Correct, the famous d*F=J differential form formulation with one of the versions of the Hodge operator, which I have seen named in several ways. Also depending on your definition of the star operator and current density, you often see this as two equations with Hodge duals, like dF=0 plus d*F=*J. The tensor equivalent can be stated as a single equation or as a set, too.

To be fair and looking back at history, the discovery of Maxwell equations, relativity and quantum theory are so intertwined with the discovery, invention and application of new Mathematical ideas, in particular emanating from the work of Hamilton, Grassmann and then Lie, Levi-Civita, Cartan, etc. that is difficult to separate at what extent those concepts influenced over each other in their attempt to explain and describe reality. The ability to express Maxwell equations in a compact form with quaternions before vector calculus was even a thing provides some evidence. One can argue that the classical formulation for electromagnetism could be expressed that way because Hamilton was trying to find the proper framework that could capture his ideas about physics. Fast forward some 60 years and you also have a similar thing happening with Pauli matrices in quantum theory, and the work of Noether in modern physics.

Mixed Hodge structure en.wiki could use better (undergrad physics) examples if it wants to be the quaternion of our time, thank you for that rabbit hole :)