從東算術士慶善徵看十七世紀朝鮮一場數學研討會

Kyong Song-jin and a Mathematics Workshop in 17th Century Choson Korea

在東亞數學史上，有關數學知識活動的參與者之社會地位，一直都是極佳的歷史個案，可以幫助我們理解數學與社會的互動關係。在本文中，我們將以十七世紀朝鮮中人算學者慶善徵及其《默思集算法》為例，考察戶曹主司究竟如何管理中人算學者的教育內容。這些相關史實的還原或重建，必定有助於我們釐清下列史實：朝鮮數學的專業化與制度化，如何可以關連到儒家明算者與中人算學者的互動關係。在《默思集算法》中，慶善徵(1616～？)記錄了一場由地方政府首長（都是兩班階級出身）參與的「相會論話」，其中討論有關稅收與支出的官僚實務之五個算學題幹，都以問答形式呈現，至於所涉及算法，則是「盈不足術」、「等比級數」以及「求一術」（解一次同餘問題）。在這一場研討會上，負責總結的「默思翁」應該就是慶善徵本人。果真如此，由中央級的中人算學者主導地方級官吏（含兩班出身的首、令等），這對於數學知識的學術地位之提升，想必助益良多。總之，這一場數學研討會，是東亞數學史上難得一見的個案，也是筆者李建宗深入研讀《默思集算法》時，首度發現並試圖賦予它的歷史意義。事實上，它相當類似今日技術官僚系統中的一場在職進修或研習會，充分反映了中人算學者社群的知識活動內容，值得我們特別注意。

Social status of mathematical practitioners in East Asia, as elsewhere, is among the best examples to help demonstrate interactions between mathematics and society. In this article, the authors will take Kyong Song-jin 慶善徵 (1616-?) as an example, and explore how the chungin mathematicians received in-service training in the bureaucratic system. The content of this training is well illustrated in Kyong Song-jin’s Muksa-jip san-hak 默思集算法, reconstruction of which against the social context would therefore help us to clarify the following historical episodes: how the professionalization and institutionalization of tongsan 東算 (Choson mathematics) can be related to relations between chungin 中人 mathematicians as opposed to Confucian mathematical practitioners. In his the Muksa-jip san-hak, Kyong Song-jin apparently documented a workshop, held for local administrative chiefs (usually of yangban 兩班 origin), in which the participants discussed taxation and fiscal budgets in terms of mathematical problem solving. This was first discovered by Li Chien- Tsung, the second author of this article. Kyong Song-jin adopted a form of dialogue between local officials and their chungin associates, and thereby presented in five problems relevant mathematical requirements for local officials. Towards the end of the workshop, as the text relates, the Old Muksa 默思翁, presumably Kyong Song-jin himself, was responsible for concluding the workshop. One cannot resist the fact that Kyong Song-jin might be the sponsor who was appointed from the central government to monitor the workshop. Whatever the case, the administrative management would have urged local officials of yangban origin to pay attention to the workshop. This may well explain why Confucian mathematical practitioners showed respect to Kyong Song-jin and in turn, the social status of chungin mathematicians would have been improved.