We owe to Heaviside
- prediction of the layer of the atmosphere which refracts radio signals back to earth, known as "The Kennelly-Heaviside Zone".
- equations for developing the theory and application of electromagnetics.
- the development of vector algebra and analysis, now known as the "Gibbs-Heaviside approach".
The course in "Laplace Transform" I took at New York University in 1953 was taught by a visiting professor from Cambridge University in Britain. The literature often claims that Laplace Theory precludes any need of special functions introduced by Heaviside. We asked our prof about this. He said that one of the most important results was "the Heaviside step-function", later found to be the derivative of the Dirac functional, essential to quantum mathematics. Our prof said this function could not be performed in Laplace Transform Theory.
He also told us that professors and instructors were not allowed to mention Heaviside's name at Cambirdge. And he reminded us of Heaviside's retort to his critics -- that "when mathematicians die, they go to Cambirdge to teach."