The French and Japanese schools of algebra in the seventeenth century: A comparative study (Q2713749)

This brief comparative article first presents Pierre de Fermat (1601-1665) as a ``Second Viète'' with regard to the kind of symbolic algebra he developed. In a second section, the author outlines the characteristics of a contemporary school of algebra in Japan, established by Seki Takakazu (?--1708). It had its roots in the Chinese thirteenth century art of ``tian yuan shu'' (celestial element technique). Although without any historical links to the European mathematical realm, Sasaki claims that Seki's school of algebra can be compared with that of Viète because ``Seki's algebra was a method for calculation in a written form \textit{in principle}'' (p. 19).NEWLINENEWLINENEWLINEThe following two sections illustrate the author's argument by showing the similarities and dissimilarities between infinitesimal analysis in modern Europe and ``\textit{wasan} analysis'' in Japan for problems of maxima and minima. The author humbly concludes on an attempt to explain the reasons why finally the system of differential and integral calculus was not discovered in Japan and why European style mathematics were adopted after the Meiji Restoration: a lack of rigorous demonstration, a disregard for mathematical symbolism and the lack of the concepts of function and indefinite integral.