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).
