François Lê

(Université Claude Bernard Lyon 1, France)

In his Historia Mathematica article, ‘“Are the genre and the Geschlecht one and the same number?’ An inquiry into Alfred Clebsch’s Geschlecht” (53 (2020), 71–107), François Lê connects to a question that Henri Poincaré posed to Felix Klein in July 1881. The author presents a detailed analysis of the reception of Riemann’s theory of Abelian integrals/ differentials within algebraic geometry by Clebsch et al. and posits it in relation to its topological and/or function-theoretic reading. The author is very careful in tracing different modes of understanding Riemann in different communities and emphasizes strongly the choice of terminology. The article shows the author’s full command of technically quite sophisticated material of undiminished importance in modern mathematics and at the same time his awareness of intriguing methodological historical questions. Although he uses the competences from his 2015 thesis on the history of algebraic geometry (supervised by Catherine Goldstein), the paper is in its content largely independent from the latter. This is also the case for another paper by Lê on “The recognition and the constitution of the theorems of closure,” which also appeared in Historia Mathematica (43 (2015), 237-276). The commission was very impressed by the broadness and versatility of the author revealed in these two largely independent works