The sources of 14th century Italian texts of Abacus: the echoes of an ongoing debate

The most common opinion among historians of mathematics is that Fibonacci's Liber Abaci - or at least the first eleven chapters - was the precursor of the Italian textual tradition of the Abacus and, with respect to the origin of Abacus algebra in Italian, the Libro di ragioni from Paolo Gerardi (1328) was the oldest text on algebra so far known. These ideas have been challenged by many works of J. Hoyrup. He maintains that Fibonacci was not a precursor, but only an important exponent of pre-existing Abacus tradition and that the first algebra text in Italian was the Tractatus Algorismi by Jacopo da Firenze. In particular, he articulated all his positions in his book, Jacopo da Firenze's Tractatus Algorismi Abbacus and Early Italian Culture, which has been the subject of a debate. The author of this article tries to summarize the central theses of Hoyrup and explain the different positions taken by the participants in the debate. She will also explain her position in a few cases and her final point of view.