In this talk we will present the “Singularity removal rigidity theorem” for minimal hypersurfaces with isolated singularities in manifolds of nonnegative scalar curvature. In particular, we observe a new phenomenon that the extremal scalar curvature condition forces smoothness, which reveals a kind of positive effect of minimal hypersurface singularities in scalar curvature geometry. As an application, we obtain a direct proof of the positive mass theorem (PMT) for asymptotically flat 8-manifolds with arbitrary ends without using N. Smale's generic regularity theorem. A key ingredient is a new spectral version of PMT for AF manifolds with arbitrary ends, whose proof relies on PMT for asymptotically locally flat (ALF) manifolds with
-symmetry. This talk in based on joint work with Shihang He and Prof. Yuguang Shi.