Study the masters, 2001-10-10The material covered ranges from ancient Babylonia (as discussed by the incomparable Neugebauer) down to some work from the early twentieth century (including for some reason an extract from Eves and Newsom). (He ought to have provided a compact table of sources in addition to the individual notes strewn through the volume. Perhaps he was dissuaded by the publisher)
As one passes beyond the 17th century the selection is wisely confined somewhat near the limits of its intended audience, with major distortions that are probably inevitable. At least the point is clearly made that the development of the calculus was in no sense the end of the history of the mathematics, though perhaps, in Churchill's words, the end of the beginning.
High school students, or other readers looking for a bit more entertainment, should go directly to The World of Mathematics by James R. Newman. (Perhaps also to the deliberately unreliable and entertaining E. T. Bell, and Infeld's novel inspired by the life of Galois.)
Readers looking to learn something substantial about the history of mathematics will find that Calinger's anthology is useful as a supplement, but not on its own. For independent reading, one might eventually tackle a substantial undergraduate text like Victor Katz' history of mathematics (whose use of footnotes is excellent, allowing the reader to both check and follow up on points of interest). But it will be more interesting to begin with a more narrowly focussed work by an expert. Neugebauer writes beautifully on the Babylonians, as does Sarton on the Hellenistic age. Marie Boas Hall has a very pleasant book on the Renaissance period, not specifically focussed on mathematics but still quite suitable. Berggren has an excellent text on Arabic mathematics aimed at undergraduates.
Graduate students and beyond should start with Felix Klein, Development of Mathematics in the 19th century.
And if you read German, the 1st three volumes of Moritz Cantor's work are wonderful (but heavy). Lüneburg has a beautiful book on Fibonacci, in German, which ought to be translated!
For a long time, the history of early mathematics was the history of Greek mathematics. In the last century, the frontiers were pushed both backward and forward significantly, with major discoveries in Babylonian mathematics and substantial elucidation of the history of Arabic mathematics. The study of Indian and Chinese mathematics seems still to be very much waiting in the wings. Whitney wrote in 1889 "All dates given in Indian literary history are pins set up to be bowled down again." Whether that observation is apposite today I will leave to the experts to debate, but one may hope that the present century will do for both the Indian and Chinese mathematical materials what the last began to do for the Arabic.
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