The Chinese mathematician Zhu Shijie (1249-1314) employed a unique mathematical language in his Jade Mirror of the Four Unknowns (1303) to express the "Siyuan shu" (technique of four unknowns), a novel algebraic technique which Zhu had developed. The studies of Jock Hoe (1976, 1977, 2007) demonstrate that Zhu’s language can be translated from written Chinese into semi-symbolic notations, which leads to the suggestion that the monosyllabic writing system of Chinese is naturally compatible with algebraic operations. This talk intends to raise two points based on Hoe’s findings.
First, how does this technical language differ from the literary written Chinese of Zhu’s time; and why did Zhu employ a different kind of mathematical language from those generally used in previous mathematical treatises? Was this particular language shaped in the way Zhu intended, to achieve certain purposes? Comparison can be made by looking at Zhu’s consciously manipulating the conventional syntax of the technical expressions and sentences of his time, resulting in Zhu’s producing unique phrases that can express his "Siyuan shu", and help his readers to better understand the relations between his algebraic operations and the language which he deliberately maneuvered.
Second, following the first point, I argue (with Chemla 2019) that the role of language in science, apart from its communicative purpose, is also an instrumental device which can be restructured and subsequently shape the way scientific knowledge is being presented and produced, depending on how scientists employ language into their work.

This presentation dives into the significance of research demonstrating that dolphins can understand sentences given in artificial languages. Herman et al. created two artificial languages for dolphins to be trained on. One of the artificial languages was gestural, while the other was acoustic; the two languages had different syntactic rules. The dolphins were taught to understand words, and sentences in the form of commands of two to five words in length. In testing, the dolphins were given novel commands that they had never encountered before and correctly followed them, suggesting that they were sensitive to word order and understood the rules of syntax in that language.

This presentation explores how the different syntactic rules of the two artificial languages are useful for showing how the dolphins were capable of syntactic processing. Specifically, the gestural language had an “inverse grammar” such that passing the behavioral test in that language gave clear evidence of certain computations, whereas doing the same task with a language using a straightforward “left-to-right” grammar would not give such clear evidence. Examples of languages with “left-to-right” grammar include the acoustic language and many natural languages such as English. Thus, this is a case where great precision in the experimental design was needed in order for scientists to probe the capacities of dolphins to learn to process sentences in these artificial languages. Certain rules of syntax, specifically rules which diverge from those of many natural languages, needed to be used in order to get a robustly designed scientific study.