I agree 100% in spirit. Electrical transmission lines were not understood when Fourier did his work. Maxwell wasn't even born yet. And the math ultimately unleashed by Fourier transforms goes way beyond applications.

In cold hard dates, though, Fourier was already using his series to solve heat transfer problems in 1822.

I don't agree with the bizarre idea that every bit of research should have a clear utility. I'm just being careful about dates. And I think FTs kind of were invented with a view towards solving differential equations for physics. Just not electrical ones.