Tuesday 1 September 2026, 16:00 - 17:00 in HG 00.616
Gert Heckman (Radboud)
History of the Riemann—Hilbert correspondence
Hilbert's twenty-first problem (from his famous list of mathematical problems from 1900) asks for the existence of a Fuchsian differential equation with arbitrarily prescribed monodromy group. Hilbert remarks that this question is quite likely what Riemann must have had in mind. The problem occurred in Riemann’s work from 1857, the year he wrote three papers on the subject. In Riemann’s Werke these are Abh. IV (Hypergeometric functions), Abh. VI (Abelian functions) and Abh XXI (Unpublished and unfinished paper on the problem). The goal of my lecture is to explain Riemann’s line of thought. But since I am not a historian of mathematics I will tell the story in my own words, also because I intend to give a pedestrian exposé, understandable for an educated high school teacher.