May 13 2025: Seminar on the 'Historiography of Mathematical Symbolism'

Speakers: Alex Garnick (Harvard University and SPHERE, CNRS—University Paris Cité) and Karine Chemla (School of Mathematics, The University of Edinburgh)

Abstract: We will start at the end, with the work of late-Ottoman historian of mathematics Salih Zeki Bey (1864-1921) and his intervention, within the pages of Journal asiatique, in the historiography of Arabic algebraic symbolism. We will compare his remarks there—which respond directly to Woepcke and Nesselmann—with the different historiographical approach he takes in the second volume of his Ottoman-Turkish-language history of mathematics, Asar-ı-bakiye.

The latter work was directed at a very different audience from the European orientalists reading Journal asiatique and emphasized rather the legacy of Sanskrit mathematical traditions in the development of ḥisāb in Arabic. From Salih Zeki, we will work backwards to explore the origins of the historiography which he sought to challenge. We will also analyse how the notations of hisāb were discussed from the perspective of a history of mathematical symbolism.

Speaker: Célestin Xiaohan Zhou (Institute for the History of Natural Sciences, Chinese Academy of Sciences)

Abstract: This presentation is a continuation of the historiographical research I have conducted within the framework of the SAW (Mathematical Sciences in the Ancient World, ERC) project. There, my analyses of nineteenth- and twentieth-century studies by various types of Chinese scholars reveal significant variation in their interpretations of the same ancient mathematical texts. These differences can largely be attributed to these scholars’ diverse educational backgrounds in mathematics. How do these differences influence their perspectives on the history of mathematical symbolism as evidenced in ancient mathematical texts?

In this seminar, I will use some of the views of Li Shanlan (1811-1882), Qian Baocong (1892-1974), and Li Yan (1892-1963) on mathematical symbolism as examples to address this issue within the framework of a new project. Li Shanlan was a prominent mathematician and translator of mathematical works from English into Chinese. In collaboration with A. Wylie, Li Shanlan developed a novel mathematical symbolism for algebra and calculus, drawing on Chinese sources. The motivation and practice of such a creation might highlight his views on the use of symbolism in English mathematical works and in ancient Chinese texts. Li Yan and Qian Baocong, as two founders of the modern history of mathematics in China, offered commentaries on the symbolism in ancient texts informed by their familiarity with modern mathematical symbolism.

My presentation will develop a comparison of Li Shanlan’s views with those of modern historians of mathematics, highlighting which aspects of symbolism these representative scholars emphasized or neglected. Moreover, as their accounts have likely contributed to shaping our present views on mathematical symbolism, gaining insight into these differences and transformations in the way of viewing the history of mathematical symbolism is beneficial to forming our new comprehension of this issue.