Born in a Japan stabilized under the Tokugawa shogunate, where scholarship grew within samurai households. Later biographers place his origins in the Edo region, but surviving records remain fragmentary and debated.

As a youth he studied literacy, abacus calculation, and administrative skills expected of a retainer in Tokugawa society. These practical foundations helped shape his later focus on algorithms, tables, and exact numerical procedures.

He became attached to a feudal domain’s bureaucracy, balancing martial status with clerical responsibilities. Service life exposed him to land records, taxation arithmetic, and the kind of structured problems that fueled wasan innovation.

He joined networks of Japanese mathematicians who exchanged methods through manuscripts rather than universities. In Edo’s book culture, he compared existing techniques and began pushing beyond standard abacus-school calculation.

Working on high-degree equations, he refined elimination-style reasoning used to reduce complex systems. His solutions emphasized repeatable procedures that other practitioners could copy, a hallmark of Edo-period mathematical writing.

By the early 1670s his name circulated among specialists as a formidable problem solver. Reputation spread through copied notes and teacher-student lineages, creating a community that treated difficult problems as public challenges.

He composed texts describing systematic manipulation of equations and numerical schemes for roots. Because printing was limited and costly, these manuscripts were often hand-copied, helping his ideas travel across domains.

To handle simultaneous equations, he organized coefficients in arrays and applied structured elimination rules. Historians later compared this to determinants, noting his independent development within Japan’s closed-border intellectual world.

He applied algebraic tools to geometry, a popular Edo mathematical genre tied to surveying and temple problems. His work encouraged treating geometry with symbolic procedures, not only diagram-based intuition or rote formulas.

As mathematical challenges spread to shrines and temples, his methods offered powerful ways to solve ornate geometry puzzles. Even when not directly cited, his approaches shaped what later authors considered elegant and authoritative solutions.

He trained pupils who carried his techniques into regional schools, preserving them through apprenticeship rather than formal institutions. This teacher-student transmission helped define a distinctly Japanese mathematical tradition for decades.

He worked on iterative procedures for extracting roots and approximating solutions to tough equations. In a society reliant on computation for administration and engineering, such algorithms made advanced mathematics practically valuable.

By the 1690s he was treated as a leading voice in difficult algebra and elimination problems. Mathematicians sought his approach as a benchmark, and later compilers framed his work as foundational to wasan’s maturity.

Scribes and students reproduced his results in circulating notebooks, which moved along travel and domain networks. This manuscript economy allowed innovations to diffuse even without open contact with European scientific institutions.

Mathematics teachers incorporated his elimination-style methods into structured lessons for advanced students. As wasan schools grew, his work became a touchstone for what counted as sophisticated, generalizable mathematical reasoning.

He sustained scholarly output alongside obligations typical of samurai-administrators under Tokugawa governance. This dual life reflected how early modern Japanese science often developed outside universities, embedded in domain service.

In his last years he focused on transmitting key methods to trusted students and polishing core procedures. Those students later helped preserve his reputation, even as original manuscripts remained scarce and sometimes contested.

He died in Edo as the Tokugawa order continued to foster literate, numerate administrative culture. Later wasan historians hailed him as a pioneer whose determinant-like elimination and algebra helped define the tradition’s peak.