In its classical setting, the Riemann–Hilbert problem refers to Hilbert’s 21st problem of constructing a Fuchsian ODE system with prescribed poles and a given monodromy group. Using singular integral equation techniques, Plemelj presented a solution to this problem in 1908 which became widely accepted. However, Kohn, Arnold and Il’yashenko noticed in the mid 1980s that Plemelj had actually worked on a problem similar to Hilbert’s 21st for so-called regular ODE systems rather than Fuchsian ones. These new investigations resulted eventually in a negative answer to Hilbert’s original problem given by Bolibruch in 1989 with further developments by Bolibruch and Kostov soon after.
