Heaviside was on the mathematician's side of this old debate: http://faculty.poly.edu/~jbain/histlight/readings/83Hunt.pdf http://faculty.poly.edu/~jbain/histli

Heaviside was on the mathematician's side of this old debate: http://faculty.poly.edu/~jbain/histlight/readings/83Hunt.pdf http://faculty.poly.edu/~jbain/histlight/readings/83Hunt.pdf He perfected operational calculus for electrical engineering: https://en.wikipedia.org/wiki/Operational_calculus https://en.wikipedia.org/wiki/Operational_calculus Norbert Wiener in 1926: "The brilliant work of Heaviside is purely heuristic, devoid of even the pretense to mathematical rigor. Its operators apply to electric voltages and currents, which may be discontinuous and certainly need not be analytic. For example, the favorite corpus vile on which he tries out his operators is a function which vanishes to the left of the origin and is 1 to the right. This excludes any direct application of the methods of Pincherle… Although Heaviside’s developments have not been justified by the present state of the purely mathematical theory of operators, there is a great deal of what we may call experimental evidence of their validity, and they are very valuable to the electrical engineers. There are cases, however, where they lead to ambiguous or contradictory results..."