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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 anunpublished 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 thecomposite $B \to \mathrm{MString} \to \mathrm{tmf}$ is surjective on homotopy.Applications to differential topology, and in particular to Hirzebruch's prizequestion, are discussed.

The Ando-Hopkins-Rezk orientation is surjective