Henry John Stephen Smith

Henry John Stephen Smith
Born	(1826-11-02)2 November 1826 Dublin, Ireland
Died	9 February 1883(1883-02-09) (aged 56) Oxford, Oxfordshire, England[1]
Resting place	St Sepulchre's Cemetery, Oxford
Alma mater	Balliol College, Oxford
Known for	Smith–Minkowski–Siegel mass formula Smith normal form Smith–Volterra–Cantor set
Scientific career
Fields	Mathematics
Institutions	University of Oxford

Prof Henry John Stephen Smith

Life

Smith was born in

At 19 he won an entrance scholarship to

Oxford University Museum

.

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

, 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.[5]

On account of his ability as a man of affairs, Smith was in demand for academic administrative and committee work: he was

; 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.^[8] 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 ${\displaystyle 4n+1}$ ex duobus quadratis." In it he proves in an original manner the theorem of Fermat---"That every prime number of the form ${\displaystyle 4n+1}$ (${\displaystyle n}$ 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

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 Liouville were deducible from the principles set forth.

In 1868, Smith 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, 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. 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 Smith's death, the

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 Königsberg, 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.

Work on the Riemann integral

In 1875 Smith published the important paper (

.

Publications

• Smith, H. J. S. (1874). "Note on continued fractions". The Messenger of Mathematics. 6: 1–13.
• Smith, H. J. S. (1875), "On the integration of discontinuous functions",
  JFM 07.0247.01
  .
• Smith, Henry John Stephen (1965) [1894], Glaisher, J. W. L. (ed.), The Collected Mathematical Papers of Henry John Stephen Smith, vol. I, II, New York: AMS Chelsea Publishing,
  ISBN 978-0-8284-0187-6, volume 1volume 2

See also

• Smith–Volterra–Cantor set

Notes

1. ^ GRO Register of Deaths: MAR 1883 3a 511 OXFORD – Henry John S. SMITH, aged 56
2. ^ Smith, Henry J.S. (1874). "On the integration of discontinuous functions". Proceedings of the London Mathematical Society. First series. 6: 140–153.
3. doi:10.1080/0025570X.1994.11996201
   – via Taylor and Francis+NEJM.
4. ^ The Cantor Set Before Cantor Mathematical Association of America
5. ^ ^{a b c} "Henry Smith (1826-1883)".
6. doi:10.1093/ref:odnb/13250. (Subscription or UK public library membership
   required.)
7. ^ Glaisher, J. W. L., ed. (1894). "Biographical sketch". The Collected Mathematical Works of Henry John Stephen Smith. Oxford Clarendon Press. Retrieved 27 November 2012.
8. doi:10.1093/mnras/44.4.138
   .
9. ^ See (Letta 1994, p. 154).
10. ^ The Riemann integral was introduced in Bernhard Riemann's paper "Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe" (On the representability of a function by a trigonometric series), submitted to the University of Göttingen in 1854 as Riemann's Habilitationsschrift (qualification to become an instructor). It was published in 1868 in Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen (Proceedings of the Royal Philosophical Society at Göttingen), vol. 13, pages 87–132 (freely available on-line from Google Books here): Riemann's definition of the integral is given in section 4, "Über der Begriff eines bestimmten Integrals und den Umfang seiner Gültigkeit" (On the concept of a definite integral and the extent of its validity), pp. 101–103, and Smith (1875, p. 140) analyzes this paper.
11. ^ ^{a b} See (Letta 1994, p. 156).
12. ^ See (Letta 1994, p. 157).

References

• J.T.Fleron, "A Note on the History of the Cantor Set and Cantor Function", Math Magazine, Vol 67, No. 2, April 1994, 136–140.
• H.J.S. Smith: "On the Integration of Discontinuous Functions", Proceedings London Mathematical Society, (1875) 140–153.
• K. Hannabuss, "Forgotten fractals", The Mathematical Intelligencer, 18 (3) (1996), 28–31.
• Paul David Gustav du Bois-Reymond and Carl Gustav Axel Harnack
  .

Further reading

• Glaisher, J. W. L. (1884), "Obituary of Henry John Stephen Smith",
  doi:10.1093/mnras/44.4.138
• Macfarlane, Alexander (2009) [1916], Lectures on Ten British Mathematicians of the Nineteenth Century, Mathematical monographs, vol. 17, Cornell University Library,
  ISBN 978-1-112-28306-2 (complete text at Project Gutenberg
  )
• O'Connor, John J.; Robertson, Edmund F., "Henry John Stephen Smith", MacTutor History of Mathematics Archive, University of St Andrews

External links

Wikiquote has quotations related to Henry John Stephen Smith.

Wikisource has the text of the 1911 Encyclopædia Britannica article "Smith, Henry John Stephen".

• The grave of Henry John Stephen Smith and his sister Eleanor in St Sepulchre's Cemetery, Oxford, with biography
• Henry John Stephen Smith at Wikiquote