Seki Takakazu

87
Seki Takakazu bigraphy, stories - Japanese mathematician

Seki Takakazu : biography

1642 – December 5, 1708

,Selin, Helaine. (1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, p. 890 also known as ,Selin, was a Japanese mathematician in the Edo period.Smith, David. (1914)

Seki laid foundations for the subsequent development of Japanese mathematics known as wasan; and he has been described as Japan’s "Newton." Restivo, Sal P. (1992).

He created a new algebraic notation system, and also, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations. A contemporary of Gottfried Leibniz and Isaac Newton, Seki’s work was independent. His successors later developed a school dominant in Japanese mathematics until the end of the Edo period.

While it is not clear how much of the achievements of wasan are actually Seki’s, since many of them appear only in writings of his pupils, some of the results parallel or anticipate those discovered in Europe.Smith, For example, he is credited with the discovery of Bernoulli numbers.Poole, David. (2005). ; Selin, p. 891. The resultant, and determinant (the first in 1683, the complete version no later than 1710) are also attributed to him. This work was a substantial advance on, for example, the comprehensive introduction of 13th-century Chinese algebra made as late as 1671, by Kazuyuki Sawaguchi.

Notes

Biography

Not much is known about Kōwa’s personal life. His birthplace has been indicated as either Fujioka in Gunma prefecture, or Edo, and his birth date ranging anywhere from 1635 to 1643.

He was born to the Uchiyama clan, a subject of Ko-shu han, and later adopted into the Seki family, a subject of the Shogun. While in Ko-shu han, he was involved in a surveying project to produce a reliable map of his employer’s land. He spent many years in studying 13th-century Chinese calendars to replace the less accurate one used in Japan at that time.

Career

Chinese mathematical roots

Seki Takakazu, from Tensai no Eikō to Zasetsu

His mathematics (and wasan as a whole) was based on mathematical knowledge from the 13th to 15th centuries. Otonanokagaku. June 25, 2008. — Seki was greatly influenced by Chinese mathematical books Introduction to Computational Studies (1299) by Zhu Shijie and Yang Hui suan fa (1274-75) by Yang Hui. (とくに大きな影響を受けたのは、中国から伝わった数学書『算学啓蒙』(1299年)と『楊輝算法』(1274-75年)だった。) This consisted of algebra with numerical methods, polynomial interpolation and its applications, and indeterminate integer equations. Seki’s work is more or less based on and related to these known methods.

Chinese algebra discovered numerical evaluation (Horner’s method, re-established by William George Horner in the 19th century) of arbitrary degree algebraic equation with real coefficients. By using the Pythagorean theorem, they reduced geometric problems to algebra systematically. The number of unknowns in an equation was, however, quite limited. They used notations of an array of numbers to represent a formula; for example,

(a b c) for ax^2 + bx + c.

Later, they developed a method which uses two-dimensional arrays, representing four variables at most, but the scope was still limited. Hence, a target of Seki and his contemporary Japanese mathematicians was the development of general multi-variable algebraic equations, and elimination theory.

In the Chinese approach to polynomial interpolation, the motivation was to predict the motion of celestial bodies from observed data. The method was also applied to find various mathematical formulas. Seki learned this technique, most likely, through his close examination of Chinese calendars.

Competing with contemporaries

In 1671, , a pupil of in Osaka, published Kokin-Sanpo-Ki (古今算法之記), in which he gave the first comprehensive account of Chinese algebra in Japan, and he successfully applied it to problems suggested by his contemporaries. Before him, these problems were solved using arithmetical methods. In the end of the book, he challenged other mathematicians with 15 new problems, which require multi-variable algebraic equations.