Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin

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In the 1920s it was recognized, largely as a result of work by Otto Neugebauer and his colleagues that Babylonian cuneiform texts included many mathematical texts. These were chiefly concerned with metrology and computation, but some also appeared to deal with algebra. But then, what could have been the reasons that induced the Babylonians to work on, for example, second-degree equations? In this new examination of the texts, Jens Hoyrup proposes a different interpretation, based on the fact that the tablets are almost entirely students’ workbooks. The knowledge of mathematics expressed in these tablets is entirely practical, for use in surveying, accounting, and building, rather than theoretical. Hoyrup argues that the notion of algebraic manipulation, like other parts of a theoretical mathematics is indeed a later invention. Craftsmen, he argues, prefer to know how to solve a problem, rather than why the answer will be true, and it is only the latter attitude that characterizes mathematics; the former is, perhaps, more akin to modern engineering. The book provides a detailed reading of many tablets and a careful examination of the context in which they were produced.