The Hilbert Problems are a set of 23 mathematical challenges presented by the German mathematician David Hilbert in 1900. Aimed at defining future research directions, these problems span various areas of mathematics. While some were clearly stated, others were more open-ended. Over the decades, a majority of these problems have been resolved, significantly advancing mathematical knowledge. Some led to the establishment of entire new fields of study. Unresolved - as of AE53 - Hilbert problems:

Mathematical Treatment of the Axioms of Physics

Rigorous Foundation of Schubert's Enumerative Calculus

Topology of Algebraic Curves and Surfaces

Analysis of Solutions of Variational Problems