Talk:William George Horner

message: A. Thomas Fuller published an article, Horner versus Holdred: An Episode in the History of Root Computation that appeared in Historia Mathematica early in 1999 a few months before he died (the exact reference is Hist. Math., 26 (1999), 29–51). Although the subject and periodical were novel for him, he enjoyed a distinguished record for scholarship. The article reads in accordance with this - until you begin checking the details. The flaws that turn up are then so numerous and so strange that it is difficult to to explain them, especially give the strong undercurrent of aspertion throughout the article, not only against Horner, but against J. R. Young, Thomas Stephens Davies, Augustus De Morgan and others. Hence the question: might the article be a hoax?
Fuller cites two contemporary reviews from The Monthly Review, in April and December, 1820, but in a partial or lopsided manner; you would never know, for example, that the reviewer is so welcoming of Horner's article. But then you would also not know from Fuller that there is a third review, in September, 1821, that specifically looks at the booklet of Theophilus Holdred and finds it wanting. The reviewer is exceptionally well-informed and, suggested in Horner's Method, would seem to be Peter Barlow. These reviews, taken together, upset, if they do not altogether scuttle, Fuller's advocacy of Holdred as the first published proponent of Horner's Method.
It is much the same with Fuller's quotation of the writings of J. R. Young, who, at first, drew on Holdred's booklet in his own exposition, possibly because Holdred first seems to have come to attention in The Gentleman's Mathematical Companion, where Young and Peter Nicholson, Holdred's associate-cum-rival, were both active. Reading Young more fully, we find that Fuller's presentation is biased: Young does say the things Fuller has him say, but he says a lot more. In the first place, Young acknowledges Horner's work as superior, but for his own purposes, specifically in the cubic case, he prefers to work with Holdred's formulation. But he is also at pains to assess Holdred's work, finding that Holdred's first method is that of Henry Atkinson in 1809 while his second method, inserted after Holdred's booklet had already appeared so that the booklet had to be reissued, followed that already proposed by Horner.
Young was not alone in fancying Holdred's handling of cubics. Fuller calls attention to an obscure footnote to the same effect which Fuller holds against Augustus De Morgan. It is true that it appears in a volume sandwiched between two pieces by De Morgan, but as many library index cards make clear, and as is made explicit in the second edition, this piece is the work of one, J. Parker. Is is difficult to see how anyone has the detective skills to track down such a footnote without following up on the authorship.
But it gets worse. Fuller tells us three times of the misprints in Horner's article in 1819, without ever saying what they are, but suggesting that the propensity of others to reprint the article without correction is indicative of their lack of understanding. T. S. Davies is one of these miscreants: he reprinted the article in The Ladies' Diary for 1838, appearing in late 1837, the year Horner died. What Fuller does not tell us is that a key points throughout this reprint, Davies supplies editorial notes. So much then for someone who might not have understood the article.
Fuller also tells us that Horner, in a contribution to Leybourn's Mathematical Repository does not acnkowledge Holdred's work whereas Horner devotes an entire section of his sequence of notes to Holdred's method as it had been presented by Nicholson. Fuller is also suspect on the dating of what appears in the Repository, failing to recognize that individual issues came out sporadically, to be bound up in volumes, with four to a volume - problems with Glendinning the printer meant that the fourth volume appeared in 1819 but the fifth only in 1830.
There is more, but I shall leave off here, in the hope that someone can answer the question.  
The answer is that it is not a hoax For omissions and bias you could only make the accusation of careless non-objective work. You cannot make another wild accusation of a hoax without a shred of evidence. So I think you should withdraw the word 'hoax' which is defamatory and against the spirit of Wikipedia. If what you say is true, there are no doubt reasons for it which you might have used your detective skills to find. For example, Fuller was retired and, as can be seen from his address given in the paper, was living in the countryside. So he might not have had the same excellent library services as you obviously enjoy. And, as you observed, he wrote shortly before his death so other reasons may easily be imagined. It is not unusual for older people to be less mentally alert. And again assuming everything you say is true, you still have not proved your case because you limit yourself to the who-said-what-when about someone else’s work. You do not appear to have done, as Fuller did, the harder work of reading and understanding the ideas in the quoted works. Have you, for example, actually read and understood Horner 1819 and Holdred 1820 in the original?  If so, which is closer to what is nowadays called 'Horner's method' ?  — Preceding unsigned comment added by JFB80 (talk • contribs) 19:13, 16 July 2012 (UTC)
thread_title:  Is Fuller's article a hoax? 

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