Whitehead's subcomplex asphericity conjecture

Let $X$ be an aspherical 2-complex, and let $Y$ be a subcomplex of $X$. Whitehead's conjecture. The subcomplex $Y$ is aspherical. This is a famous conjecture about asphericity inherited by subcomplexes of aspherical 2-complexes; the source uses it as motivation for studying non-positive immersion properties, and does not state a resolution here.