Whitehead's problem, which asks whether every Whitehead abelian group is a free abelian group, was a prominent open question in group theory in the mid-20th century. In 1974, Shelah proved that the problem is independent of ZFC, which was a surprising development and provided one of the first instances of a major problem coming from outside logic and set theory to be proven independent of ZFC. In recent years, Clausen and Scholze have introduced the category of condensed abelian groups, which can be seen as an enrichment of the category of topological abelian groups with nicer algebraic properties. Through some deep structural analysis of this category, they showed that, when appropriately interpreted, Whitehead's problem is not independent in the category of condensed abelian groups: it is provable in ZFC that every abelian group that is Whitehead in the condensed category must be free. In this talk, we sketch a new, more concrete proof of Clausen and Scholze's result, in the process highlighting some connections between condensed mathematics and the theory of forcing. This is joint work with Jeffrey Bergfalk and Jan Šaroch.