Interestingly, Maxwell's equations have been drastically reduced into a language of di fferential geometry. These four sets of equations which perfectly describe the theory of electromagnetism have been reduced to a set of two equations which lay the foundations of most new theories in the physical world today.(from Maxwell's Equations in Terms of Differential Forms (pdf) by Solomon Akaraka Owerre)
The most revolutionary quantum leap in the history of theoretical physics is the birth of general relativity and quantum eld theory (the standard model of elementary particle). These theories describe nature better than any physicist ever had at hand, although they have not been uni ed into a coherent picture of the world. One of the main ingredients of these theories is di erential geometry. Euclidean geometry was abandoned in favour of di erential geometry and classical eld theories had to be quantized.
Maxwell's equations in the language of di erential geometry lead to a generalization to these new theories, and these equations are a special case of Yang-Mills equations (beyond the scope of this essay), which is also gauge invariant and describe not only electromagnetism but also the strong and weak nuclear forces. This essay is nothing but the tip of the iceberg.
Read also: The poem of the Maxwell's equations in pdf written by Lynda Williams.