Is it possible to point to a specific development in mathematics that allowed Maxwell's equations to happen? Similarly to Newton's laws of physics that depended on the invention of calculus? And immediately acknowledging that Maxwell's equations in fact had disparate sources, one of which was not even originally formulated as a mathematic equation. Could it be possible to name a major breakthrough or a general field of math that was intensely innovating at that time and without which Maxwell's work would've been totally impossible?
(Maxwell's equations are today commonly explained in terms of vector calculus which was not in fact invented at the time, so don't post that as an answer:)