# Smith, Henry John Stephen (DNB00)

**SMITH**, HENRY JOHN STEPHEN (1826–1883), mathematician, born in Dublin on 2 Nov. 1826, was the youngest of the four children (two sons and two daughters) of John Smith (1792–1828), an Irish barrister, who married, in 1818 Mary, one of fourteen children of John Murphy, a country gentleman living near Bantry Bay. The mathematician was named after his father's law tutor, Henry John Stephen [q. v.] After the elder Smith's death, in 1828, his widow removed to the Isle of Man in 1829, and settled at Ryde in the Isle of Wight in 1831.

Henry Smith, who was a delicate child, taught himself some Greek at the age of four, and at seven became absorbed in Prideaux's ‘Connection.’ His education was entirely conducted by his mother, a highly accomplished woman, until 1838, when he was placed under his first tutor, Mr. R. Wheler Bush, who was astonished by his classical proficiency. In 1840 Mrs. Smith came to reside at Oxford, where Henry became the pupil of Henry Highton [q. v.] Next year he went to Rugby, where Highton had been appointed a master; but in 1843, after the death of his brother Charles of rapid consumption, he spent the winter at Nice, and the following summer by the Lake of Lucerne. Nevertheless he won the Balliol scholarship easily on 30 Nov. 1844, and at the examination made the acquaintance of Benjamin Jowett, then tutor, who became his lifelong friend. ‘He was,’ wrote Jowett, ‘possessed of greater natural abilities than any one else whom I have known at Oxford. He had the clearest and most lucid mind, and a natural experience of the world and of human character hardly ever to be found in one so young.’

Smith passed the years 1845–6 on the continent. At Rome, where he suffered a severe illness, he acquired a sound knowledge of Roman antiquities and inscriptions, and a satisfactory command of Italian, German, and French. While still convalescent he attended lectures in Paris, at the Sorbonne and the Collège de France, and was the delighted auditor of Arago and Milne-Edwards. He resumed his Oxford career at Easter 1847. It proved of almost unexampled brilliancy. He gained the Ireland University scholarship in 1848; he took a double first-class, and was elected a fellow of Balliol in 1849 (B.A. 1850, M.A. 1855). In 1850 he accepted a mathematical lectureship at Balliol College, and obtained the senior mathematical scholarship in 1851. Up to this date he was undecided whether to pursue classics or mathematics, and showed as much aptitude for the one as for the other. ‘I do not know,’ John Conington [q. v.] once said, ‘what Henry Smith may be at the subjects of which he professes to know something; but I never go to him about a matter of scholarship, in a line where he professes to know nothing, without learning more from him than I can get from any one else.’ He continued to lecture on mathematics at Balliol till 1873, when he resigned his fellowship and lectureship on receiving a sinecure fellowship at Corpus Christi College. He was elected an honorary fellow of Balliol in 1882.

In 1853 there seemed a danger of his being diverted to chemistry. Being called upon to lecture on the subject, he studied under Professor Story-Maskelyne, with whom he formed an enduring friendship, and reached the conviction that the properties of the elements are so connected by mathematical relations as to be discoverable by reasoning in anticipation of experience.

Smith was elected in 1860 to the Savilian chair of geometry, and became both F.R.S. and F.R.A.S. in 1861. He acted as president of the mathematical section of the British Association at Bradford in 1873, and of the Mathematical Society of London in 1874–6. In 1877 he became the first chairman of the meteorological council in London; and attended, as its representative, the international meteorological congress at Rome in 1879.

On the death of his mother, in 1857, he had been joined at Oxford by his sister, Eleanor Elizabeth Smith (1822–1896), a woman of exceptional ability and judgment, whose main energies were devoted to philanthropic and educational objects, and their house was the scene of much genial hospitality. During the vacations Smith travelled in Italy, Greece, Spain, Sweden, and Norway, and attended the meetings of the British Association. In 1874 he was appointed keeper of the university museum. The office ‘gave him a pleasant house, a small stipend, and not very uncongenial duties.’ But much of his time was still taken up with educational business. He was for many years a member of the Hebdomadal Council, as well as of innumerable boards and delegacies. From 1870 he sat on the royal commission on scientific education, and in great measure drafted its report. In the same year he accepted the post of mathematical examiner at the university of London, and was in 1871 appointed by the Royal Society a member of the governing body of Rugby school. In commenting on his nomination in 1877 as one of the Oxford University commissioners, Sir M. E. Grant Duff spoke of him in the House of Commons as ‘a man of very extraordinary attainments,’ even apart from the special qualifications implied by his position in the first rank of European mathematicians, while ‘his conciliatory character made him perhaps the only man in Oxford who was without an enemy.’ He received the honorary degrees of LL.D. from the universities of Cambridge and Dublin.

In 1878 Smith unsuccessfully contested the parliamentary representation of the university of Oxford in the liberal interest. He was a ready and telling speaker, but his candidature was urged on academic rather than on political grounds.

Smith's health had strengthened as he grew up; but in 1881 it began to be impaired by overwork. He died unmarried on 9 Feb. 1883, aged 56, and was buried at St. Sepulchre's cemetery, Oxford. His death evoked a chorus of eulogies. ‘Among the world's celebrities,’ in Lord Bowen's opinion, ‘it would be difficult to find one who in gifts and nature was his superior.’ He impressed Professor Huxley ‘as one of the ablest men I ever met with; and the effect of his great powers was almost whimsically exaggerated by his extreme gentleness of manner, and the playful way in which his epigrams were scattered about. I think that he would have been one of the greatest men of our time if he had added to his wonderfully keen intellect and strangely varied and extensive knowledge the power of caring very strongly about the attainment of any object.’

