James Clerk Maxwell was the 19th century theoretician who discovered electromagnetic waves. He is often described as a "physicist", but I would argue that he was a mathematician. Certainly some of his research was in the area of "pure mathematics" (see for instance his geometric work on curves and a paper entitled "On Transformations of Surfaces by Bending"). However, even his physical work was mathematical in the sense that it was done by manipulating formulas with pencil and paper rather than by manipulating physical objects in a laboratory.
In this short story, I imagine what could have been going through his mind as he toyed with the formulas describing the influence of a magnetic field on the motion of electrons and noticed unexpectedly a wave equation. The recognition of D'Alembert's wave equation (originally derived to describe the motion of a vibrating string on an instrument like a violin or guitar) in this new context was an important scientific discovery  one that arguably led to later developments like radio, television, and even the special theory of relativity  but it was one that was achieved purely mathematically.
I did not put anything in this story which actually contradicts known history, but it was not my intention to be entirely accurate either. The point is to see what it would feel like to make such a discovery...or to be the sort of person who makes discoveries about the real world using only mathematics as a tool.
The story appears in the collection Reality Conditions.
