Comparison of histories, history of comparison: A plea to re-investigate mathematical cases from india and china

The comparative method is intrinsic to the history of science. Despite this fact, studies comparing Chinese and Indian mathematical texts remain few. Scholars have long noticed similarities between Chinese and Indian algebraic results and procedures, numeration systems and astronomy. Yet, these comparisons raise interesting questions for historiography: as mathematical texts are written in classical Chinese and Sanskrit, corpuses became representative of so-called ‘Chinese mathematics’ or ‘Indian mathematics’, thus reducing the concept of culture to nation or civilization. Since Wylie’s first comparative study in 1852, many scholars have focused on the resemblance between Chinese and Indian indeterminate equations. The analysis of India’s contribution to the solution of indeterminate equations (kuṭṭaka) and the dayan method of Qin Jiushao constitutes an essential part of the historiography of the comparative study of mathematics in India and China. The aim of this article is twofold: 1) to investigate the construction of this history, in particular how the concept of transmission depends on prejudice regarding algorithms; and 2) to propose an alternative ways of comparison and show their promise. To reveal the heuristic dimensions of contrast, I am going incorporate recent studies on epistemic cultures as well as an example based on two medieval treatizes by Li Ye and Nārāyaṇa and their relation to cognitive tasks.