歷史比較，比較歷史：試論重新檢視印度與中國數學案例的必要

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

比較研究法是科學史不可或缺的一部分，但以中國和印度數學文本進行的比較研究仍然不多。學者們長期以來都注意到中國和印度的代數成果、程序、計數系統和天文學間有著相似之處。然而，這些比較研究為史學提出了一個有趣的疑問：因為兩國的數學文本分別以文言文和梵文書寫，兩者的文本成為了所謂「中國數學」或「印度數學」的代表，從而將文化概念降為國族或文明概念。自Wylie在一八五二年首次提出比較研究，許多學者不斷致力於研究中國和印度在不定方程組間的相似性。對印度在不定方程組（kuṭṭaka）的貢獻和解法，以及秦九韶大衍術的研究，都構成了印度和中國數學比較研究史的重要部分。本文具有雙重目的：1）研究歷史書寫的構造，尤其概念傳輸是如何取決於算法的偏見；2）提出一個可替代的比較研究方法和展示其前景。研究者將結合近期有關認識論文化的研究、基於李冶和那拉衍那（Nārāyaṇa）中世紀文本例子和他們與認知研究的關係，以展示這項比較研究的啟發性面向。

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 大衍 method of Qin Jiushao 秦九韶 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 李冶 and Nārāyaṇa and their relation to cognitive tasks.