In 1904, as a lecturer at the University of Liverpool, he began work on a new theorem in relativity with fellow lecturer Harry Bateman. They brought the methods of inversive geometry into electromagnetic theory with their transformations (spherical wave transformation):
- Each four-dimensional solution [to Maxwell's equations] could then be inverted in a four-dimensional hypersphere of pseudo-radius K in order to produce a new solution. Central to Cunningham's paper was the demonstration that Maxwell's equations retained their form under these transformations.
In August 1911 he returned to St John's College where he made his career. When drafted for the war in 1915 he did alternative service growing food and in an office at the YMCA. He held a university lectureship from 1926 to 1946.
His book The Principle of Relativity (1914) was one of the first treatises in English about special relativity, along with those by Alfred Robb and Ludwik Silberstein. He followed with Relativity and the Electron Theory (1915) and Relativity, Electron Theory and Gravitation (1921). McCrea writes that Cunningham had doubts whether general relativity produced "physical results adequate return for mathematical elaboration."
- "Cunningham, Ebenezer (CNNN899E)". A Cambridge Alumni Database. University of Cambridge.
- Warwick, page 423.
- Cunningham, Ebenezer (1910). "The principle of Relativity in Electrodynamics and an Extension Thereof". Proceedings of the London Mathematical Society. 8: 77–98. doi:10.1112/plms/s2-8.1.77.
- William McCrea (1978), "Ebenezer Cunningham", Bulletin of the London Mathematical Society 10: 116–126 subscription required.
- Andrew Warwick (2003), Masters of Theory: Cambridge and the Rise of Mathematical Physics, University of Chicago Press, pp. 409–36.
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