June 17 2025: Seminar on the 'Historiography of Mathematical Symbolism'

Speaker: Ivahn Smadja (Nantes Université, CAPHI — Institut Universitaire de France)

Abstract: In this contribution, I will analyze how Alexander von Humboldt addressed central issues in the warp and weft of the historiography of mathematical symbolism, as it took shape in the first half of the nineteenth-century. Owing to a specific check-and-balance “epistolary technique”, he created a dialogue between contrasting views, his non-expert status qualifying him as a sounding board resonating with competing historiographic approaches.

I will focus on two different contexts in which Humboldt circulated suggestions, queries and replies on mathematical symbolism, engaging with two different communities, whether with philologists, linguists and orientalists, or with mathematicians and historians of mathematics, whether on ancient numeral systems, or on when, where and how algebra started.

Speaker: Marie-José Durand-Richard (Honorary Lecturer Université Paris 8 Vincennes & Researcher associated to SPHERE, CNRS, CNRS—University Paris Cité)

Abstract: My talk will analyze how Charles Babbage (1791-1871) and George Peacock (1791-1858) conceived the history of algebraic notations in the first half of the 19th century. They were mainly guided by John Locke's Essay on Human Understanding (1690), for which language, a human creation, is an instrument of thought, and mathematical language is an instrument of reasoning. They also drew on contemporary linguistics, from Degerando's Des signes et de l'art de penser considérés dans leurs rapports mutuels (1799-1900) to the accounts of numerous discoverers and travelers.

During the decade of the 1820s, Babbage wrote several papers and an unfinished Philosophy of Analysis, in which he focused on principles governing the invention of notations, with the opened intention of reforming algebraic language. Later, after publishing his influential Report on the Recent Progress and Present State of certain Branches of Analysis (1833), Peacock published a paper entitled “Arithmetic” (1836) for the Encyclopedia Metropolitana (1845), which presented a history of algebraic notations based entirely on the idea that an underlying conception of operations presided over the invention of numerical and literal notations throughout the world.