I will present a historical account of some work of Schoenberg in metric geometry: from his metric space embeddings into Euclidean space and into spheres (Ann. of Math. 1935), to his characterization of positive definite functions on spheres (Duke Math. J. 1942). It turns out these results can be viewed alternately in terms of matrix positivity: from appearances of (conditionally) positive matrices in analysis, to the classification of entrywise positivity preservers in all dimensions. I will also discuss Gram matrices and GPS-triangulation, plus Cayley–Menger matrices and how they prove a 2000-year old result of Heron.