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At 19 he became a student at Balliol, but while spending the vacation in Italy his health problems became acute. He could not return to Oxford but this had the advantage that he was able to study with some of the top mathematicians at the Sorbonne and the Collège de France. After his health recovered he returned to Oxford and in 1849 was awarded a double first in mathematics and classics.
Smith became a fellow, then a tutor at Balliol. In 1860 he was appointed Savilian professor of geometry despite a strong field of applicants including George Boole.
While on the continent he had been learnt French, German and Italian and read widely. He had been most influenced by the work of Gauss. Smith said:
If we except the great name of Newton (and the exception is one that the great Gauss himself would have been delighted to make) it is probable that no mathematician of any age or country has ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute vigorousness in demonstration...Influenced by Gauss, Smith's most important contributions are in number theory where he worked on elementary divisors. He proved that any integer can be expressed as the sum of 5 squares and as the sum of 7 squares. Eisenstein had proved the result for 3 squares and Jacobi for 2, 4 and 6 squares. Smith also extended Gauss's theorem on real quadratic forms to complex quadratic forms.
From 1859 to 1865 he prepared a report in five parts on the Theory of Numbers. In it Smith analyses the work of other mathematicians but adds much of his own. This work has been described as the
the most complete and elegant monument ever erected to the theory of numbers.Smith also wrote on geometrical topics. His first two papers were on geometry and, in 1868, he wrote Certain cubic and biquadratic problems which won him the Steiner prize of the Royal Academy of Berlin.
Smith is remembered for the Smith normal form for matrices. It appears to be less well known that, around 1875, he gave examples of discontinuous sets which are similar to the Sierpinski gasket, see [3].
Article by: J J O'Connor and E F Robertson
Click on this link to see a list of the Glossary entries for this page
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List of References (5 books/articles)
| Some Quotations (3)
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| Mathematicians born in the same country
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| Honours awarded to Henry Smith (Click a link below for the full list of mathematicians honoured in this way) | |
| Fellow of the Royal Society | Elected 1861
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| London Maths Society President | 1874 - 1876
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| Savilian Professor of Geometry | 1861 |
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JOC/EFR December 1996
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School_of_Mathematics_and_Statistics University_of_St_Andrews,_Scotland |
http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Smith.html
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