QED, in native tongues and translations

November 27, 2008

Mathematics Emerging: A Sourcebook 1540-1900

Author: Jacqueline Stedall

Edition: First

Publisher: Oxford University Press

Pages: 680

Price: £49.50

ISBN 9780199226900

This book offers the reader significant passages from the works of major mathematicians of the period in which Western mathematics matured and the subjects covered in the university curriculum today emerged: each is set in context by a helpful commentary. Mathematics Emerging will provide a valuable resource for students of the history of mathematics, material for the enrichment of the studies of undergraduate mathematicians, and much enjoyment and fascination for anyone who loves mathematics. The topics include the early history of algebra, the origins of calculus and its subsequent development, complex analysis, sequences and series, the beginnings of group theory and linear algebra, and many more.

Jacqueline Stedall's sourcebook differs from others in offering the texts in their original languages as well as in English translation: thus we have texts in Latin, French and German. Her aim is to give students a feel for the original document. The originals are generally photographic reproductions, and the translations follow their layout as closely as possible: the author's infectious love of old books is clear. Older texts are included, so that we get Archimedes in Commandino's 1558 Latin version and Euclid in Isaac Barrow's English translation (with an editorial warning that the 17th-century use of the apostrophe in "it's" should not be imitated).

The introduction gives a concise but illuminating account of the difficulties in reading old mathematics and the problematic nature of translation. Stedall's translations seem to me to be a model of their kind: they are close enough to the original to make parallel reading rewarding even for those with limited knowledge of the original languages, and they will give many readers the confidence to tackle the originals. I was particularly pleased to note that her translation preserves a typo in an equation in d'Alembert's reflections on series: it's good that students should be aware that printed mathematics sometimes contains such errors.

The selections are carefully chosen, and include less familiar names such as Hudde and Tschirnhaus: sadly, but perhaps inevitably given the subject and the time period, the authors reproduced are all white and male. Readers will have their own views on the choices: I personally would have liked more on combinatorics and cryptography.

But Stedall's hope is that her book will send readers to the library to the sources for their particular interests, and the volume seems to me very likely to inspire such research. It might have been helpful for Stedall to have offered more guidance on the increasing availability of facsimiles on the web. Digital versions are likely to be more accessible to many (one of my undergraduates, who is studying mathematics with French, has already been prompted by this book to find electronic copies of further French-language sources).

I hope that my admiration for this treasure trove is apparent. The author and publisher are to be congratulated on the care with which this beautiful volume has been produced.

Who is it for? Anyone interested in mathematics and its history, but especially students.

Presentation: Beautifully and lovingly presented - a joy to read.

Would you recommend it? Very highly. Anyone who enjoys mathematics will love it.

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