Number Theory and Combinatorial Analysis

Summary

First introduced in the 10th century, Diophantus’ Arithmetica contributed much to the development of mathematics in the Middle Ages. Most notably it permitted the extension of classical Diophantine analysis, which existed already among the Arabic algebraists, independently of the Arabic translation of Diophantus.

Less well-known but more original, is the contribution of the Arithmetica to the development of new research on modern Diophantine analysis, as that term was understood by Bachet de Méziriac and Fermat. The examination of two unpublished documents in this article demonstrates this fact more clearly than before. The author shows that this research, inspired by a reading of Diophantus, was the work of mathematicians who deliberately placed themselves outside the algebraic tradition and chose an intentionally different style from that of the Arithmetica.