Salmon, George

(1819-1904), mathematician and theologian

by Julia Tompson

© Oxford University Press 2004 All rights reserved

Salmon, George (1819-1904), mathematician and theologian, was born on 25 September 1819, probably in Dublin, the only son of Michael Salmon, linen merchant, and Helen, daughter of the Revd Edward Weekes. His family came from Cork, and he was educated there, at a private school, up to the age of fourteen. He entered Trinity College, Dublin, in 1833, was awarded a scholarship in classics in 1837, and afterwards turned to the study of mathematics. Eighteen months later, in 1838, he obtained his degree as first mathematical moderator (that is, the best student in his year). Scholars were expected to attend some theology lectures, which he did in 1839, and he was persuaded to take the fellowship examination in 1840, although he felt unprepared. To his astonishment he won Madden's prize, which was awarded to the candidate placed second. After another year of study he was elected to a fellowship.

Salmon settled down to the work of a college tutor and to the study of pure mathematics. The statutes of Trinity College required that he be ordained in the Church of Ireland, and he became deacon in 1844 and priest in 1845. His marriage to Frances Anne (d. 1878), daughter of the Revd J. L. Salvador of Staunton, Herefordshire, took place in 1844. They had four sons and two daughters, of whom the eldest son (Edward William) and younger daughter (Fanny Mary) survived him. Salmon began lecturing in theology as well as mathematics in 1845, and became devoted to both subjects. In 1858 he was appointed Donegal lecturer in mathematics and in 1859 he received the degrees of BD and DD. When, after about fifteen years, no professorship in mathematics was forthcoming at the university, Salmon, frustrated by the heavy teaching load, turned his attention more to theology. In 1866 he became regius professor of divinity and resigned his fellowship. He remained at Trinity College for the rest of his life, and in 1888 was appointed provost (an appointment made by the crown), with the unanimous approval of the fellows. He presided over the governing body of the college and exercised a wide and powerful influence over its affairs, and in 1892 led the tercentenary celebrations of Dublin University. His years as provost were characterized by consolidation rather than reform; the admission of women to university degrees, carried out in the last year of his life, was almost the only important change that he disliked.

Mathematical work
The contributions to mathematics for which Salmon is chiefly remembered are his textbooks. They dealt, as did his original research, with geometry and algebra. He had the rare ability to present a theory as an organic whole and not as a series of disjointed propositions. After his death Horace Lamb remarked on the 'brilliant contrast which they [Salmon's books] exhibited with most of the current textbooks of that time' (Lamb, 421).

The best known of Salmon's textbooks was the first to be written, A treatise on conic sections, containing an account of some of the most important modern algebraic and geometric methods (1848). In this book he exhibited the power of Cartesian co-ordinates and drew together methods of analytic and descriptive geometry. It was translated, as were his other three textbooks, into many western European languages, and, like the others, ran to many editions. It was still a standard text in 1948, when the centenary of publication was remembered by an article in the Mathematical Gazette, and brought Salmon recognition from the leading mathematicians of his day. He followed up this success with A Treatise on the Higher Plane Curves (1852), a subject which was then little known and previously only accessible through the memoirs of scientific societies. By the simplicity of his methods he was able to minimize the difficulties of this subject; for example, he realized that the axes of a Cartesian co-ordinate system can be placed anywhere, and in this way the equation of a curve can be greatly simplified.

At this time the theory of the invariants of quantics was being investigated by Cayley and Sylvester in England, and by others on the continent. Salmon perceived the importance of this work and began to apply their results to geometrical theory. The result was Lessons Introductory to the Modern Higher Algebra (1859), a textbook containing much original material. He was a prodigious calculator: the second edition of this book (1866) contained a formula which ran to thirteen printed pages. His last textbook was A Treatise on the Analytic Geometry of Three Dimensions (1862), in which he applied the methods he had developed for conics to curves of three dimensions. He never dealt with four-dimensional space or non-Euclidean geometry; R. S. Ball 'heard him say, jestingly, that he reserved such themes for the next world' (Ball, xxvi).

In addition to textbooks Salmon published his own research in various journals, including the Philosophical Magazine, Quarterly Journal of Mathematics, Cambridge and Dublin Mathematical Journal, and Proceedings of the Royal Irish Academy. He published forty-one papers between 1844 and 1873, mainly on numerical characteristics of curves and surfaces. He corresponded with many mathematicians, and became a close friend of Cayley and Sylvester. When he approached Cayley to find a young mathematician to help with a second edition of Higher Plane Curves, Cayley offered to do the work himself; the discovery of the twenty-seven lines on a cubic surface was made by the two men.

Theological work
From the time Salmon was ordained priest in 1845 he began to take part in the work of the divinity school at Trinity College, as assistant to the regius professor. His ability as a preacher was soon recognized; his first publication on a theological topic was a sermon on prayer in 1849, and he had many sermons published, all characterized by his vigorous common sense, originality, and bold but unaffected style. His contemporaries recorded that these addresses were better to read than to hear, because his delivery was bad, but that he was an excellent extemporaneous speaker, especially in synod.

In 1852 Archbishop Whately made Salmon an examining chaplain, and the archbishop's influence on Salmon's theological opinions seems to have been considerable. Both were strong protestants and deeply suspicious of the rise of the Oxford Movement. Responding to the publication of Tracts for the Times by the Oxford Movement, Whately, Salmon, and others issued their Cautions for the Times (1853). Salmon was a regular contributor to the Catholic Layman on the Roman Catholic controversy, and had three short stories published anonymously in 1854 dealing with the same subject. This material proved useful later when, as professor of divinity, he lectured on the points of debate between Roman Catholics and Anglicans. These lectures formed the basis of The Infallibility of the Church (1889), a brilliant display of polemic which exhibited his learning, humour, and critical abilities to the full.

