How Do We Understand Mathematical Practices in Non-Mathematical Fields? Reflections Inspired by Cases from 12th and 13th Century China (2020)
Recent studies of the history of mathematics have shed light on the diversity of mathematical practices in the ancient world. In this article, I address this issue from two perspectives. First, I analyze different mathematical instruments used in different domains in 12th and 13th century China. Second, by analyzing how the text is related to the problems written down in the same period, I argue that there existed two categories of mathematical problems. As a result, I suggest that problems, textual procedures, and material operations should be considered together when regarding various mathematical practices in mathematical and non-mathematical fields. 摘要 最近的數學史研究已經清楚地揭示出古代世界數學實作的多樣性。在本文中, 我從兩方面探討這一問題。首先, 我分析12至13世紀中國的四個不同領域所使用的數學工具。其次, 透過分析12至13世紀中國關於數學問題的文本是怎樣寫下來的, 我論證存在兩種不同類型的數學問題。因此, 我認為當研究數學和非數學領域內多樣的數學實作的時候, 問題文本、算法文本和物質操作必須放在一起考慮。
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