Takakazu Seki Kowa
Takakazu Seki Kowa
Takakazu Seki Kowa was one of the few notable Japanese mathematicians prior to the late modern era. At a time when his country was shut off from most of the world and controlled by military dictators called shoguns, Seki Kowa—himself a samurai under the shogunate—sparked Japanese scholars' interest in mathematics. In the course of his career, he developed his own system of notation, as well as an early form of calculus.
The son of a samurai named Nagaakira Utiyama, Seki was born in the town of Fujioka in March 1642. It is not clear whether his father died, or if the father himself sent the boy to live with the family of accountant Seki Gorozayemon; but in any case this occurred when the boy was very small, and he took on the name of his adoptive father. From an early age, Seki Kowa showed himself a mathematical prodigy, earning the nickname "divine child" because of his remarkable abilities.
At some point Seki Kowa married, though he never had any children, and went to work as an examiner of accounts for the Lord of Koshu. The latter eventually became shogun, and thus Seki Kowa—a member of the samurai class by birth—was named a shogunate samurai. His work as an accountant, a trade he must have learned from his adoptive father, naturally dovetailed with his interests as a mathematician, and during his late twenties, he began to teach and write on the subject.
Seki Kowa's one notable publication was Hatubi sanpo, which appeared in 1674. The book was written in response to the announcement of some 15 supposedly unsolvable problems that had been put forth four years before; in Hatubi sanpo, Seki Kowa solved them all. However, it was not the Japanese custom to show how one had arrived at one's solutions, and it appears that even Seki Kowa's students remained unaware of his methodology.
Much of what the Japanese knew about mathematics had been derived (as had many other aspects of their civilization) from older Chinese models. Chinese math at the time made it possible to solve equations with a single variable, but Seki Kowa took this several steps further. In the course of his work, he implemented notation he had created to express these unknown quantities.
His work was all the more remarkable in light of the fact that Japanese mathematicians were unaware of algebra. It was Seki Kowa's achievement, however, to provide a number of advancements without the benefit of input from other scholars, a situation quite unlike that of his counterparts in Europe. Like Sir Isaac Newton (1642-1727), who was born the same year as he, he developed a method for approximating the root of a numerical equation, and he created his own table of determinants at about the same time this idea made its debut in Europe. In addition, he calculated the value of π to some 20 places.
In his latter years, Seki Kowa was granted the title of master of ceremonies for the shogun's household, an esteemed position. He died on October 24, 1708, in the village of Edo, which is now Tokyo.