Diophantus’s Arithmetica represents the most extensive treatment of arithmetic problems involving determinate and indeterminate equations from Greek times. It is clear from the sources that Diophantus did not create the field anew but was heavily dependent on the older Greek tradition. Although it is difficult to assess how much he improved on his predecessors’ results, his creativeness in solving so many problems by exploiting new stratagems to supplement the few general techniques at his disposal was impressive.
The Arithmetica was instrumental in the development of algebra in the medieval Islamic world and Renaissance Europe. The Arabic writers al-Khazin (fl. c. 940), Abul Wefa (940-998), and al-Karaji (fl. c. 1010), among others, were deeply influenced by Diophantus’s work and incorporated many of his problems in their algebra textbooks. The Greek books have come to the West through Byzantium. The Byzantine monk Maximus Planudes (c. 1260-c. 1310) wrote a commentary on the first two Greek books and collected several extant manuscripts of Diophantus that were brought to Italy by Cardinal Bessarion. Apart from a few sporadic quotations, there was no extensive work on the Arithmetica until the Italian algebraist Rafael Bombelli ventured into a translation (with Antonio Maria Pazzi), which was never published, and used most of the problems found in IG-VIG in his Algebra, published in 1572. François Viète, the famous French algebraist, also made use of several problems from Diophantus in his Zetetica (1593). In 1575, the first Latin translation, by Wilhelm Holtzmann (who grecized his name as Xylander), appeared with a commentary. In 1621, the Greek text was published with a Latin translation by Claude-Gaspar Bachet. This volume became the standard edition until the end of the nineteenth century, when Paul Tannery’s edition became available. A new French-Greek edition of the Greek books is planned since the Tannery edition is long outdated.