Miller began his professional career at the Ballistics Research Laboratory at the Aberdeen Proving Ground where he worked with physicist Jane Dewey.

In 1967, he moved to the Naval Research Laboratory where he developed high-fidelity mathematical models of interactions between physical systems and electromagnetic fields.

Miller maintained an academic affiliation with George Washington University as an adjunct professor after retiring from the Naval Research Laboratory in 1991.

[1] Miller made numerous contributions in the area of special functions and addressed several significant open problems.

Notable among these include his work with Emanuel Vegh in formulating an exact closed-form solution for the grazing angle for specular reflection on a sphere (Alhazen's problem).