Smith, Henry John Stephen

(1826-1883), mathematician

by Keith Hannabuss

© Oxford University Press 2004 All rights reserved

Smith, Henry John Stephen (1826-1883), mathematician, was born on 2 November 1826 in Dublin, the youngest of the four children of John Smith (1792-1828), an Irish barrister, and his wife, Mary (d. 1857), one of the fourteen children of John Murphy from near Bantry Bay. After his father died in 1828, his widowed mother moved with the family several times before settling at Ryde on the Isle of Wight in 1831. A precocious child, Smith was educated first by his mother and then, from 1838, by private tutors. He went to Rugby School in 1841, but left after the death of his brother in 1843, when his family moved abroad.

On 29 November 1844 Smith was awarded a scholarship at Balliol College, Oxford, but his early undergraduate career was soon disrupted, when, on successive visits to his family on the continent, he contracted first smallpox and then malaria. None the less, he put his enforced convalescence during 1845-7 to good use. He spoke French and Italian fluently, and had a good command of German. While recuperating in Paris he was able to attend lectures at the Collège de France and the Sorbonne, in particular those of Arago and Milne Edwards. He returned to Oxford at Easter 1847, and the following year won the Ireland scholarship for classics. In 1849, just two years after resuming his studies at Oxford, he gained first-class honours in both classics and mathematics (BA 1850, MA 1855) and was elected a fellow of Balliol. In 1850, after careful consideration, he accepted the mathematical lecturership at the college, and in the following year added the senior mathematical scholarship to the list of his university distinctions.

In 1853, in response to the introduction of the new honour school of natural science, Balliol built the first college teaching laboratory and asked Smith to run it. To equip himself for this task he studied in Oxford with Nevil Story-Maskelyne, who became a close friend, and at the Royal College of Chemistry with August Hofmann. He gave chemistry lectures and practical instruction for two years, until, in December 1855, the laboratory was handed over for the use of Benjamin Brodie.

In 1861 Smith was elected Savilian professor of geometry, in succession to Baden Powell who had died suddenly the previous year, and in the same year he became both FRS and FRAS. However, he could not afford to give up the mathematical lecturership, and it was only in 1873 that his election to a sinecure fellowship at Corpus Christi College enabled him to relinquish his teaching duties at Balliol. (He retained his association with Balliol, however, by virtue of his election to an honorary fellowship.) During the late 1860s, in his capacity as Balliol's lecturer, he collaborated with his colleagues at Merton, Exeter, and University colleges in setting up the first combined college lectures. These served as a model for other subjects and groups of colleges, and formed the prototype for the system of lectures later adopted by the university.

Smith never married, and on the death of their mother in 1857 his sister Eleanor [see below] moved to keep house for him in Oxford during the terms, first at 64 St Giles' and, following his appointment as keeper of the University Museum in 1874, at the keeper's house, University Museum, South Parks Road. He was a tall, good-looking man, renowned for his charm, generosity, warmth, and spontaneous wit, who greeted the appointment of a pessimistic friend to high office in India with the words 'How fortunate! It will give him another world to despair of' ('Biographical sketches', xxxiv). It is reported that he broke off one mathematics lecture to observe that 'it is the peculiar beauty of this method, gentlemen, and one which endears it to the really scientific mind, that under no circumstances can it be of the smallest possible utility' (ibid., xxxiii-xxxiv).

Smith, who read widely and retained a strong interest in classics, enjoyed the respect of colleagues who knew little of his achievements within mathematics. His 1855 essay on the plurality of worlds in an Oxford collection was widely admired. John Conington, the professor of Latin, once remarked:

I do not know 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. ('Biographical sketches', xix)
Charles Pearson described him as 'the only one I have known whose superiority was so incontestable that it extinguished jealousy, and whose popularity was such that he had no personal enemies' (Charles Henry Pearson, 108).
Smith sought to promote the natural sciences and research within the university, without compromising its older studies or teaching. His ability to find the acceptable compromise which defuses angry debate, coupled with his unrivalled range of experience, made him an invaluable member of the numerous university committees on which he served. His friends, deploring his lack of ambition, urged him to spend less time on routine chores which could as well be done by others, but his strong sense of public duty forbade this. He saw no conflict of interests, believing that mathematics demanded a concentration impossible to maintain for more than short periods, but he did grow uneasy at the accumulation of unpublished results in his notebooks.

