Seki Takakazu
Native spelling: 関孝和
1642–1708, Edo or Fujioka, Japan (birthplace disputed), Edo (present-day Tokyo), Japan
Japanese samurai-bureaucrat and mathematician, the central figure of wasan (traditional Japanese mathematics), who was the first known person to study determinants systematically, independently discovered the numbers now called Bernoulli numbers, and developed infinite-series methods for computing pi and areas and volumes bounded by curves, entirely independently of contemporary European work by Newton and Leibniz.
Seki Takakazu, also known as Seki Kōwa, was born around 1642 — sources disagree on the exact year, with some placing it as early as 1635 — in Japan, possibly in Edo (present-day Tokyo) or Fujioka, and was later adopted into the Seki family, a samurai household. He spent most of his career as a high-ranking accountant and bureaucrat serving the Tokugawa family in the Kōshū (Kōfu) domain, rising to the status of a direct shogunate retainer when his lord's son became the sixth shogun, Tokugawa Ienobu, shortly before his own retirement. He died on 5 December 1708 in Edo.
Working in Japan's largely isolationist Edo period, Seki began from Chinese mathematical texts available in translation but transformed the subject from a collection of practical calculation techniques into a rigorous theoretical discipline. In his 1683 manuscript Kaifukudai no Hō he laid out matrices and evaluated determinants up to 4×4, and in his more complete later treatise, Taisei Sankei, he gave a general expansion method for determinants equivalent to what would later be called Laplace's formula in Europe — roughly half a century before Laplace. He also devised a symbolic notation using kanji characters to represent multiple unknowns and literal coefficients (endan-jutsu), enabling systematic manipulation of simultaneous equations.
Seki independently discovered the sequence of rational numbers today known as Bernoulli numbers; his results were published posthumously in 1712, one year before Jacob Bernoulli's independent publication in Europe, and in Japan they are sometimes called Seki-Bernoulli numbers. Although he never developed a Western-style differential and integral calculus, he created a parallel framework known as yenri ('circle principle') using infinite series and iterative approximation to compute the rectification of curves and the areas and volumes they bound, applying acceleration techniques mathematically equivalent to the modern Aitken's delta-squared process to compute pi to ten correct decimal digits. Seki founded an influential school (Seki-ryū) that dominated wasan for more than a century; because he transmitted many results privately to inner-circle disciples such as Takebe Katahiro rather than publishing them, much of his work reached wider circulation only through his students.
Workplaces: Kōshū (Kōfu) domain, service of the Tokugawa family
Japan