Prof Henry John Stephen Smith FRS FRSE FRAS LLD (2 November 1826 – 9 February 1883) was an Irish mathematician and amateur astronomer remembered for his work in elementary divisors, quadratic forms, and Smith–Minkowski–Siegel mass formula in number theory. In matrix theory he is visible today in having his name on the Smith normal form of a matrix. Smith was also first to discover the Cantor set.
Life
Smith was born in Dublin, Ireland, the fourth child of John Smith (1792–1828), a barrister, who died when Henry was two. His mother, Mary Murphy (d.1857) from Bantry Bay, very soon afterwards moved the family to England. He had thirteen siblings, including Eleanor Smith, who became a prominent educational activist. He lived in several places in England as a boy. His mother did not send him to school but educated him herself until age 11, at which point she hired private tutors. At age 15 Smith was admitted in 1841 to Rugby School in Warwickshire, where Thomas Arnold was the school's headmaster. This came about because his tutor Henry Highton took up a housemaster position there.
At 19 he won an entrance scholarship to Balliol College, Oxford. He graduated in 1849 with high honours in both mathematics and classics. Smith was fluent in French having spent holidays in France, and he took classes in mathematics at the Sorbonne in Paris during the 1846–7 academic year. He was unmarried and lived with his mother until her death in 1857. He then brought his sister, Eleanor Smith, to live with him as housekeeper at St Giles.
Smith remained at Balliol College as a mathematics tutor following his graduation in 1849 and was soon promoted to Fellow status.
In 1861, he was promoted to the Savilian Chair of Geometry at Oxford. In 1873, he was made the beneficiary of a fellowship at Corpus Christi College, Oxford, and gave up teaching at Balliol.
In 1874 he became Keeper of the University Museum and moved (with his sister) to the Keeper's House on South Parks Road in Oxford.
On account of his ability as a man of affairs, Smith was in demand for academic administrative and committee work: he was Keeper of the Oxford University Museum; a Mathematical Examiner for the University of London; a member of a Royal Commission to review scientific education practice; a member of the commission to reform University of Oxford governance; chairman of the committee of scientists overseeing the Meteorological Office; twice president of the London Mathematical Society; etc.
He died in Oxford on 9 February 1883. He is buried in St Sepulchre's Cemetery in Oxford.
Work
Researches in number theory
An overview of Smith's mathematics contained in a lengthy obituary published in a professional journal in 1884 is reproduced at NumberTheory.Org. The following is an extract from it.
Smith's two earliest mathematical papers were on geometrical subjects, but the third concerned the theory of numbers. Following the example of Gauss, he wrote his first paper on the theory of numbers in Latin: "De compositione numerorum primorum formæ ex duobus quadratis." In it he proves in an original manner the theorem of Fermat---"That every prime number of the form ( being an integer) is the sum of two square numbers." In his second paper he gives an introduction to the theory of numbers.
In 1858, Smith was selected by the British Association to prepare a report upon the Theory of Numbers. It was prepared in five parts, extending over the years 1859–1865. It is neither a history nor a treatise, but something intermediate. The author analyzes with remarkable clearness and order the works of mathematicians for the preceding century upon the theory of congruences, and upon that of binary quadratic forms. He returns to the original sources, indicates the principle and sketches the course of the demonstrations, and states the result, often adding something of his own.