Maxwell's contributions to electromagnetism primarily involved generalizing Ampère's law, demonstrating that a changing electric field produces a magnetic field, which led to the prediction of electromagnetic waves traveling at light speed. He formulated electromagnetism mathematically, although the notation used was not the modern vector calculus due to its absence at the time. While some critique his work as poorly organized and difficult to understand, his equations, which are essentially partial differential equations, ultimately define the electromagnetic field. Maxwell's realization of the completeness of these equations was pivotal, culminating in the understanding that light itself is an electromagnetic wave. His work is regarded as one of the greatest achievements in science.
