Heaviside was on the mathematician's side of this old debate: <a href="http://faculty.poly.edu/~jbain/histlight/readings/83Hunt.pdf" rel="nofollow">http://faculty.poly.edu/~jbain/histlight/readings/83Hunt.pdf</a><p>He perfected operational calculus for electrical engineering: <a href="https://en.wikipedia.org/wiki/Operational_calculus" rel="nofollow">https://en.wikipedia.org/wiki/Operational_calculus</a><p><pre><code> 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..."</code></pre>