Take up a question, then pass it on.

Opening arithmetic to a wider public

Yoshida Mitsuyoshi 1598–1672

Author of Jinkōki. By bringing abacus instruction together with practical and recreational problems, he widened the entry point to arithmetic. The book’s unanswered challenge problems also encouraged later authors to respond with solutions and new problems.

The National Diet Library authority record gives 1672 as his year of death, while an NDL exhibition page gives 1673; the site does not conceal that source difference.

Extending symbolic and elimination methods

Seki Takakazu birth year uncertain–1708

Seki developed written methods for handling numbers and symbols and advanced techniques for eliminating unknowns. He also left important work on circle calculation and finite power sums. Because his birth year remains disputed, this page does not present a single conjectural year as settled fact.

Finding methods from numerical patterns

Takebe Katahiro 1664–1739

A student of Seki who explained and carried forward Seki’s work while developing his own investigations of π, arcs, and numerical procedures. Tetsujutsu Sankei is also important for the way it reflects on how mathematical questions are investigated.

Building a system together

Takebe Kataakira 1661–1716

Katahiro’s elder brother and a participant, with Seki and Katahiro, in the compilation of Taisei Sankei. Keeping the brothers distinct prevents a collaborative body of work from being collapsed into a single biography.

Carrying circle theory into the next generation

Matsunaga Yoshisuke birth year uncertain–1744

An important mathematician of the generation after Seki, especially for later developments in circle theory and series. Reference works do not agree on his birth year: one major Japanese encyclopedia gives around 1690, while a 2022 peer-reviewed study uses 1694?. This site therefore leaves the birth year unsettled rather than forcing one value.

Deepening tangency and mensuration

Ajima Naonobu 1732–1798

A major late-Edo mathematician whose work includes circle theory, tangency, and mensuration. The circle configurations associated with Ajima and Irisawa’s later six-sphere-chain problem are treated here as distinct pieces of research.

Pushing later circle theory further

Wada Yasushi 1787–1840

Wada developed later techniques of enri (circle theory) and strongly influenced subsequent practitioners. English-language histories often render his name as Wada Nei; the Japanese reading used on this site is Yasushi. Circle theory was not one completed formula from Seki’s lifetime, but a research area developed across generations.

Asking how a chain of spheres closes

Irisawa Shintarō Hiroatsu documented by his 1822 sangaku

Known for the six-sphere-chain problem dedicated at Samukawa Shrine in 1822. The key issue is not only that the sphere sizes repeat, but that the spatial chain closes. Rather than inventing uncertain birth and death dates, this page starts from the work that can be documented.

Preserving records into the modern period

Uchida Itsumi 1805–1882

Editor of Kokon Sankan, which preserves material from sangaku that no longer survive. Bibliographic records also use the name Uchida Yatarō Kyō. His work connected late-Edo mathematical practice with the preservation and study of earlier records.