« Antiquity in the shape of a Canon.

In the ancient extant Chinese writings in which practitioners evoke the genesis and history of mathematics, Antiquity plays a key part. Features of mathematical knowledge on which these texts place emphasis and which are in fact, as we now know, specific to China (such as a conception of the overall architecture of mathematics, its organization in nine sections), properties attached to it (such as its power), are referred to the way in which it developed in Antiquity. In addition to this, representations of Antiquity play an essential role in shaping practices of mathematics to which these writings attest. These remarks lead me to the two main issues I shall address in this paper. In a first part, I shall focus on analyzing the perception of Antiquity disclosed by how the discourse about mathematics put it into play. In the following two parts, I shall describe how representations of Antiquity shaped some of the mathematical practices to which these texts bear witness: respectively, editing scriptures from Antiquity and investigating them. The earliest of such writings turns out to be the commentary Liu Hui 咸 敲 completed in 263 on the Canon The Nine Chapters on Mathematical Procedures (Jiuzhang suanshu ù 珍偬置)—hereafter abbreviated to The Nine Chapters—, which is today believed to hav