Needham and Wang go on to argue that the numerals attested indicate that an evolution took place in China, at the end of which a decimal place-value notation emerged. They begin their account with the earliest forms found, those on “Shang oracle-bones (-14th to -11th centuries)” (column E in the table). The account of numeral notations given by Needham and Wang draws on a table entitled ‘Ancient and medieval Chinese numeral signs,'. Mathematics,” published in Joseph Needham’s (1900-1995) famous encyclopaedic book Science and Civilisation in China, and jointly composed by Needham and Wang Ling (1917-1994). To explain this point, I will focus on how the history of numbers in China was treated in a monograph that served as a basis for Guitel’s and Ifrah’s chapters on China, namely section “19. In a way, it seems natural to us that a “History of Numbers” adopts a structure of this kind -that is, to use Guitel’s words, that it gives pride of place to “peoples” and “civilizations.” However, is it so obvious that a structure like this is appropriate? I argue that this feature derives from a tacit assumption that has been widely adopted when it comes to the history of numbers and that needs to be reconsidered. Moreover, horizontal arrows marking the “evolution” of numeration systems are added to the tree, and they also connect “Egypt I” with “Egypt II” and “Egypt III” as well as “Greece II” and “Greece III,” etc. The leaves of the tree read: “Egypt I (hieroglyphic),” “Aztecs”, “Greece I (attic),” “Rome”, “Sumer,” “Egypt III (hieratic),” “China I (oracle-bones),” and so on. Similarly, the structure of Geneviève Guitel’s Histoire Comparée derives from a classification of the numeration systems she considers.
For instance, Georges Ifrah’s monograph is organized as: ‘Numbers of Sumer’, ‘The Development of Written Numerals in Elam and Mesopotamia’, ‘Mesopotamian Numbering after the Eclipse of Sumer’, ‘The Numbers of Ancient Egypt’, ‘Greek and Roman Numerals’, ‘The Numbers of Chinese Civilisation’, and so on. Beyond the differences between books of this kind, they all share a similar structure. The world history of numeration systems is a subject on which many synthetical books are available today, such as Georges Ifrah’s The Universal History of Numbers and Geneviève Guitel’s Histoire comparée des numérations écrites ( Comparative History of Written Numerations), on which the former draws. A Widespread Assumption in the Histories of Numbers
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