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This paper aims to shed light on two different mathematical practices in late eighteenth-century China. For this purpose, we analyze two solutions to the “three problems of the eastward motion of fixed stars” (恒星東行三題) that were given separately by Jiang Sheng (江聲) and Li Rui (李銳), who were both Qian-Jia scholars in the same region of eastern China. By comparing their modes of problem-solving, of reasoning and of computation, we suggest that the mathematical practices they employed represent the recreation of two traditions of mathematical commentaries by Qian-Jia scholars. [ABSTRACT FROM AUTHOR]

Abstract: The algorithms used in Arabic and medieval European mathematics for extracting cube roots are studied with respect to algebraic structure and use of external memory (dust board, table, paper). They can be separated into two distinct groups. One contains methods used in the eastern regions from the 11th century, closely connected to Chinese techniques, and very uniform in structure. The other group, showing much wider variation, contains early Indian methods and techniques developed in central and western parts of the Arabic areas and in Europe. This study supports hypotheses previously formulated by Luckey and Chemla on an early scientific connection between China and Persia. [Copyright &y& Elsevier]

Abstract: Is a mathematical problem a cultural invariant, which would invariably give rise to the same practices, independent of the social groups considered? This paper discusses evidence found in the oldest Chinese mathematical text handed down by the written tradition, the canonical work The Nine Chapters on Mathematical Procedures and its commentaries, to answer this question in the negative. The Canon and its commentaries bear witness to the fact that, in the tradition for which they provide evidence, mathematical problems not only were questions to be solved, but also played a key part in conducting proofs of the correctness of algorithms. [Copyright &y& Elsevier]