Despite his popularity within the university, the solid Conservative vote of the old members, aware of his Liberal sympathies, ensured Smith's defeat when he stood as a candidate for a university seat in the 1878 by-election. None the less, there were other opportunities for him to use his skills on the national stage. He was first chairman of the Meteorological Council, which he represented at the International Meteorological Congress at Rome in 1879, and sat on the royal commission into scientific instruction (the Devonshire commission) and on the royal commission into the universities. He was president of the mathematical section of the British Association at Bradford in 1873 and of the London Mathematical Society (which he had joined in the first year of its foundation) in 1874-6. His presidential address, 'On the present state and prospects of some branches of pure mathematics' (Proceedings of the London Mathematical Society, 8, 1876, 6-29), was influential and often quoted. He received honorary degrees of LLD from the universities of Cambridge and Dublin, and shared the 1868 Steiner prize of the Königliche Preussische Akademie der Wissenschaften (Royal Prussian Academy of Sciences) in Berlin for his solution of a problem on the intersection of quartic curves.

Smith's mathematical work lay mostly within geometry, number theory, and elliptic function theory. One exception is a paper on the integration of discontinuous functions (Proceedings of the London Mathematical Society, 6, 1875, 140-53), in which he constructed various fractal sets, including the Cantor set, some eight years before Cantor's own paper. His main contributions were, however, in number theory. The six-part 'Report on the theory of numbers', commissioned by the British Association, and presented at its meetings between 1859 and 1865, provided a systematic account of the subject as it had developed until that time, and was widely acclaimed by continental mathematicians as well as those in Britain. In his paper on systems of linear equations and congruences (PTRS, 101, 1861, 293-326) he showed that any matrix with integer entries can be put into what is now often called Smith normal form. This provided an elegant procedure for deciding when a system of simultaneous linear equations with integer coefficients has integer solutions, and to determine them when they exist, thus completing the solution to a problem studied since antiquity.

In 'The orders and genera of quadratic forms containing more than three indeterminates' (PRS, 16, 1867, 197-208) Smith applied the same result to find the number of ways in which a given positive integer can be expressed as a sum of some fixed number of squares. Various algebraic and analytic techniques had already provided answers for sums of two, three, four, and six squares and partial answers for five and seven squares. Smith outlined a uniform algebraic method for dealing with all the cases simultaneously and gave the full solutions to the problem for five and seven squares, thus completing the whole project. In 1882 the Paris Académie des Sciences, through some oversight, offered its grand prix de sciences mathématiques for this very problem, which Smith had already solved fifteen years earlier. When Smith alerted Charles Hermite to his priority, he was asked to help the académie avoid embarrassment by submitting his detailed work for the competition. He complied with this request, but died two months before the announcement that the prize had been awarded jointly to him and to a young Prussian student, Hermann Minkowski. After considerable public discussion of whether Minkowski had plagiarized Smith's earlier publications, a second prize was created so that each winner was awarded a full prize.

Apart from one recurrence of malaria, Smith had generally enjoyed good health, but about 1881 the strain of overwork began to show. He died at home of an abscess of the liver on 9 February 1883 and was buried on 13 February in St Sepulchre's cemetery, Oxford. After his death his mathematical papers were collected and edited by James Glaisher and, prefaced by biographical reminiscences, were published in 1894.

Smith's sister, Eleanor Elizabeth Smith (1822-1896), was born on 30 September 1822. Like her brother she travelled widely on the continent, and was a good linguist with an extensive knowledge of European literature. She taught herself Hebrew at the age of seven. In the 1860s, before the foundation of the first women's colleges in Oxford, she persuaded various professors sympathetic to the education of women to give a series of women's lectures and organized the first course in 1866. She was one of the women who gave evidence as expert witnesses to the royal commission on schools of 1864 (published in 1868 as the Taunton report). When the Oxford schools board was set up in 1871 she stood as a non-sectarian candidate and was elected as its first woman member. She remained on the board until 1883 but did not achieve her object of founding a non-denominational board school.

