Tenzan 点竄 is a Japanese mathematical term from the Edo period. It spread after the publication of Shūki-Sanpō, which was written by ARIMA Yoriyuki. Although Tenzan became a candidate for the translation of algebra, its origin has not been well studied. This essay considers the origin and formation of Tenzan based on examples of mathematicians.

 The previous research that has evaluated Tenzan as algebra often focuses on the relationship between Tenzan and Endan. However, this study shows that Endan was initially interpreted as “an account” and subsequently considered as the solution of Fukudai. Therefore, Endan is not related to Tenzan.

This essay also suggests that mathematicians had different interpretations of Tenzan. MATSUNAGA Yoshisuke related Tenzan to bōsyohō. IRIE Syūkei, who defined Tenzan as “revealing the hidden,” had much in common with the views on mathematics by SEKI Takakaze and TAKEBE Katahiro. Moreover, Irie influenced Arima, and Arima’s description was based on the Irie’s definition. In addition, Arima appended bōsyohō, which explained how to write a numerical formula to Tenzan in Shūki-Sanpō. As a result, later mathematicians and previous research might have considered Tenzan the same as bōsyohō, which was also algebra.

This paper compares Mori Ogai’s three papers, written during a controversy about statistics and the statistical method, with Friedrich Martius’s 1881 paper, which has been neglected by the extant scholarship on this topic. The European medical community at the time was divided between the protagonists of experimental methods based on medical determinism and those of numerical methods focussing on statistical data. Martius’s paper was written from the standpoint of the experimentalists, seeking to demarcate the limits of the epistemic claims of statistical approaches in medicine. Mori’s view of statistics, owing much to Martius’s paper, can be characterised as a conditional approval à la Bernard that recognises the auxiliary significance of statistics only when the cause cannot be identified using experimental methods.