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

He perfected operational calculus for electrical engineering: 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..."

What about Gibbs?

https://en.m.wikipedia.org/wiki/Willard_Gibbs

I thought del operator was his?

and what about Gauss? the whole field was working or knew about the problem and each other knew the other researches, we just slapped the Maxwell name for recognition as he explained how the stuff worked (pretty much as Einstein equations weren't is own), and in the centuries became 'ownage' - it's interesting however to see how 'legends' form

For those interested in the history and mathematical development of Maxwell's Equations as we know them today, Paul J. Nahin's book on Heaviside[1] is a must read.

[1] http://www.amazon.com/Oliver-Heaviside-Electrical-Genius-Vic...

Ditto. Good book.

Heaviside's name hasn't faded entirely. The step function is named after him.

And the Heaviside Method [1] for determining coefficients in partial fraction expansion.

[1] https://en.wikipedia.org/wiki/Heaviside_cover-up_method

As is the Heaviside Layer, which has even made it into popular culture.

Cats!

[1] https://en.wikipedia.org/wiki/Kennelly%E2%80%93Heaviside_lay...

Why don't other basic functions (constant, reciprocal, parabola …) actually have a name as well? I.e. why did Heaviside’s name stick with the step function?

He apparently invented it [1], or at least popularized it via Laplace transforms for solving differential equations.

[1]: http://hsm.stackexchange.com/questions/1984/why-is-the-heavi...

The step function is about techniques for analyzing discontinuous functions. You can create discontinuous functions by multiplying a normal continuous function by the unit step function. Which was at the time a new thing. It took the mathematical community a long time to get comfortable the techniques. Indeed if you take college math they call it the 'unit step function' in order to avoid referring to it as the Heaviside equation, which is what it's called if you take engineering math.

Constants, reciprocals, parabolas have been known since the time of the ancient Greeks or earlier. Classically they are called Conic Sections. There are other types functions that are named after people. Taylor Series and Bessel Functions come to mind (after Brook Taylor and Friedrich Bessel). There are more of course.

Because it's more fitting to give his name to a function that has a "heavy side".

Indeed, and the function has a heavy side. ;-)

He also managed to recognize a relationship between electromagnetism and gravity before Einstein.

http://serg.fedosin.ru/Heavisid.htm

He invented coax too.

side note: they have a page on another not-famous-enough pioneer

http://theinstitute.ieee.org/technology-focus/technology-his...