The purpose of my talk is to introduce peridynamics as a proxy for discussing the role of an applied mathematician at a national lab. The peridynamic balance of linear momentum replaces the local source term of the classical continuum balance law with a nonlocal term. The source term represents internal force interaction, and in peridynamics is represented by an integral operator that sums internal forces separated by a finite distance. This integral operator is not a function of the deformation gradient, allowing for a more general notion of deformation than in the classical theory that is well aligned with the kinematic assumptions of molecular dynamics. I review some of the mathematical results achieved during the last two years.