Henry John Stephen Smith (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.

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.

[5] 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.

An overview of Smith's mathematics contained in a lengthy obituary published in a professional journal in 1884 is reproduced at NumberTheory.Org.

Following the example of Gauss, he wrote his first paper on the theory of numbers in Latin: "De compositione numerorum primorum formæ

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.

During the preparation of the Report, and as a logical consequence of the researches connected therewith, Smith published several original contributions to the higher arithmetic.

For a memoir on "Certain cubic and biquadratic problems" the Royal Academy of Sciences of Berlin awarded him the Steiner prize.

In February, 1882, Smith was surprised to see in the Comptes rendus that the subject proposed by the Paris Academy of Science for the Grand prix des sciences mathématiques was the theory of the decomposition of integer numbers into a sum of five squares; and that the attention of competitors was directed to the results announced without demonstration by Eisenstein, whereas nothing was said about his papers dealing with the same subject in the Proceedings of the Royal Society.

He wrote to M. Hermite calling his attention to what he had published; in reply he was assured that the members of the commission did not know of the existence of his papers, and he was advised to complete his demonstrations and submit the memoir according to the rules of the competition.

There were still three months before the closing of the concours (1 June 1882) and Smith set to work, prepared the memoir and despatched it in time.

When the envelopes were opened, the authors were found to be Smith and Minkowski, a young mathematician of Königsberg, Prussia.