Seminar 6: Diagrammatization of written mathematical practices Zehra Bilgin (School of Mathematics, The University of Edinburgh)Abstract TBA Mathematical Expressions by school in Japan During the Edo Period Tanaka Noriko 田中紀子 (Department of Education for Human Growth, Naragakuen University)During the Edo period (1603-1867) there were several schools of mathematics in Japan. The most famous and popular school was the Seki school [関流] of the renowned mathematician Seki Takakazu [関孝和] (?-1708). In addition to the Seki school, there were various other schools such as Takuma school [宅間流], Shisei-Sanka school [至誠賛化流], Saijyo school [最上流],Miike school [三池流] etc.Mathematical texts were written vertically, and the methods of mathematical expression also differed according to the school. The Seki school's way of expressing mathematics is inspired by the motif of Sangi [算木] (arithmetic sticks), which was introduced from China to Japan. The Sangi were placed vertically for the first, hundred, and ten thousand places and horizontally for the tenth, thousand, and hundred thousand places. The red blocks represent positive numbers, and the black blocks represent negative numbers. When writing in books, negative numbers were represented by diagonal lines to express them in black ink only. Seki Takakazu developed Bō-Shohō [傍書法], which enabled the representation of both numbers and letters within a single formula, thereby improving the expression of mathematical equations. Saijyo school was a school founded by Aida Yasuaki [会田安明](1747-1817). The Saijyo school’s way of writing formula is almost identical to that of Seki school. Aida continued to criticise the Seki school, yet his mathematical expressions showed little originality.Shisei-Sanka school was a school founded by Hurukawa Ujikiyo [古川氏清](1758-1820). The expression of the formula is almost the same as the expression of Seki school's formula. This school has preserved a rare book entitled “Kiou Collection”[淇澳集], which details methods for studying Japanese mathematics. This book reveals that mathematics was kept secret within each school.Takuma school was a school founded by Takuma Yoshikiyo [宅間能清] in Osaka. Takuma school does not use numerical expressions of arithmetic sticks. Negative numbers are written as fu (フ) in Japanese katakana [カタカナ], and numbers are one (一), two (二), three (三) in Japanese kanji [漢字].The mathematics of Takuma School involves complex factorization, which we believe this is made possible by the notation of the School.The Miike School was founded by Miike Ichibei [三池市兵衛]. The algebraic notation of the Miike School possesses a special form. A hook is placed above the vertical line. When there are numerous positive and negative terms respectively, these are grouped separately; negative terms are indicated by drawing a diagonal line through the vertical line.Furthermore a license was required to teach Japanese mathematics in the Edo period. Licences varied by school, and those who received them were able to teach mathematics. The Seki school was the largest, but whether due to the secrecy surrounding Japanese mathematics, a nationwide standardisation of notation was never achieved. I would like to deepen my consideration of the spread of the schools of mathematics during the Edo period and why the Seki school could not unify all the schools.ReferencesJapan Academy [日本学士院](ed.). A History of Japanese Mathematics before Meiji Era [明治前日本数学史]. 5 vols. Iwanami Shoten[岩波書店]. 1954-1960.Tanaka Noriko [田中紀子]. Looking at Takuma School's Collection of exquisite formulate and Methods of transformation of equations from an educational point of view. RIMS Kôkyûroku Bessatsu B92,151-166. 2023. Jun 02 2026 13.00 - 17.00 Seminar 6: Diagrammatization of written mathematical practices Join Zehra Bilgin (School of Mathematics) and Tanaka Noriko 田中紀子 (Department of Education for Human Growth, Naragakuen University) for the sixth seminar of the second year of the 'Rethinking the history of mathematical symbolism' project. Location TBC
Seminar 6: Diagrammatization of written mathematical practices Zehra Bilgin (School of Mathematics, The University of Edinburgh)Abstract TBA Mathematical Expressions by school in Japan During the Edo Period Tanaka Noriko 田中紀子 (Department of Education for Human Growth, Naragakuen University)During the Edo period (1603-1867) there were several schools of mathematics in Japan. The most famous and popular school was the Seki school [関流] of the renowned mathematician Seki Takakazu [関孝和] (?-1708). In addition to the Seki school, there were various other schools such as Takuma school [宅間流], Shisei-Sanka school [至誠賛化流], Saijyo school [最上流],Miike school [三池流] etc.Mathematical texts were written vertically, and the methods of mathematical expression also differed according to the school. The Seki school's way of expressing mathematics is inspired by the motif of Sangi [算木] (arithmetic sticks), which was introduced from China to Japan. The Sangi were placed vertically for the first, hundred, and ten thousand places and horizontally for the tenth, thousand, and hundred thousand places. The red blocks represent positive numbers, and the black blocks represent negative numbers. When writing in books, negative numbers were represented by diagonal lines to express them in black ink only. Seki Takakazu developed Bō-Shohō [傍書法], which enabled the representation of both numbers and letters within a single formula, thereby improving the expression of mathematical equations. Saijyo school was a school founded by Aida Yasuaki [会田安明](1747-1817). The Saijyo school’s way of writing formula is almost identical to that of Seki school. Aida continued to criticise the Seki school, yet his mathematical expressions showed little originality.Shisei-Sanka school was a school founded by Hurukawa Ujikiyo [古川氏清](1758-1820). The expression of the formula is almost the same as the expression of Seki school's formula. This school has preserved a rare book entitled “Kiou Collection”[淇澳集], which details methods for studying Japanese mathematics. This book reveals that mathematics was kept secret within each school.Takuma school was a school founded by Takuma Yoshikiyo [宅間能清] in Osaka. Takuma school does not use numerical expressions of arithmetic sticks. Negative numbers are written as fu (フ) in Japanese katakana [カタカナ], and numbers are one (一), two (二), three (三) in Japanese kanji [漢字].The mathematics of Takuma School involves complex factorization, which we believe this is made possible by the notation of the School.The Miike School was founded by Miike Ichibei [三池市兵衛]. The algebraic notation of the Miike School possesses a special form. A hook is placed above the vertical line. When there are numerous positive and negative terms respectively, these are grouped separately; negative terms are indicated by drawing a diagonal line through the vertical line.Furthermore a license was required to teach Japanese mathematics in the Edo period. Licences varied by school, and those who received them were able to teach mathematics. The Seki school was the largest, but whether due to the secrecy surrounding Japanese mathematics, a nationwide standardisation of notation was never achieved. I would like to deepen my consideration of the spread of the schools of mathematics during the Edo period and why the Seki school could not unify all the schools.ReferencesJapan Academy [日本学士院](ed.). A History of Japanese Mathematics before Meiji Era [明治前日本数学史]. 5 vols. Iwanami Shoten[岩波書店]. 1954-1960.Tanaka Noriko [田中紀子]. Looking at Takuma School's Collection of exquisite formulate and Methods of transformation of equations from an educational point of view. RIMS Kôkyûroku Bessatsu B92,151-166. 2023. Jun 02 2026 13.00 - 17.00 Seminar 6: Diagrammatization of written mathematical practices Join Zehra Bilgin (School of Mathematics) and Tanaka Noriko 田中紀子 (Department of Education for Human Growth, Naragakuen University) for the sixth seminar of the second year of the 'Rethinking the history of mathematical symbolism' project. Location TBC
Jun 02 2026 13.00 - 17.00 Seminar 6: Diagrammatization of written mathematical practices Join Zehra Bilgin (School of Mathematics) and Tanaka Noriko 田中紀子 (Department of Education for Human Growth, Naragakuen University) for the sixth seminar of the second year of the 'Rethinking the history of mathematical symbolism' project.
