Which texts should be canonized, and what mathematical knowledge could be considered “standard,” were important issues for practitioners of mathematics in premodern East Asia. The Jiuzhang suanshu had been listed as one of the mathematical canons in Korea since the seventh century before it was lost by the fifteenth century. The canons were replaced by texts from China's Song-Yuan period. Those texts introduced an algebraic method called Tianyuan shu (the “old” method), which was well kept in Korea after its introduction to the peninsula but lost in China from the fifteenth century until its recovery in the eighteenth century. So the Tianyuan shu became a distinctive mark of traditional Korean mathematics. Since the mid-eighteenth century, the imperially composed Shuli jungyun was recognized as the mathematical canon in Qing China and Chosŏn Korea, and the main algebraic method Jiegenfang (the “new” method), a kind of cossic algebra introduced by the Jesuits, was used by both Chinese and Korean scholars. The works of Korean mathematician Nam Pyŏng-Gil (1820–69) include some of the most interesting examples of “dialogues” between the two algebraic methods. At first he believed that the two methods were identical. After he studied the newly recovered Siyuan shu, also originating in the Song-Yuan period, Nam realized that it could be seen as a generalization of the Tianyuan shu, thus enabling the “old” method to solve a wider range of problems than the “new” one. Influenced by the evidential studies in China and the trend of “practical learning” in Korea, Nam changed his mind, favoring the “old” method for its practical usefulness and its status as a distinctive mark of Korean scholarship. He tried to make the “old” method a standard in his country, and he did it in a subtle way. Nam wrote a compendium of mathematics, suggesting that it was a “standard,” and in the text he used the “new” method in the imperial canon to endorse the “old” one, and then solved problems with the “old” method. Nam Pyŏng-Gil's case provides an interesting example of the interaction between mathematical knowledge and its social context.
