James MacCullagh (1809 – 24 October 1847) was an Irish mathematician. Early Life MacCullagh was born in Landahaussy, near Plumbridge, County Tyrone, Ireland, but the family moved to Curly Hill, Strabane when James was about 10. He was the eldest of twelve children and demonstrated mathematical talent at an early age. He entered Trinity College Dublin as a student in 1824, winning a scholarship in 1827 and graduating in 1829. Career He became a fellow of Trinity College Dublin in 1832 and was a contemporary there of William Rowan Hamilton. He became a member of the Royal Irish Academy in 1833. In 1835 he was appointed Erasmus Smith's Professor of Mathematics at Trinity College Dublin and in 1843 became Erasmus Smith's Professor of Natural and Experimental Philosophy. He was an inspiring teacher and taught notable scholars, including Samuel Haughton, Andrew Searle Hart, John Kells Ingram and George Salmon. He had been involved in repeated priority disputes with Hamilton. In 1832, Hamilton published a prediction of conical refraction. In 1833, MacCullagh claimed that it is a special case of a theorem he published in 1830 that he did not explicate, since it was not relevant to that particular paper. In 1842, Hamilton speculated on a model of ether, to which MacCullagh claimed that he had speculated on the same model. Although he worked mostly on optics, he is also remembered for his work on geometry; his most significant work in optics was published in the mid-to-late 1830s; his most significant work on geometry On surfaces of the second order was published in 1843. He was awarded the Cunningham Medal of the Royal Irish Academy in 1838 for his paper on On the laws of crystalline reflexion and refraction. He won the Copley medal for his work on the nature of light in 1842. MacCullagh was involved with British Association for the Advancement of Science. He corresponded with many notable scientists, including John Herschel and Charles Babbage. In Passages from the Life of a Philosopher, Charles Babbage wrote that MacCullagh was "an excellent friend of mine" and discussed the benefits and drawbacks of the analytical engine with him. Work on Light and Optics MacCullagh's most important paper on optics, An essay towards a dynamical theory of crystalline reflection and refraction, was presented to the Royal Irish Academy in December 1839. The paper begins by defining what was then a new concept, the