Bennett, Joseph
(2023)
Henry Smith and the Arithmetical Theory of Quadratic Forms.
PhD thesis, National University of Ireland Maynooth.
Abstract
Henry John Stephen Smith (3:48–3::5) FRS was Savilian Professor of Geometry
at Oxford University from 3:83 to 3::5 (Figure 3). He distinguished himself
as a superb lecturer and researcher who brought international recognition to
Oxford mathematics. His unique and caring personality ensured he was held in
widespread affection and admiration by his students and the University community.
The two volumes of Henry Smith’s collected mathematical papers, first
published in 3:;6, are little read today. They include interesting biographical
material, but it may not be immediately obvious why he was regarded, and not
just at his alma mater, as being in the front rank of European mathematicians.
To understand the reasons behind this it will be helpful to look more closely
at Henry Smith’s life in mathematics.
His mathematical writings, on which his reputation chiefly rests, were on
the theory of numbers and elliptic functions, topics in which European mathematicians
were pre-eminent. He prepared a series of Reports on the Theory
of Numbers, commissioned by the British Association for the Advancement of
Science, from 3:7; to 3:87. These were followed by his memoirs on the arithmetical
theory of integral quadratic forms leading eventually to his crowning
memoir to the French Académie des Sciences for its Grand Prix des Sciences
Mathématiques of 3::4. He advanced the theory of quadratic forms by returning
to original sources and remaining true to arithmetic, confirming Henry Smith’s
reputation as a brilliant arithmetician for whom fine arithmetical details and
presentation mattered. The principle theme of these memoirs was the classification
of quadratic forms. In addition to considering his early education and
life in mathematics, this thesis will include a careful distillation of some of the
mathematical techniques contained in these memoirs. It will reveal that Henry
Smith’s mathematical techniques and presentation style was guided and influenced
by the earlier writings of Gauss, Eisenstein, and Dirichlet. In any attempt
to assess Henry Smith’s reputation in his day, and since, such considerations
will be important.
| Item Type: |
Thesis
(PhD)
|
| Keywords: |
Henry Smith; Arithmetical Theory; Quadratic Forms; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: |
19021 |
| Depositing User: |
IR eTheses
|
| Date Deposited: |
14 Oct 2024 13:53 |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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