The diversity of mathematical cultures: one past and some possible futures (Q2410949)

This paper is a translation of a French-language article [the author, Gaz. Math., Soc. Math. Fr. 150, 15--30 (2016; Zbl 1358.01173)]. The author promises an expanded version to appear in the proceedings of the 2016 Berlin meeting of the European Congress of Mathematicians. The title phrase ``mathematical cultures'' refers to ``collectively shared ways of practising mathematics''. The article stresses that careful attention to such practices can help with interpreting source texts and provide insights into the ideas and knowledge with which the authors worked. In the particular case that forms the focus of this paper, a set of seventh-century Chinese texts, the practices included a certain ``way of working with the processes of calculation and an interest in uniform algorithms''. The author uses these to discern conceptual linkages the Chinese mathematicians forged among the operations of multiplication, division, root extraction, and solution of systems of linear equations.