  An explicit lower bound for the mass of an asymptotically flat Riemannian
3-manifold is given in terms of linear growth harmonic functions and scalar
curvature. As a consequence, a new proof of the positive mass theorem is
achieved in dimension three. The proof has parallels with both the Schoen-Yau
minimal hypersurface technique and Witten's spinorial approach. In particular,
the role of harmonic spinors and the Lichnerowicz formula in Witten's argument
is replaced by that of harmonic functions and a formula introduced by the
fourth named author in recent work, while the level sets of harmonic functions
take on a role similar to that of the Schoen-Yau minimal hypersurfaces.
