Seki Takakazu

Timeline

1. c. 1661–1674Edo · KantōBorn into a samurai family, adopted by Seki Gorōzaemon in childhood. After instruction from a retainer at age nine, he self-studied Chinese and Japanese mathematical texts, copying Yang Hui's works around 1661 and studying magic squares. As an accountant (kantei) for the Kōfu Tokugawa house, he handled finances while teaching pupils, gradually earning the reputation of 'saint of mathematics'.
2. 1674–1683Edo · KantōIn 1674 he published Haiwei Suanfa, the only printed book of his life, answering fifteen unsolved problems from Sawaguchi Kazunori's Kokin Suanpoki using side notation, extending tenzanjutsu into a writable algebraic notation. His disciple Tatebe Norihiro later wrote the Haiwei Suanfa Yanduan Yange (1685) to elucidate his methods, and the Seki school thereby became the mainstream of wasan.
3. 1683–1700Edo · KantōThe 1683 manuscript Kaifutsudai no Ho used elimination for multivariate higher-degree equations and gave an expansion equivalent to a determinant; correct for third and fourth order, the fifth-order formula was erroneous, later corrected into a general formula in the Daisei Sankyo co-authored with Tatebe Norihiro and others. He also studied circle-squaring (enri), finite differences, and Bernoulli numbers, predating similar European results.