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REVIEWS Contents
A Week in the Life of a Mathematician A WEEK IN THE LIFE OF A MATHEMATICIAN (with apologies to Michael Flanders and Donald Swann) FERMAT’S ROOM COMPETITION Thanks to the generosity of Revolver Entertainment, the July Newsletter contained a competition offering tickets for the film Fermat’s Room, which was reviewed in that issue. The answer to the question is that the pseudonyms of the characters in the film are Hilbert, Pascal, Galois and Oliva. The two winners were Nadia Mazza and Niels Laustsen, both of Lancaster University. Congratulations!
Thomas Harriot’s Doctrine of Triangular Numbers: the Magisteria Magna by Janet Beery and Jacqueline Stedall, European Mathematical Society, 144 pp, 39 illus., €64.00, ISBN-10: 3-03719-059-0, ISBN-13: 978-3-03719-059-3. Compter en 1619: Le livre d’arithmetique de Johan Rudolff von Graffenried by Alain Schärlig, Presses Polytechniques et Universitaires Romandes, 160 pp, 44 illus., €37.50, ISBN 978-2-88074-777-0. Thomas Harriot (c. 1560–1621) is a fascinating figure. Under the patronage of, first, Walter Ralegh and later the ’Wizard Earl’ of Northumberland, he acquired a reputation as the leading English mathematician of his time. A plaque commemorating his telescopic observations of the moon in July 1609, in which he anticipated Galileo, has just been unveiled at Syon Park. He worked on a wide variety of topics, not all mathematical. His work circulated in manuscript but none of his mathematics was published in his lifetime (his only published book was the Brief and True Report of the New Found Land of Virginia of 1588). The posthumous Artis Analyticae Praxis gives only a limited view of his achievements and it is only with the recent study of his extensive surviving manuscripts that we are becoming fully aware why he was so highly regarded by his contemporaries and immediate successors. It is therefore extremely appropriate that Harriot’s Magisteria Magna (the title he gave to a treatise analysing the mathematics of constant differences) should be published in the European Mathematical Society’s Heritage of European Mathematics series. Harriot’s manuscript consists of almost 40 pages, each of which is reproduced here. In this manuscript Harriot expounds his analysis of the use of constant differences in interpolation for the construction of mathematical tables. The editors provide a lucid introduction which gives the background to Harriot’s work, discusses the seventeenth-century mathematicians who engaged with Harriot’s theory, and shows how it relates to later work by Newton and Gregory. The Magisteria Magna is a wonderful example of Harriot’s expository style. He doesn’t use many words – ’hoc est’ (that is) on the fourteenth page are the first words after the title! The mathematics is clearly set out and a delight to follow. The editors provide notes to each page (facing the reproduction) to help the modern reader. I imagine many mathematicians will thoroughly enjoy working through this interesting seventeenth-century mathematics in the original, and the editors and the European Mathematical Society deserve our gratitude for making it available. Harriot wrote a fair copy of the Magisteria Magna in 1618, so it makes an interesting contrast with the idiosyncratic arithmetic book of 1619 which Alain Schärlig found in a flea market. Johan Rudolff von Graffenried’s Arithmeticae Logisticae Popularis Libri IIII is written in old German and printed in Gothic script. Its length, at over 700 pages, makes it too long to reproduce in full so Schärlig summarises each section, with copious reproductions showing examples and notation. The mathematics is very different from Harriot’s (although constant differences come up in Book IV), but Schärlig’s enthusiasm is infectious and my limited schoolboy French proved perfectly adequate. For anyone who loves old mathematics books, this is a joy. Tony Mann
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