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As a theme of historical research, Diophantus' Arithmetica (ca 300 AD) raises two main issues that have been most intensively debated: the first concerns the proper understanding of Diophantus' practice, while the other relates to the identification of the mathematical tradition to which this practice belongs. Since the time of medieval Islam, through the Renaissance and the early modern period, the thesis that the work of Diophantus belongs to the history of algebra has enjoyed broad consensus among mathematicians, despite the fact that the term `algebra' was introduced in the language of mathematics five centuries after Diophantus. Thus, as early as the Middle Ages, the work of Diophantus was recognized by mathematicians as a work on algebra, avant la lettre. The consensus was maintained during the nineteenth and the most part of the twentieth century-this time among historians of mathematics. It is essential to stress, however, that, when associating Diophantus' work with algebra, premodern mathematicians on the one hand and modern historians of mathematics on the other did not start from the same understanding of algebra. Those mathematicians understood algebra with its premodern meaning and, accordingly, characterized the Arithmetica as `algebraic' in the premodern meaning of the term. In contrast, modern historians of mathematics approach the Arithmetica mostly through the viewpoint of a loose understanding of modern algebra and, precisely for this reason, their accounts are often exposed to anachronism. This explains why some contemporary historians of ancient mathematics are reluctant to accept the conclusions of the traditional historiography, while others deny without reservation any relation of Diophantus' practice to algebra. However, criticizing the methodology by which the traditional historiography has reached its conclusion does not necessarily mean that the conclusion itself was wrong. This paper discusses some crucial issues related to Diophantus' problem solving practice, thus, giving support to the traditional view of the algebraic character of his work, but put in a totally new framework of ideas. |
