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The history of mathematics. A very short introduction. (English) Zbl 1244.00001

Oxford: Oxford University Press (ISBN 978-0-19-959968-4/pbk). 123 p. (2012).
Jacqueline Stedall’s “very short introduction” to “The History of Mathematics” is very short, but it is not a history of mathematics. It is an “imaginative and thought-provoking” booklet that should be read by everyone interested in the history of mathematics, but the reader should be warned that it deals more with the writing of history (and perhaps, if I am allowed to say so, with rewriting the history of mathematics in a politically corrected way) than with history itself.
Stedall does not want “to outline some key mathematical events and discoveries in roughly chronological order” because a) this tends to “portray a whig version of mathematical history”, b) chronological accounts often omit the connections between the main discoveries, and that c) “key events and discoveries come to be associated with key people”, most of which seem to have committed the crime of having “lived in western Europe” and having been born male. Since “this book can do only a little to redress the masculine bias of most depictions of the history of mathematics”, Stedall instead explores “how, where, and why mathematics has been practised by people whose names will never appear in standard histories”. Consequently, the index does not contain the names of Jacobi, Kronecker or Poincaré, whereas Gauss, for example, is mentioned only as a means for introducing Sophie Germain. Their place is taken by Stedall’s friend Tatjana Tekkel, who creates quilts although she was not good at maths in school, or, on a more serious level, by Edward Davenant’s daughter Anne, who solved elementary problems from an algebra book in the middle of the 17th century.
Of course, the mathematical work of women like Anne belongs to the history of mathematics, just as the fate of Gaius Quintus, a soldier in one of Caesar’s armies whose name I just made up, belongs to the history of the Gallic Wars. And yes, dead ends are part of the history of mathematics, and Pell’s unpublished rewriting of Diophantus’s Arithmetica is interesting for professional historians of mathematics that deal with the reception of Diophantus. But the historian’s task as I understand it is not giving a picture of the world as it was down to the most minute detail: collecting all emails and web pages ever written into a gigantic computer is a data cemetary and not a history of the internet. From a consumer’s point of view (those who buy this book), historians should use their vast knowledge to separate the wheat from the chaff, emphasize the important developments and omit irrelevant material, and they should be able to mention Archimedes, Newton or Gauss without having to fear being called sexist, racist or eurocentric.
There is also some “orthodox” history of mathematics in Stedall’s book; the first chapter, for example, is mainly about looking at Fermat’s Last Theorem from various angles. What I miss sorely there (in Chapter 1 as well as elsewhere) are references for evidence in favor of various statements. It is claimed, for example, that Fermat withdrew to his mathematical isolation during the 1640s “as the political pressures on him increased”; perhaps this is meant to be a short version of Mahoney’s list of reasons given on p. 60 of [M. S. Mahoney, The mathematical career of Pièrre de Fermat, 1601–1665. 2nd ed. Princeton, NJ: Princeton University Press (1994; Zbl 0820.01017)]; Mahoney mentions parlamentary duties, the press of local business, ill health, troubles with the authorities in Paris, the Fronde, Spanish raids on Languedoc and the plague. There are a few other claims in connection with the depiction of the history of Fermat’s Last Theorem that are presented without giving evidence or are incorrect or misleading: the first hint of it did not appear in Fermat’s challenge to the English mathematicians in 1657 but long before in various Arabic sources, where the claims that \(x^4 + y^4 = z^4\) and \(x^3 + y^3 = z^3\) do not have solutions in positive integers first emerged. Similarly, the claim that Fermat was led to his Last Theorem via Diophantus’s problem of dividing a square into two squares is not easily backed up with facts; in fact he might just as well have been led to it either by word of mouth (the two Arabic problems were mentioned by contemporaries of Fermat as well) or by studying right-angled triangles whose area is a square.
It was probably a wise decision not to try and write a history of mathematics on 100 small pages, and the idea of looking at a few events from various angles is very pleasing. But I strongly disagree with the philosophical standpoint taken by Stedall in this book: there is hardly a student of mathematics out there who knows the original work done by Archimedes, Newton or Gauss; why should they study the feeble attempts of a mediocre 17th century student at solving elementary problems in high school algebra?

MSC:

00-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general
00A05 Mathematics in general
01-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography
01A05 General histories, source books

Citations:

Zbl 0820.01017
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