Henry John Stephen Smith
Henry John Stephen Smith (November 2 1826 - February 9 1883) was an Irish mathematician, remembered for his work in number theory: elementary divisors, quadratic forms) and matrices. The Smith normal form for matrices are named after him.
He was born in Dublin, Ireland, the fourth child of John Smith, a barrister, who died when he was two. Mrs. Smith moved to Oxford, and at the age of 15 Henry Smith went to Rugby school (1841). At 19 he won an entrance
scholarship at Balliol College, Oxford. For health reasons he went to Paris, and took courses at the Sorbonne
and the CollÃÂège de France.
In 1849, when 23 years
old, finished his undergraduate career with a double-first; that
is, in the honors examination for bachelor of arts he took
first-class rank in the classics, and also first-class rank in the
mathematics. He suffered from poor health, missing his final year at Rugby while convalescing in Italy. In late 1844 he tried for and obtained the Balliol scholarship. While at Oxford his health did not improve, he was struck down with malaria while in Frascati in 1845 and he did not return to Oxford until 1847. He graduated in 1849 with a double first in mathematics and classics. Soon after,
he became one of the mathematical tutors of Balliol.
Smith remained at Balliol, becoming a fellow (1850), then working as a tutor before being appointed Savilian Professor of Geometry in 1861. He was elected to the Royal Society and to the Royal Astronomical Society in 1861.
On account of his ability as a man
of affairs, Smith was in great demand for University and
scientific work of the day. He was made Keeper of the University
Museum; he accepted the office of Mathematical Examiner to the
University of London; he was a member of a Royal Commission
appointed to report on Scientific Education; a member of the
Commission appointed to reform the University of Oxford; chairman
of the committee of scientists who were given charge of the
Meteorological Office, etc. It was not till 1873, when offered a
Fellowship by Corpus Christi College, that he gave up his tutorial
duties at Balliol.
The London Mathematical Society was founded in 1865. He was for
two years president.
His 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 number) is the sum of
two square numbers." In his second paper he gives an introduction
to the theory of numbers.
In 1858 he was selected by the British Association
that body 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.
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. Some were in
complete form and appeared in the Philosophical Transactions of the Royal Society of London; others were
incomplete, giving only the results without the extended
demonstrations, and appeared in the Proceedings of that Society.
One of the latter, entitled "On the orders and genera of
quadratic forms containing more than three indeterminates,"
enunciates certain general principles by means of which he solves
a problem proposed by Eisenstein, namely, the decomposition of
integer numbers into the sum of five squares; and further, the
analogous problem for seven squares. It was also indicated that
the four, six, and eight-square theorems of Jacobi, Eisenstein and
Lionville were deducible from the principles set forth.
In 1868 he returned to the geometrical researches which had first
occupied his attention. For a memoir on "Certain cubic and
biquadratic problems" the Royal Academy of Sciences of Berlin
awarded him the Steiner prize.
In February, 1882, he was surprised to see in the Comptes rendus that the subject proposed by the Paris Academy of Science
for the Grand prix des sciences mathÃÂématiques 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. According to the rules each manuscript bears a motto,
and the corresponding envelope containing the name of the
successful author is opened. 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.
Two months after his death the Paris Academy made their award. Two
of the three memoirs sent in were judged worthy of the prize. When
the envelopes were opened, the authors were found to be
Smith and Minkowski, a young mathematician of Koenigsberg,
Prussia. No notice was taken of Smith's previous publication on
the subject, and M. Hermite on being written to, said that he
forgot to bring the matter to the notice of the commission.
Education
Academic career
Mathematical publications
External link