Ancient Mathematics [Book Review]
Isis 93:295-296 (2002)
AbstractThis book treats so‐called Greek mathematics, developed in the Greek‐speaking world between about 600 b.c. and 600 a.d. It consists of four parts: early Greek mathematics, Hellenistic mathematics, Graeco‐Roman mathematics, and late ancient mathematics. Each part is divided into two chapters, “The Evidence” and “The Questions.”This separation of evidence and questions is significant. Serafina Cuomo has refused to follow the familiar method of weaving an apparently seamless history of Greek mathematics out of fragmentary and heterogeneous documents and conjectures about them. The chapters of questions, where she points to issues that remain open, are very suggestive. For example, most important documents about the early development of Greek mathematics derive from a single lost work, the History of Geometry by Eudemus. Cuomo dares to cast doubt on its authenticity. Though her reservations seem extreme, we should remember that no document is neutral: Eudemus's history is a compilation, which involved choices, and the fragments we have now are the result of selection, partly intentional, partly by chance.Another merit of this book is that it considers a wide range of activity as mathematics. Practical mathematics—such as land surveying and accounting, with their sociopolitical importance—is emphasized.Cuomo's chief claim is that the standard historiography that associates the development of Greek mathematics with Plato's philosophy is only the version promulgated by Proclus; other descriptions are also possible. In fact, Pappus, Iamblichus, and others had their own versions. This claim is reasonable and contributes to a better understanding of Greek mathematics and the authors of late antiquity.In her citations, the author tries to let the text speak for itself, allowing as much as a full page to a passage or a proposition, and she refrains from using modern symbolism to explain mathematical content. Though this attitude is admirable, its cost is not negligible. Readers expecting to acquire a basic knowledge of Greek mathematics may find themselves at a loss when faced with highly technical propositions presented without elucidation.What this compact book does not include should also be mentioned. In contrast to her enthusiasm for the social and political dimensions of ancient mathematics, the author seems somewhat indifferent to its technical and theoretical aspects. Archimedes and Apollonius command only 16 pages—less than 7 percent of the text—whereas T. L. Heath dedicated 150 pages of his 1,000‐page history to them . Though documents showing the importance of land surveying are frequently quoted, little is said about the practice and the technical development of this art. The technical details of Ptolemy's works are practically dismissed—but should he not have an especially important role in alternative versions of the history of ancient mathematics because of his ingenious reconciliation of rigorous theory and the limitations imposed by reality in fields like astronomy and geography?The scantiness of the technical ingredients makes Ancient Mathematics more a history of discourses about mathematics than a history of mathematics—though this is to some extent inevitable given the character of late ancient mathematics, as Cuomo correctly emphasizes. The plan of the series to which this book belongs may be too modest to accommodate the author's ambition. Another problem attributable to the publisher is that the notes appear at the end of each chapter, so checking the references is annoying. Short references could be put in parentheses, and footnotes would be more convenient for longer notes
Similar books and articles
Reflections on Mathematics.Edward N. Zalta - 2007 - In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Lakatos' Philosophy of Mathematics: A Historical Approach.T. Koetsier - 1991 - Distributors for the U.S. And Canada, Elsevier Science Pub. Co..
Essays in the Philosophy and History of Logic and Mathematics.Roman Murawski (ed.) - 2010 - Rodopi.
uNiTy iNaNCiENT aND mODErN PHilOSOPHy aNDTHE HyPOTHESiS Of uNivErSal HiSTOry.Burt Hopkins - 2012 - Problemos 82:82-69.
History of Mathematics in Mathematics Education.Michael N. Fried - 2014 - In Michael R. Matthews (ed.), International Handbook of Research in History, Philosophy and Science Teaching. Springer. pp. 669-703.
History of Mathematics in Mathematics Teacher Education.Kathleen M. Clark - 2014 - In Michael R. Matthews (ed.), International Handbook of Research in History, Philosophy and Science Teaching. Springer. pp. 755-791.
The Architecture of Modern Mathematics: Essays in History and Philosophy.José Ferreirós Domínguez & Jeremy Gray (eds.) - 2006 - Oxford, England: Oxford University Press.
Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
Pappus Of Alexandria And The Mathematics Of Late Antiquity. [REVIEW]Ali Behboud - 2002 - Isis 93:102-103.
The Role of History and Philosophy in University Mathematics Education.Tinne Hoff Kjeldsen - 2014 - In Michael R. Matthews (ed.), International Handbook of Research in History, Philosophy and Science Teaching. Springer. pp. 837-871.
Added to PP
Historical graph of downloads