Eleanor Smith helped to found and was one of the original (1879) members of the council of Somerville, the women's college at Oxford, and served for many years as a trustee of Bedford College, London. In 1895 she supported the campaign to open Oxford degrees to women. In addition to her keen interest in women's education, Eleanor Smith gave generous support to schemes for improving the health of the poor. She served on the committees of both the Radcliffe Infirmary and the Sarah Acland Home for Nurses, and was a promoter and director of the Provident Dispensary. She died at her home, 27 Banbury Road, Oxford, on 15 September 1896, and was buried at St Sepulchre's cemetery, Oxford, on 19 September. The jurist A. V. Dicey, a lifelong friend, was her executor.


'Biographical sketches', The collected mathematical papers of H. J. S. Smith, ed. J. W. L. Glaisher (1894)
The Times (10 Feb 1883)
Oxford Magazine (14 Feb 1883)
Oxford Magazine (21 Feb 1883)
Nature, 27 (1882-3), 381-4
Monthly Notices of the Royal Astronomical Society, 44 (1883-4), 138-49
Fortnightly Review, 39 (1883), 653-66
Comptes Rendus, 96 (1883), 1095
Atti dell'Accademia dei Lincei, 3/7 (1883), 162-3
admissions book and minutes of college meetings, Balliol Oxf.
Pearson MSS, Bodl. Oxf., MS Eng. lett. d. 191
A. G. V. Harcourt, 'The Oxford Museum and its founders', Cornhill Magazine, [3rd] ser., 28 (1910), 350-63
M. E. G. Duff, Notes from a diary, kept chiefly in southern India, 1881-1886, 2 vols. (1899)
E. B. Elliott, 'The honour school of mathematics and physics', The English education exhibition 1900
H. A. Miers, 'Prof. N. Story Maskelyne', Nature, 86 (1910-11), 452-3
T. Smith, 'The Balliol-Trinity laboratories', Balliol Studies, ed. J. M. Prest (1982), 187-224
K. C. Hannabuss, 'Henry Smith', Oxford figures, ed. J. Fauvel, R. Flood, and R. J. Wilson (1999)
W. Stebbing, ed., Charles Henry Pearson: fellow of Oriel and education minister in Victoria (1900)
The Times (18 Sept 1896) [Eleanor Smith]
Oxford Chronicle and Berks and Bucks Gazette (19 Sept 1896) [Eleanor Smith]
Englishwoman's Review, 27 (1896), 279-80 [obit. of Eleanor Smith]
Englishwoman's Review, 28 (1897), 65-6 [obit. of Eleanor Smith]
M. J. Tuke, A history of Bedford College for Women, 1849-1937 (1939)
P. Hollis, Ladies elect: women in English local government, 1865-1914 (1987) [Eleanor Smith]

RS |  Bodl. Oxf., Pearson and English MSS
CUL, letters to Sir George Stokes
MHS Oxf., corresp. with Sir B. C. Brodie

J. E. Boehm, marble bust, 1883, RS
A. Macdonald, engraving, 1885, repro. in Glaisher, ed., Collected mathematical papers, frontispiece
S. Acland, slides (Eleanor Smith), Bodl. Oxf.
J. E. Boehm, stone bust (posthumous), Balliol Oxf.; copy, NPG
S. P. Hall, caricature, Bodl. Oxf.
Story-Maskelyne, photograph, MHS Oxf.; repro. in Morton, Oxford rebels
P. Ward-Jackson, photograph, RS
bronze bust, CCC Oxf.
carte-de-visite, repro. in V. Morton, Oxford rebels: the life and friends of Nevil Story Maskelyne (1987)
photograph, Sci. Mus., Tucker collection
photograph, Balliol Oxf.
photograph (Eleanor Smith), Bodl. Oxf.
terracotta bust, NPG

Wealth at death  
£3216 11s. 11d.: administration, 27 April 1883, CGPLA Eng. & Wales
£13,306 3s. 4d.--Eleanor Smith: probate, 23 Nov 1896, CGPLA Eng. & Wales

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