The Li Shanlan Identity and its argumentative mode
Speaker: Prof. Andrea Breard from Université Paris-Saclay.
Attitudes towards reasoning in mathematics were seldom spelled out explicitly in texts from early modern China. A historical shift nevertheless can be observed after the second wave of influx of Western modes of argumentation and proof during the second half of the 19th century. Taking the well known Li Renshu combinatorial identity in Li Shanlan’s 李善蘭 (1811-1882) Comparable Categories of Discrete Accumulations (Duoji bilei 垛積比纇, 1867) as a case study, the talk investigates the epistemology and history of a specific mode of reasoning underlying the combinatorial procedures listed rhetorically and illustrated visually in this work, arguing that they reflect a mode of nineteenth-century mathematical argumentative practice, merging „analogical“ reasoning with practices of (incomplete) induction found in foreign mathematical texts, which Li Shanlan himself had translated into Chinese. Li is a particularly interesting and original figure since he taught and worked in mathematics in a compartmentalized fashion: either in purely traditional Chinese style or by adopting a syncretistic mathematical language with strong cultural components, mixing, for example, more specifically in his combinatorial work, practices of diagrammatic representations of finite series with rhetorical inductive arguments. This kind of mathematical discourse places Li Shanlan historically within the broader issue of the construction of modern global mathematics and reveals him as an individual mediator who established connections that crossed seemingly insurmountable epistemological borders between European and Chinese scientific practices and linguistic cultures that were claimed to be incommensurable.