William George Horner - Mathematics

Mathematics

Horner's name first appears in the list of solvers of the mathematical problems in The Ladies' Diary: or, Woman's Almanack for 1811, continuing in the successive annual issues until that for 1817. Up until the issue for 1816, he is listed as solving all but a few of the fifteen problems each year; several of his answers were printed, along with two problems he proposed. He also contributed to other departments of the Diary, not without distinction, reflecting the fact that he was known to be an all-rounder, competent in the classics as well as in mathematics. Horner was ever vigilant in his reading, as shown by his characteristic return to the Diary for 1821 in a discussion of the Prize Problem, where he reminds readers of an item in (Thomson's) Annals of Philosophy for 1817; several other problems in the Diary that year were solved by his youngest brother, Joseph.

His record in The Gentleman's Diary: or, Mathematical Repository for this period is similar. Leaving the headmastership of Kingswood School would have given him more time for this work, while the appearance of his name in these publications, which were favoured by a network of mathematics teachers, would have helped publicize his own school.

At this stage, Horner's efforts turned more to The Mathematical Repository, edited by Thomas Leybourn, but to contributing occasional articles, rather than the problem section, as well as to Annals of Philosophy, where Horner begins by responding to other contributors and works up to independent articles of his own; he has a careful style with acknowledgements and, more often than not, cannot resist adding further detail.

Several contributions pave the way for, or are otherwise related to, his most celebrated mathematical paper, in Philosphical Transactions of the Royal Society of London in 1819, which was read by title at the closing meeting for the session on 1 July 1819, with Davies Gilbert in the Chair. The article, with significant editorial notes by Thomas Stephens Davies, was reprinted as a commemorative tribute in The Ladies' Diary for 1838. The issue of The Gentleman's Diary for that year contains a short obituary notice. A careful analysis of this paper has appeared recently in Craig Smoryński's History of Mathematics: A Supplement (Springer, New York, NY, 2008; esp. Chap. 7).

While a sequel was read before the Royal Society, publication was declined for Philosophical Transactions, having to await appearance in a sequence of parts in the first two volumes of The Mathematician in the mid-1840s, again largely at the instigation of T. S. Davies.

However, Horner published on diverse topics in The Philosophical Magazine well into the 1830s. Davies mooted an edition of Horner's collected papers, but this project never came to fruition, partly on account of Davies' own early death.