The List of Hilbert’s Twenty-Three Problems: Hilbert’s Twenty-first Problem

Hilbert’s Twenty-first Problem: Proof of the existence of linear differential equations having a prescribed monodromic group

Hilbert’s 21st problem is about the existence of certain systems of differential equations with given singular points and the systems’ behavior around those points, called monodromy. Josip Plemelj published what was believed to be a solution in 1908, though much later Andrei Bolibrukh found a counterexample to Plemelj’s work, showing that such systems of equations do not have to exist.