Abstract: In 1938 Einstein, Infeld, and Hoffmann claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that they had generalized their results to charged point singularities. While their analysis falls apart upon closer scrutiny, the key idea merits our attention. In this talk we discuss how various weak forms of Bianchi identities can be obtained, and how they may hold the key to obtaining well-defined equations of motion in curved spacetime for charged matter particles.