This is not a book on the history of mathematics but a manifesto of postmodern historiography. The historiography of mathematics has "evolved" (as the title of chapter 7 would have it) to the point where mathematical content itself is so incidental that the reader must be warned so as to not fall off his seat on the exceedingly rare occasions where "we need to digress briefly to some mathematics" (p. 3).
Modern historiographers are a self-satisfied bunch to say the least. Thus for example they lament that "a good deal of early 20th-century scholarship in the history of mathematics ..., often carried out by mathematicians rather than historians, ... [translated ancient mathematics] into the symbols and concepts of modern mathematics." Although their "motives ... were not in themselves reprehensible", "the gains in historical understanding are incomparably greater" when modern historiographical standards are used. (pp. 108-109)
Stedall's attempts to justify her haughtiness fall well short of the mark, and are clearly more dogmatic than rational. For example:
"The use of modern algebraic notation ... should never be mistaken for what the original writer was 'really' trying to do, or what he would have done with the advantage of a good modern education. At best, such modernization obscures the original method and at worst can lead to serious misunderstandings." (p. 35)
One would like to ask these modern historians: Have you never had an idea that you could not quite formulate or work out to your satisfaction? And has it never happened that someone else, perhaps someone with experience and expertise in this area, was able to put his finger on precisely what you were "really" trying to say? And if you then had to explain your original idea to someone else, would you not do it with the aid of this better formulation? Surely this has happened to us all, both in mathematics and elsewhere. This is common sense to most people, but there is no point in saying as much to the modern historians because they have checked theirs at the door.
Then again one wonders what these rants are doing in this book in the first place since Stedall is not interested in understanding mathematical ideas at all, whether in one notation or the other. Instead her mantra for the book is a strange kind of egalitarianism:
"Focusing on big discoveries rules out the mathematical experience of most of the human race: women, children, accountants, teachers, engineers, factory workers, and so on, often entire continents and centuries of them. Clearly this will not do." (p. xvi)
I for one do not find this "clear." I suppose these people also sketched a few drawings and perhaps even kept a diary, so would Stedall have them displace Rembrandt and Shakespeare from histories of art and literature as well? Evidently so, for anything else would be "elite history" (p. 12), and "Elite history does not have any space for ... my mother Irene, who at age 89 trusted neither banks nor computers, but tallied every penny of her household expenditure in carefully ruled notebooks; or my friend Tatjana, who repeatedly tells me she was no good at mathematics at school but who creates intricately designed quilts." (pp. 16-17)