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Those are the familiar "Maxwell's Equations" we all learned in E&M, but they aren't the ones Maxwell wrote. If you read his original Treatise, you will find 20 differential equations in ordinary differential equation form. These are the original Maxwell's Equations.

William Rowan Hamilton (of Hamiltonian Mechanics fame) re-cast Maxwell's original equations into a shorter version, which were 10 differential equations in ordinary differential equation form. It was not until Oliver Heaviside invented operator calculus that the form we see today was first expressed, so these are more formally known as the Maxwell-Heaviside Equations of electromagnetism.

Heaviside himself was criticized by the more rigorous mathematicians of his day for using operator calculus without really understanding the underlying mathematical theory. He was said to have remarked, somewhat raffishly, that he didn't understand the process of digestion, either, but that did not stop him from enjoying his dinner.

There was a wonderful article on Heaviside in the IEEE spectrum about 15 years ago by a Dartmouth Professor. Heaviside is one of history’s underappreciated geniuses, for sure.