韓國數學史에 관한 硏究

Abstract

The whole world has been moving toward one goal regardless of each individual's concern. Since man's beginning, all races have desired increasing wealth, and the establishment of the welfare state has been a common desire through all ages ever since mankind had wisdom. This tendency inevitably has brought the development of technology to humen beings, and further desire for broad application of the technology organized the farework for science : it has been accelerating the development of civilization. Korean traditional scientific endeavor has been in the mainstream of this development of science. The main purpose of this thesis is to survey Korean traditional mathematics and to try to trace the mathematical thinking of our races. Because of the nature of mathematical achievement, it is not independent from social phenomena like other cultural achievements, therefore, we must discuss the matter along with cultural history, By the bntare of Korea's geographic situation our culture has been heavily influenced by the Chinese. The most influential Chinese mathematical book for Koreans was "Kujang Sansul". It is a mathematical classic for orientals and its influence is not less than the influence which Euclidean geometry has had on western people. Even though it is very elementary, there must have been mathematical developments in the Pre-Three Kingdom Age, but there are no historical remains to show us their nature. Therefore it is necessary to begin with the Three Kingdom Age. Since the kingdom of Koguryo and Paekche were located in the northen part of the peninsula, they enjoyed earlier contact with Chinese civilization than the Silla kingdom. Their agriculture was based on a slave system, International trade with China may have required elementary mathematics and sufficient knowledge was obtained through Chinese books, including "Kujang". Chinese civilization was very highly developed compared to Korea's at that time, and Korea adopted many ideas without hesitation. It is well known that the Kingdom of Paekche re-exported these books and ideas to Japan and Contributed to basic cultural resource of Japan. Lacking records of the Koguryo and Paekche Ages, we simply judge their geometrical knowledge through their rcyal tombs and temples. The agricultural method of United Silla age (668 A.D-935 A.D)was not advanced enough to use higher mathematics, but the administrative system was highly developed with complex taxation requiring skilled mathematics. Silla's school system for mathematicians was well organized. It was the Tang dynasty in China which existed along with Silla, and Tang had a good educational system for mathematicians. It was a sevaen-year training courses and was separated into two ports. In the beginning of Koryo dynasty, the authorities strove to reform Silla's disorganized land system, and land was distributed to government officials according to their rank and degree. However, judging from the fact that had no well organized measurement system, it is doubtful that this attempt was effectively carried out. Koryo imported many books from China, and mathematics were considered one of the important subjects for officials. As a practical matter, governmental officials needed mathematical knowledge for financial and accounting furthermore, measurement of land and composing of calendars reqrired fairly high-level mathematics. The demand for mathematician was small during Koreyo. They could get only lower positions in governmental offices with Rank 9 (Ku-p'um, 九品). It is natural to suppose that economic activities were not developed enough to provide many position for mathematicians. The main mathematical book of Koryo was still "Kujang Sansul", the "Sanhak-Gemong" was used along with Kujang Sansul, Sanhak-gemong was written by Chu Sai-kol and contained many problems concerned with taxation. In particular, Chu Sai-Kol contributed "Chon Wonsul(天元術)". Chon Wonsul was a kind of theory of hemogeneous linear equation. Later, during The Yi dynasty, it was taken to Japan from Korea and become one of the main resource of Japanese mathematics Hwasan (和算). In the beginning of the Yi dynasty(1392-1910), the most important task for the ruler was land reformation, as it was in Koryo's beginning. The Yi dynasty established a well-organized civil service examination and mathematics were selected by examination. These mathematicians were mostly middle class so called "Chang-in (中人)", and the standard textbooks were Sanhak-gemong, Yanghwi-Sanpob (揚輝算法) and Sangmyong Sanbpob (詳明算法). Sejong emphasized the importance of mathematics and his administration was based on his scientific was of thinking. Ch'onwon means literally Heaven's Secrey. Chinese mathematicians in old days put a philosophical interpretation on the theory of equations. "Heaven is chaos and unknown," which nowdays we denote simply by X. Ch'onwiosul is a study for the solution of equations whose coefficients are integral numbers. In the traditional Korean Society astronomers formed a group and independently learned mathematics. This thesis treated mathematical works of these categories with the chronological consideration.;敎學은 人間의 理性的 思考와 직결되어 있으며, 一般的으로 人間文明의 성쇠와 호흡을 같이하고 있으므로, 그 數學이 형성된 思想的 社會的 배경이 數學의 性格 決定을 한다. 따라서 수학은 傳統社會의 東洋과 西洋에 있어서는 이질적인 內容을 갖고 있다. 따라서 수학의 發展을 자극하고 기른 社會的인 條件, 또 그것은 이질적연 體系로 전이시킨 思想的인 배경을 무시할 수 없다. 그러므로 韓國의 數學史를 社會史와 文化史의 側面에서 數學과 一般史의 關係를 考察하며, 東洋과 西洋의 差異點을 比較한다. 特히 東洋에서도 中國·日本과 틀린점을 알아보았다. 韓國의 數學史에서 各 時代마다의 特徵과 그 時代의 日本·中國과 比較.檢討하여 特히 算學制度에 力點을 두고 考察하였다. 西洋數學이 논리위주의 數學이 된 理由는 희랍의 論理思想이 그 배경에 깔려 있기 때문이다. 한편 東洋에서 말한다면 中國의 墨子·孔孫龍·惠施등의 名家思想이나 인도의 論理學인 因明이 있었으면서도 끝내 數學이 論理形式을 重要視 하는 것은 이루지 못하였다. 方程式論을 中心에 두고 考察한다면 西洋數學史에 있어서 가우스(Gauss, 1777~1855)의 存在定理에서 비롯되어 갈로아(Galois, 1811~1832)의 五次方程의 不能問題로 이어지는데 現實的인 호너(Horner, 1786~1837)의 高次方程式의 近似解法은 극히 最近의 일이었다. 한편 東洋에 있어서는 存在定理가 數學의 課題로서 정면으로 取扱될 수 없었으며, 天元術의 이름으로 Horner의 高次方程式의 근사해법을 存在定理를 前提로 하지 않은 狀況에서 論理化하였다. 이러한 數學의 이질현상은 思想的인 側面에서 說明된다. 즉 西毆의 存在論과 東洋의 不可知論의 對立을 高察하지 않을 수 없다. 本 論文에서는 天元術의 導入과 保存의 過程에서 韓國數學의 特殊性을 考察했으며 特히 그것이 天文曆算과 關聯해서 韓國數學의 황금기를 이루어 놓은 數學의 特徵과 關聯해서 생각한 것이다. 이조 중기이후의 中人의 算學制度는 韓國의 독특한 것이라 해서 그들이 세습적으로 전승에 성공한 배경을 생각했다. 이러한 뜻에서 韓國數學은 天元術의 보급을 中心으로 日本·中國의 數學과 比較해서 부각될 수 있다. 本 論文은 韓國·日本·中國의 東洋三國에 있어서의 韓國數學의 위치와 特徵에 대해서 高察했으며, 이러한 條件하에서의 고구려, 백제,신라의 三國時代에 있어서의 數學的 基礎와 기점및 통일신라시대의 擴張된 영토의 管理體制하에서의 산학제도, 그리고 高麗時代의 算學制度를 그 時代의 中國의 宋·元과 比較하여 考察했으며 이조에서의 數學을 考察하여 韓國 數學의 흐름을 소개하는 形式을 취했으며 傳統的인 思考위에서 數學에 대한 한 分野를 硏究하였다.