SMITH, HENRY JOHN STEPHEN (1826-S31. An eminent English mathematician, born in Dublin. lie was educated at Oxford. In 1848 he gained the Ireland University scholarship, and in 1849 was elected Fellow of Balliol. In 1850 he was appointed lecturer in mathematics at Balliol College. and in 1851 senior scholar in mathe matics. In 1860 Smith became Savilian professor of geometry, and in 1861 was elected Fellow of the Royal Society and of the Royal Astronomi cal Society.
Smith was the leading English writer on the theory of numbers and a disciple of Gauss, whose writings he thoroughly examined. These re searches occupied his time from 1S54 to 1864, and are contained in his Report on the Theory of Numbers, presented to the British Association in six parts, 1859-65. His most important con tributions were contained in two papers: Systems of Linear Indeterminate Equations and Congruences" and "On the Orders and Genera of Ternary Quadratic Forms" (1861, 1867). Smith
gave the formula• relating to the representation of a number as a sum of five squares, and also of seven squares. Jacobi had proved the cases of two, four, and six squares: Eisenstein had proved the ease of three squares, but left that. of five squares without demonstration. This was supplied by Smith, but through an unaccountable oversight the French Academy set this as time subjett of their 'Grand prix des sciences matInhnatiques' for 1882. The prize of 3000 francs was awarded him two months after his death. Smith also devoted his attention to elliptic functions, the results of which were published in the Proceed. in (IS of the London :Mathematical Society. Smith's published writings were collected and edited by Olaisher, in two volumes (Oxford. 1894). Consult: Monthly Yotices of the Royal Astronomical Society, vol. xliv.; and the Fort nightly Hegira' (May, 1883).