Beads and Brushes: Elementary Arithmetic and Western Learning in China, 1600‒1800

Catherine Jami, “Beads and Brushes: Elementary Arithmetic and Western Learning in China, 1600‒1800”, Historia Scientiarum 29,1 (2019): 26-49.


The Jesuits who worked in China from 1583 to 1773 taught and practised the mathematical sciences as part of their missionary strategy. Besides Euclidean geometry, they also introduced written calculation. At that time, the abacus was universally used in China, and mathematical works such as the Suanfa tongzong 算法統宗 (1592) relied on it. By contrast, the Jesuits’ Tongwen suanzhi 同文算指 (1614), partially based on Clavius’ Epitome Arithmeticæ Practicæ (1583), introduced the written layout of the four elementary operations. After its publication, a number of Chinese scholars advocated the adoption of written calculation on the grounds that it was more consistent with the scholarly practice of writing than abacus calculation. However, as the rhymes that underlay abacus calculation describe the movement of the beads rather than the result of elementary arithmetic operations, changing to written calculation entailed a complete retraining in mental calculation. This may explain why, despite the publication by Chinese scholars of a number of treatises that adopted and adapted the layout and techniques of the Tongwen suanzhi, it appears that not only merchants, but also scholars specialised in mathematics who studied Western methods, continued to use the abacus to perform calculations until the end of the imperial era.

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