James MacCullagh (1809 – 24 October 1847) was an Irish mathematician. He was a fellow of Trinity College Dublin and a contemporary there of William Rowan Hamilton. He worked mostly on optics; the field equations stemming from this purely gyrostatic medium were shown to be in accord with all known laws, including those of Snell and Fresnel but were then mostly forgotten with his death.

in 1880, FitzGerald re-discovered and re-interpreted his findings in the light of Maxwell's work.