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

Further Developments in the Calculus of Variations: Further development of the calculus of variations

The calculus of variations has undergone robust development — including the solutions to the 19th and 20th problems — in the 120 years since Hilbert posed these questions. But Hilbert’s phrasing does not specifically indicate a clear endpoint, so this ‘problem’ can never be considered resolved per se.