Misnomer or Mistranslation? Western Arithmetic Textbooks by E. T. R. Moncrieff and Alexander Wylie in China in the 1850s

Academia is fascinated by the process of how Western science and mathematical knowledge converged with the Chinese mathematical tradition. This topic not only reflects East-West interaction, but also turns upon the philosophical question of whether the Chinese have the scientific or cognitive ability to comprehend critical, logical, and abstract thinking. Fundamental to mathematical knowledge is arithmetic, which deals with numbers and their operations. This paper re-evaluates the significance of Alexander Wylie's (1815-1887) pioneering role in translating Western arithmetical knowledge in China, through (1) unearthing a mathematician-missionary, Edward Moncrieff (1824-1857), who compiled a textbook of arithmetic and translated associated mathematical knowledge, in particular Euclidian geometry, one year earlier than Wylie, and (2) critically analyzing the concept of arithmetic in their textbooks by means of the method of Begriffsgeschichte.