Salmon, George (1819–1904), mathematician and theologian, was born 25 September 1819 and baptised at St George's church, Temple Street, Dublin on 28 September 1819. He was the only son of Michael Salmon, linen merchant at the Linen Hall, Dublin, and subsequently at 80 Grand Parade, Cork, and Helena Salmon, daughter of the Rev. Edward Weekes. His cousin, Alicia Dowden, whose family were linen drapers in Cork, was the mother of Edward Dowden (qv), professor of English literature at TCD, and John Dowden (qv), bishop of Edinburgh. Salmon was educated at the school of Hamblin and Porter in Cork. In 1833 he matriculated at TCD, and graduated as first senior moderator in mathematics and physics in 1838. He was elected a fellow of the college in 1841 and served twenty-five years as a college tutor; his pupils included Edward and John Dowden and the two sons of William Rowan Hamilton (qv). In 1845 he was ordained priest in the Church of Ireland; thereafter, in addition to his tutoring duties, he lectured in the divinity school of Trinity College.
Salmon began his mathematical research in the mid 1840s, concentrating on the geometry of curves and surfaces. His preference was for algebraic and analytic methods, although he was influenced by the synthetic techniques of the French geometers Poncelet and Chasles, whose ideas he popularised in his textbooks. His main original result was the enumeration of the twenty-seven straight lines on a non-singular cubic surface, work done in correspondence with Arthur Cayley in 1849, but he also contributed significantly to the study of reciprocal surfaces and singularities.
Salmon's mathematical reputation is based on the four textbooks he wrote: A treatise on conic sections (1848; 6th ed. 1879); A treatise on higher plane curves (1852; 3rd ed. 1879); Lessons introductory to the modern higher algebra (1859; 4th ed. 1885); and A treatise on the analytic geometry of three dimensions (1862; 5th ed. 1912). Translations of these works were made into French, German, Italian, Russian, and Spanish. The most popular was Conic sections, intended mainly for undergraduates and based on the tutorial lectures he gave in the 1840s. A reprint of the final edition was still on sale at the beginning of the 21st century. Modern higher algebra is less geometric than his other works. It aimed to disseminate knowledge of the discoveries made in invariant theory by the English mathematicians A. Cayley and J. J. Sylvester, with whom Salmon had been in regular correspondence in the 1850s. Salmon's books were held in high esteem in Germany, where Wilhelm Fiedler reworked and translated them; Analytische Geometrie der Kegelschnitte, freely adapted from Conic sections, appeared in nine editions between 1860 and 1918. The seventh edition (1907) is prefaced by Fiedler's ten-page commemoration of Salmon. The best appraisal of Salmon's work is by Max Noether, professor at the University of Erlangen, Germany, in Math. Annalen, lxi (1905), 1–19.
Salmon was elected regius professor of divinity at Trinity College in 1866. His mathematical activity subsequently diminished as he established himself as a leading New Testament scholar. In his Historical introduction to the study of the books of the New Testament (1885; 10th ed. 1913), he poured scorn on the destructive criticism and scepticism of those theologians influenced by the Tübingen school of Ferdinand Baur, who questioned the authenticity of many of the New Testament sources. His Infallibility of the church (1888; 5th ed. 1952) was a powerful polemic which affirmed traditional protestant teaching in the light of recent claims of papal infallibility. Although he lectured convincingly and with great knowledge, Salmon was not considered to be a great theologian, as his strength lay in critical analysis and robust argument, not in making uplifting affirmations on moral and spiritual issues. His influence was strong in the Church of Ireland as a member of the general synod and Representative Church Body following the disestablishment act of 1869, and he exercised his authority to ensure that the revision of the Prayer Book, undertaken in the 1870s, was not too radical.
In 1888 Salmon was appointed provost of Trinity College, and he governed the college until his death on 22 January 1904. Salmon recognised the growing importance of pure research as a discipline in its own right in the university but he opposed its endowment, preferring to cultivate research simultaneously with teaching. His conservatism also led him to oppose the admission of women to Dublin University degrees, but he withdrew his veto in July 1903, and the first women undergraduates were admitted in January 1904.
In 1844 Salmon married Frances Anne Salvador (d. 1878), daughter of the Rev. J. L. Salvador, and he lived with his family for forty years at 81 Wellington Road, Dublin. He had four sons and two daughters, but some died in infancy or early adulthood, and only his eldest son Edward and younger daughter Fanny survived him. There are portraits of Salmon in the Common Room and Provost's House of Trinity College. There is also a seated marble statue by John Hughes (qv) in Front Square at the college. Salmon was a member of the RIA (1843) and a fellow of the Royal Society (1863), and received honorary degrees from Oxford (1868), Cambridge (1874), Edinburgh (1884), and Christiania (Oslo) (1902). Only a small part of his academic papers appears to have been preserved. Marsh's Library, Dublin, has the manuscript of Salmon's The human element in the Gospels (pub. posthumously, 1907). TCD MSS 4738–47 include family papers and photographs; MSS 1827–36, 2384–85a, and 3147–54 contain letters to W. E. H. Lecky (qv), J. H. Bernard (qv), and E. Dowden.