  We show that the map $\pi_\ast \mathrm{MString}\to \pi_\ast \mathrm{tmf}$
induced by the Ando-Hopkins-Rezk orientation is surjective. This proves an
unpublished claim of Hopkins and Mahowald. We do so by constructing an
$\mathbf{E}_1$-ring $B$ and a map $B \to \mathrm{MString}$ such that the
composite $B \to \mathrm{MString} \to \mathrm{tmf}$ is surjective on homotopy.
Applications to differential topology, and in particular to Hirzebruch's prize
question, are discussed.
