Global Mathematical Arts in 13th Century Influenced on Japanese Mathematics

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K01162
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Sociology/History of science and technology
• Research Institution: Osaka Kyoiku University
• Principal Investigator: Jochi Shigeru 大阪教育大学, グローバルセンター, 教授 (00571283)
• Research Collaborator: Liu Bowen
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 科学技術史 / 数学史 / 和算 / 「古代」と「近世」

Outline of Final Research Achievements

In 13th century,Chinese mathematicians studied high degree equations,that is to say, "Tianyuan-shu" and solving method of them. They used "counting rods”, thus it was the last era of the“ancient are”. In other hands, the 15-17th century, Southern Chinese mathematicians used abacus, studied merchants'mathematics.
Because the "Yang Hui Suanfa" was used the "counting rods", therefore it must be the ancient era. We, however,discovered some version of "Yang Hui Suanfa" at south Korean, and Korean mathematicians in the pre-modern age proofread it. They studied not only the "Yang Hui Suanfa" for the classical mathematical arts, but also studied it as the highest mathematical science. Seki Takakazu (1645?-1708) also proofread the "Yang Hui Suanfa", but his method was not the same as Korean mathematicians (Yonsei University, rear book no. (1) 510). We conclude that Eastern mathematicians studied the "Yang Hui Suanfa", as the highest mathematical science for the pre-modern era.

Free Research Field

科学技術史

Academic Significance and Societal Importance of the Research Achievements

13世紀に起こった中国数学は、古代の完成形ではなく、ユーラシア大陸にまたがる文明の成立による新たな数学の誕生と言える。
近世日本の寺子屋で学ばれた鶴亀算は、同じ問題が古代の『孫子算経』（孫子、5世紀頃）にあるが解き方は異なっている。さらに、建部賢弘（1664-1739）は『算学啓蒙』（朱世傑、1299年）に注釈を行い、近世数学を完成させている。しかし、数学の進歩という観点だけではなく、古代数学を超克する態度をもつものとして、「近世」数学は13世紀から始まったものと言える。『楊輝算法』（楊輝、1275年）の開方法（高次方程式の解法）、『算学啓蒙』の天元術が挙げられる。