Smith was, in fact, devoid of ambition and initiative. His strong sense of public duty almost compelled him to accede to the innumerable demands upon his time; and the work for which he was supremely fitted was constantly pushed on one side by tasks within the range of ordinary capacity. Many of his intimate friends scarcely knew that he was a great mathematician. Some of his witticisms are worth preserving. Thus, to the remark, ‘What a wonderful man Ruskin is, but he has a bee in his bonnet,’ he replied ‘Yes, a whole hive of them; but how pleasant it is to hear the humming!’ In appearance Smith was tall and good-looking, with an air of intellectual nobility. He was ‘very manly in his bearing,’ according to Professor Jowett, and ‘a thorough man of the world.’ His manner to all classes was singularly urbane. A bust by Sir Edgar Boehm is in the National Portrait Gallery, and an engraved portrait is prefixed to his ‘Collected Mathematical Papers.’

As a mathematician, Smith was the greatest disciple of Gauss. He resembled him in the finish of his style, in the rigour of his demonstrations, above all in the special bent of his genius. ‘The Theory of Numbers’ predominantly attracted him; his *magnum opus* was to have been a treatise on the subject, his preliminary studies for which were embodied in his masterly ‘Report on the Theory of Numbers,’ presented to the British Association in six parts, during 1859–1865. This is an account of the progress and state of knowledge in that branch, with critical commentary and original developments. Two final sections remained unwritten. The most important advance in the higher arithmetic since Gauss's time was made in Smith's papers, ‘On Systems of Linear Indeterminate Equations and Congruences’ (*Phil. Trans*. cli. 293, 1861), and ‘On the Orders and Genera of Quadratic Forms’ (*ib*. clvii. 255, 1867), with a supplementary communication, in which he extended and generalised the results already enounced. Through an unaccountable oversight, the problem which he had thus completely solved, was proposed by the French Academy as the subject of their ‘Grand Prix des Sciences Mathématiques’ for 1882. Smith was induced to compete by the assurance that full justice should be done to his earlier investigation; but the promise was forgotten. Two months after his death two prizes were awarded—one to a memoir in which Smith had given the demonstrations of his former theorems, the other to the work of a competitor who might have followed the indications which Smith had previously published. M. Bertrand offered a partial apology for this obvious injustice at the sitting of the academy on 16 April 1883 (*Comptes Rendus*, xcvi. 1096).

Smith had a remarkable power of verbal exposition in abstruse mathematical subjects. A great number of his researches, never written out for publication, were thus laid before the British Association and the Mathematical Society. Only their titles have been preserved (for a list of them, see Dr. Glaisher's ‘Introduction’ to Smith's *Mathematical Papers*, p. 76). He was less concerned to record than to obtain new results. ‘Most of his mathematical work he did in his head by sheer mental effort. … The fact that he used pen and paper so little, relying on his brain as it were, increased the mental strain of his mathematical production.’ ‘Moreover, the high standard of completeness which he exacted from himself in his published writings added considerably to the effort with which his finished work was produced’ (ib. p. 87). Unfinished results accumulated, and, towards the end, inspired him with uneasiness about their fate.

Smith left forty mathematical notebooks, more than a dozen of which were filled with records of original theorems, suggestions or divinations; but in too disjointed a condition to be rescued from oblivion by print. His published writings were, however, brought together under the editorship of Dr. Glaisher, and issued from the Clarendon Press in 1894, with the title, ‘The Collected Mathematical Papers of Henry John Stephen Smith, M.A., F.R.S.’ (2 vols. 4to); and biographical sketches and recollections by Dr. Charles Henry Pearson [q. v.], Professor Jowett, Lord Bowen, and Mr. Strachan-Davidson, besides a mathematical introduction by the editor, were prefixed. The contents of the volumes fall under three headings: (1) geometry; (2) the theory of numbers; (3) elliptic functions. The memoirs are models of form. The reasonings wrought out in them are of invincible strength, and the clear-cut symmetrical manner of their presentation attests both labour and genius. Their author followed Gauss's maxim, *Pauca sed matura*.

Smith contributed to the ‘Oxford Essays’ in 1855 a brilliant paper on the ‘Plurality of Worlds;’ wrote a memoir of Professor Conington, prefixed to his ‘Miscellaneous Writings’ (London, 1872); and an introduction to the ‘Mathematical Papers of William Kingdon Clifford’ (London, 1882).

[Authorities cited; Times, 10 Feb. 1883, and (for Miss Smith) 18 Sept. 1896; Fortnightly Review, xxxiii. 653 (Glaisher); Monthly Notices Royal Astronomical Society, xliv. 138; Nature, 16 Feb. 1883 (Spottiswoode), and 27 Sept. 1894 (MacMahon); Athenæum, 17 Feb. 1883; Academy, 17 Feb. 1883; Comptes Rendus, xcvi. 1095 (Jordan); Rouse Ball's Short History of Mathematics, p. 424; Foster's Alumni Oxon.; Rugby School Register, i. 224; Proceedings London Math. Society, xiv. 322.]