A study on the innovative nature of Seki Takakazu's mathematics: centering on his theory of equations

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03609
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12030:Basic mathematics-related
• Research Institution: Yokkaichi University
• Principal Investigator: Ogawa Tsukane 四日市大学, 関孝和数学研究所, 研究員 (90204081)
• Co-Investigator(Kenkyū-buntansha): 森本 光生 四日市大学, 関孝和数学研究所, 研究員 (80053677)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 関孝和 / 宅間流 / 岡之只

Outline of Final Research Achievements

The results of this research, including one of Seki Takakazu's equation theories, Byoudai-meichi, were published in the “Complete Works of Seki Takakazu” (co-edited, Iwanami Shoten, October 2023). The remaining descriptions are inadequate, and some points remain unclarified, which will be challenging to understand further without discovering new materials. A detailed examination of Seki's works through the compilation of the complete works reveals that his mathematical thought was innovative in its aim to create a unified method and that no mathematician inherited its essence.
The study of Oka Yukitada's Kijutsu-Kairohou of the Takuma school clarified the historicity of the Seki school of mathematics.

Free Research Field

東アジア数学史

Academic Significance and Societal Importance of the Research Achievements

2023度刊行した『関孝和全集』（上野健爾，小川束，小林龍彦，佐藤健一，岩波書店）は新しい関孝和像を提示し，将来の研究への第一歩としての著作類の解読・現代語訳，新資料の発見を含む詳細年表，関係する用語事典，標準的読み下し，膨大な関係資料を収録したものである．関孝和は高等学校の教科書にもその名が出て来るがその実態はほとんど知られていない．本全集によってそれが現段階で得られるかぎりの資料において明らかにされた．また宅間流の研究は関流外の研究を通じて，関流を客観的に理解することを可能にする点で意義がある．