When Salmon accepted the regius professorship of divinity in 1866 he embarked on theology and biblical criticism with the same enthusiasm and vigour which had characterized his mathematical studies. His Introduction to the New Testament (1885) is a criticism of the work of Baur and the Tübingen school on the origin and character of the books of the New Testament. Salmon's conservative views were influential throughout the United Kingdom. He became an authority on the Christian writers of the second century when he was asked to contribute articles for the Dictionary of Christian Biography (1877-87). He was foremost a historian and did not care for textual criticism, but he revealed his considerable abilities in this area when he published Thoughts on the Textual Criticism of the New Testament (1897).

During the last ten years of his life Salmon devoted much time to the synoptic problem. His notes were edited after his death by a former pupil, N. J. D. White, as The Human Element in the Gospels (1907). In addition to pamphlets and several books of sermons, Salmon wrote academic essays for biblical commentaries and popular articles for magazines. He took part in current debates about the keeping of the sabbath, eternal punishment, and above all the continuing 'Roman Catholic question'.

The years after Salmon's appointment as regius professor were critical for the Irish church, which was disestablished and disendowed in 1869, and it was vitally important that the divinity school at Trinity College should be properly led. Salmon played an active part in the reconstruction of the church and held a unique and influential position in the general synod and as a member of the Representative Church Body. He managed the church's finances and investments with great skill and was involved in the revision of the prayer book. He was remembered by his colleagues as a formidable debater, able to hold the attention of his audience even in old age when his voice was failing.

Salmon's great strength as a theologian was his critical ability. He founded no school of theological thought, although he was greatly admired by his many pupils. His friend J. H. Bernard recorded that 'he was more anxious to train men to see clearly than to train them to see what he saw' (PBA, 314). Salmon tended towards a liberal evangelicalism, which distrusted more and more an appeal to any authority other than that of individual conscience. In politics he was strongly Conservative, and although he disliked political controversy, he considered it his duty to oppose Irish home rule, which he was convinced would be disastrous.

Honours and character
Salmon received many academic honours in addition to those which his own university bestowed. He was a member of the Royal Irish Academy (1843), which awarded him the Cunningham medal in 1858. The Institut de France elected him a foreign member, and the royal academies of Berlin, Göttingen, and Copenhagen elected him honorary member. He was fellow of the Accademia dei Lincei of Rome (1885); he was made honorary DCL Oxford (1868), LLD Cambridge (1874), DD Edinburgh (1884), and DMath Christiania (1902). In 1863 he was elected fellow of the Royal Society, which awarded him the royal medal in 1868 and the Copley medal in 1889; he became FRS Edinburgh, and was on the founding list of the fellows of the British Academy (1902). He was president of the mathematical and physical section of the British Association in 1878. He was also chancellor of St Patrick's Cathedral (1871), and was presented with the freedom of the city of Dublin in 1892.

Salmon was a competent musician and an excellent chess player, and found time to pursue his love of music and chess throughout his career. He was an omnivorous reader (excepting metaphysics and poetry, which he disliked), described as 'an indefatigable devourer of fiction' (Stokes, 164). He was a well-known figure in Dublin, where his theological works were widely read and his jokes widely circulated, and was remembered by friends as a skilled impersonator with a fund of entertaining anecdotes. His hospitality was generous, although he himself lived in simplicity despite the luxuries available to him as provost. He was described by a contemporary as having strong and vigorous features, a well-set jaw, and massive forehead: 'His very body, mountainous in its bulk ..., inspires a feeling of respect in smaller men' (ibid.). After several months of increasing physical weakness, he died at the provost's house, Trinity College, Dublin, on 22 January 1904, and was buried in Mount Jerome cemetery.

JULIA TOMPSON

Sources  
J. Ossory, The Times (23 Jan 1904)
Nature, 69 (1903-4), 324-6
C. J. J. [C. J. Joly], PRS, 75 (1905), 347-55
R. S. Ball, Proceedings of the London Mathematical Society, 2nd ser., 1 (1904), xxii-xxviii
DNB
J. H. Bernard, New Liberal Review, 7/38 (March 1904), 156-67
G. T. Stokes, 'Leaders of religious thought and action: Rev. George Salmon, D.D.', Review of the Churches, 2/9 (15 June 1892), 159-64
M. Noether, Mathematische Annalen, 61 (1905), 1-19
J. H. Bernard, 'Dr George Salmon', PBA, [1] (1903-4), 311-15
H. Lamb, Report of the British Association for the Advancement of Science, 74 (1904), 421
H. Fehr, L'enseignement mathématique, 6 (1904), 232

Archives  
TCD, corresp. and papers |  TCD, letters to Edward Dowden
TCD, letters to William Lecky
UCL, letters to Thomas Hirst

Likenesses  
S. Purser, portrait, 1888, TCD
Lawrence, photograph, before 1892, repro. in Stokes, 'Leaders of religious thought and action', facing p. 159
photograph, 1892, RS
B. Constant, portrait, 1897, TCD, provost's house
A. B. Joy, bronze bas-relief, after 1904, St Patrick's Cathedral, Dublin
J. Hughes, marble statue, 1911, TCD
photograph, RS

Wealth at death  
£16,514 17s. 3d.: Irish administration with will sealed in London, 16 April 1904, CGPLA Ire.
£28,431 2s. 9d.: resworn administration, 8 March 1904, CGPLA Ire.


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