Japanese mathematics

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Japanese mathematics (和算, wasan) denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term wasan, from wa ("Japanese") and san ("calculation"), was coined in the 1870s [1] and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 yōsan). [2]


In the history of mathematics, the development of wasan falls outside the Western realms of people, propositions and alternate solutions.[ clarification needed ] At the beginning of the Meiji period (1868–1912), Japan and its people opened themselves to the West. Japanese scholars adopted Western mathematical technique, and this led to a decline of interest in the ideas used in wasan.


The soroban in Yoshida Koyu's Jinkoki (1641 edition) Yoshida Soroban.jpg
The soroban in Yoshida Koyu's Jinkōki (1641 edition)

This mathematical schema evolved during a period when Japan's people were isolated from European influences. Kambei Mori is the first Japanese mathematician noted in history. [3] Kambei is known as a teacher of Japanese mathematics; and among his most prominent students were Yoshida Shichibei Kōyū, Imamura Chishō, and Takahara Kisshu. These students came to be known to their contemporaries as "the Three Arithmeticians". [4]

Yoshida was the author of the oldest extant Japanese mathematical text. The 1627 work was named Jinkōki. The work dealt with the subject of soroban arithmetic, including square and cube root operations. [5] Yoshida's book significantly inspired a new generation of mathematicians, and redefined the Japanese perception of educational enlightenment, which was defined in the Seventeen Article Constitution as "the product of earnest meditation". [6]

Seki Takakazu founded enri (円理: circle principles), a mathematical system with the same purpose as calculus at a similar time to calculus's development in Europe; but Seki's investigations did not proceed from conventionally shared foundations[ clarification needed ]. [7]

Select mathematicians

Replica of Katsuyo Sampo by Seki Takakazu. Page written about Bernoulli number and Binomial coefficient. Seki Kowa Katsuyo Sampo Bernoulli numbers.png
Replica of Katsuyo Sampo by Seki Takakazu. Page written about Bernoulli number and Binomial coefficient.

The following list encompasses mathematicians whose work was derived from wasan.

See also


  1. Selin, Helaine. (1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures , p. 641. , p. 641, at Google Books
  2. Smith, David et al. (1914). A History of Japanese Mathematics, p. 1 n2. , p. 1, at Google Books
  3. Campbell, Douglas et al. (1984). Mathematics: People, Problems, Results, p. 48.
  4. Smith, p. 35. , p. 35, at Google Books
  5. Restivo, Sal P. (1984). Mathematics in Society and History, p. 56. , p. 56, at Google Books
  6. Strayer, Robert (2000). Ways of the World: A Brief Global History with Sources. Bedford/St. Martins. p. 7. ISBN   9780312489168. OCLC   708036979.
  7. Smith, pp. 91–127. , p. 91, at Google Books
  8. Smith, pp. 104, 158, 180. , p. 104, at Google Books
  9. 1 2 3 4 List of Japanese mathematicians -- Clark University, Dept. of Mathematics and Computer Science
  10. 1 2 Fukagawa, Hidetoshi et al. (2008). Sacred Mathematics: Japanese Temple Geometry , p. 24.
  11. Smith, p. 233. , p. 233, at Google Books

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