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 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.[7]

Select mathematicians[edit]

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[edit]


  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). Bedford/st.Martins. p. 7.  Missing or empty |title= (help)
  7. ^ Smith, pp. 91-127., p. 91, at Google Books
  8. ^ Smith, pp. 104, 158, 180., p. 104, at Google Books
  9. ^ a b c d List of Japanese mathematicians -- Clark University, Dept. of Mathematics and Computer Science
  10. ^ a b Fukagawa, Hidetoshi et al. (2008). Sacred Mathematics: Japanese Temple Geometry, p. 24., p. 24, at Google Books
  11. ^ Smith, p. 233., p. 233, at Google Books


External links[edit]