Nevertheless, the aspiration, reflected in references for this article, is for an analytic geometry of spacetime and charges providing a deductive route to forces and currents in practice. Such a royal route to electromagnetic understanding may be lacking, but a path has been opened with differential geometry : The tangent space at an event in spacetime is a four-dimensional vector space, operable by linear transformations. Symmetries observed by electricians find expression in linear algebra and differential geometry. Using exterior algebra to construct a 2-form F from electric and magnetic fields, and the implied dual 2-form * F, the equations d F = 0 and d* F = J (current) express Maxwell's theory with a differential form approach.