MacCullagh, James (1809–47), mathematician and mathematical physicist, was born in Landahussy townland in the parish of Upper Badoney, Co. Tyrone, eldest among twelve children of James MacCullagh (1777–1857), farmer, and his wife Margaret (née Ballentine; 1784–1839). He was educated initially at the parish school at Castledamph, but on noting his intellectual precocity, his father moved to Strabane to ensure a better education for his son. After completing his classical studies he was sent to Lifford, where he was educated at the schools of the Rev. John Graham (qv) and the Rev. Thomas Rollestone (1789–1850). He entered Dublin University in November 1824 as a pensioner, winning a sizarship (1825) and scholarship (1827) before graduating BA (1829). During this period he took up rooms in the university and resided there till his death in 1847. On graduation he twice competed unsuccessfully for a fellowship, eventually being awarded one in 1832. While an undergraduate, he completed an original theory of the rotation of a solid body around a fixed point. He communicated his work on this area to his professor, Bartholomew Lloyd (qv), but the work had already been preceded by French mathematician Louis Poinsot's theory of rotary motion (1834).

MacCullagh's great contribution in mathematical physics was to the contemporary debate over the nature of light and its propagation throughout the universe. By the mid 1820s the wave theory of light propounded by Augustin Fresnel (1788–1827) had gained preeminence over the competing corpuscular theory. Wave phenomena demanded the existence of the ether (a hypothetical medium for transmitting light or heat) as a mechanical medium subject to dynamical laws. MacCullagh's first published paper, ‘On the double refraction of light in a crystallised medium, according to the principles of Fresnel’ and ‘Geometrical theorems on the rectification of the conic sections’ (*RIA* *Trans.*, xvi (1830), 65–83), criticised the obscure mathematical methods used by Fresnel in his theoretical studies on the laws of double refraction of light in crystals. MacCullagh presented a series of conic theorems aimed at providing the mathematical tools, which would enable the theory of light to be placed on a simpler geometric basis, presenting a simpler method for constructing the Fresnel wave surface. The papers contained little that was original but were characterised by clarity and mathematical elegance, highlighting his undoubted skill as a geometer. His first major paper, ‘Geometric propositions applied to the wave theory of light’ (1833) contained many original applications to the wave theory of light, obtaining a set of underlying hypotheses more physically acceptable than Fresnel's. He was awarded the Cunningham medal by the RIA (1838) for his paper ‘On the laws of crystalline reflexion and refraction’ (*RIA Trans.*, xviii (1838), 31–74), which developed a mechanical model for the propagation of light in a crystalline medium. This led to a priority dispute with Franz Ernst Neumann (1798–1895) who had read a paper on the same subject to the Berlin Academy in December 1835 (published 1837).

His most important contribution to the theory of light, ‘An essay towards a dynamical theory of crystalline reflexion and refraction’ was read before the RIA in December 1839 (and published in *RIA Trans.*, xxi (1848), 17–50) and verified all his preceding predictions respecting the laws of propagation and reflection, by showing that both sets of laws, although so widely different in their nature, had nevertheless a common origin in a higher and more ultimate law, from which they were particular deductions. In this paper he succeeded in deducing from a single physical hypothesis, and from strictly mechanical principles, all the known laws of crystalline propagation, reflection, and refraction. This provided a mathematical framework capable of describing accurately a wide range of optical phenomena, and was his greatest achievement as a natural philosopher. However, the key feature of his ether was that it had the unfamiliar characteristic of purely rotational elasticity. He provided no justification for this property, as he was unable to provide a dynamical basis for the restoring forces that were required. In 1843 he published a paper ‘On surfaces of the second order’ which constituted his most important contribution to mathematics.

In 1835 he was appointed Erasmus Smith professor of mathematics at the University of Dublin, and later received the degrees of LLB and LLD (1838). He developed the school of mathematics, giving it a geometrical bias, and as examiner (1837–43) in mathematics at the annual fellowship examinations, he ensured that a high standard was maintained. In 1843 he was appointed Erasmus Smith professor of natural and experimental philosophy, and extended the range of subjects for the fellowship examination to include heat, magnetism, and electricity, while making provision for practical work in these and related subjects. He was an inspiring teacher and counted Samuel Haughton (qv), George Salmon (qv), John Kells Ingram (qv), and John Jellett (qv) among his students. In 1841 he, along with Humphrey Lloyd (qv) and Thomas Luby (qv), petitioned the university to establish a chair of engineering; he subsequently taught mechanics and physics in that department. In 1842 he won the Royal Society's Copley medal for his work on the nature of light; he was elected a fellow in the following year.

He became a member of the RIA (1833), served as its secretary (1842–6), and with his close friend George Petrie (qv) played an important role in the development of its collection of Irish antiquities. A keen patriot devoted to his country, he purchased the early twelfth-century Cross of Cong and contributed over £300 towards the purchase of the Domhnach Airgid, a fourteen-century Irish shrine, for the Academy's national collection. Both are now held in the NMI.

In 1847, appalled that the university was putting forward two Oxford graduates (Frederick Shaw (qv) and G. A. Hamilton (qv)) for election for one of the parliamentary Dublin University seats, he unsuccessfully contested the August general election as a liberal candidate, though he was not associated with any party. His defeat and his general state of overworking brought on a severe bout of depression, to which he was periodically susceptible. On 24 October 1847 he was found in his rooms with his throat cut. The coroner gave a verdict of suicide under temporary insanity. There remains an element of mystery surrounding the disappearance of some of his manuscripts at this time. He was buried in Upper Badoney, Co. Tyrone. At the time of his death he was supporting three sisters and a younger brother; a civil list pension was procured for his sisters after an appeal to the prime minister. A marble bust of MacCullagh by Christopher Moore (qv) is located in the common room of TCD.

In the wake of James Clerk Maxwell's electromagnetic theory, George Francis Fitzgerald (qv) and Joseph Larmor (qv) showed that MacCullagh's ether theory could support both magnetic and electrical fields. However, the work of Albert Einstein rendered ether concepts irrelevant.