is its greatest merit