book reviews

The true shortcoming of this book is that, a larger audience. Devlin has taken the despite Rose’s attempts to penetrate Heisen- opportunity to add two new chapters, one on berg’s “German mentality”, the author’s chance and one on space-time, but has had to prosecutorial analysis gives the reader little manage without the profusion of artwork understanding of Heisenberg as a human and colour photographs that adorned the being, or of how difficult it was to live and earlier book. work under such a regime. He covers a wide range of topics with an Mark Walker is in the Department of History, enviably light touch. The fact that there are Union College, Schenectady, New York, 12308- infinitely many prime numbers sits along- 8 3163, USA side tests to see if a number is prime, and leads into a discussion of public key encryp- tion systems (unhappily the details of the system are not explained). There is a chapter The science on logic and set theory, topics on which Devlin is an expert, and this leads to a hint or of patterns? two about Noam Chomsky’s ideas on lin- The Language of Mathematics: guistic structures. There is some calculus and Making the Invisible Visible Newtonian mechanics, some geometry, by Keith Devlin including Desargues’s theorem and the idea W. H. Freeman: 1998. 344 pp. $24.95, £14.95 of spaces in any number of dimensions. Jeremy Gray We get some discussion of groups, including wallpaper patterns and lattices, In recent years there has been a profusion of which leads to the unresolved question of the books aimed at making mathematics com- densest packing of spheres. Topology leads to prehensible and interesting to the general the theory of knots, the Jones polynomial reader. Keith Devlin is the successful author which almost classifies them, and their rela- Point of infinity: Renaissance artists discovered of Mathematics: The Science of Patterns and tion to the study of DNA. Fermat’s Last The- how to create a sense of depth in a painting . this book is a spin-off from that one, aimed at orem passes by, as does a discussion of chance, from Quetelet’s ‘average man’ to the New in paperback Black-Scholes formula much used in the derivatives market. The book closes with a T. rex and the Crater of Doom earnestness, the inevitability and the beauty of quick trip through gravity, electromagnetic by Walter Alvarez many of their constructs, even those theory, and the idea of space-time. Penguin, £7.99 condescendingly dismissed as ‘foolishness’ by All this is done with clarity and wit, a “Alvarez portrays a modern geology that builds less perceptive historians”, Frank Gonzalez- novel collection of puns, and a willingness to on the interdisciplinary resources of physics, Crussi, Nature 390, 41 (1997). cut corners. The history of mathematics is chemistry and astronomy to fashion a synthesis taken up when it helps and dropped when it about how our planet has evolved . . . . One can Women Scientists in America, does not; it is accurate when it is easy and less read T.rex and the Crater of Doom in a single Volume Two: Before Affirmative so when simplification is judged appropriate sitting and I recommend it highly — if only as a Action, 1940-1972 to the greater aim. The same is true of the jumping-off point to other perspectives on this by Margaret W. Rossiter mathematics, and the subjects to which it is dramatic scientific revolution”, Clark R. John Hopkins University Press, £15 applied. The book is weakest when dis- Chapman, Nature 387, 33 (1997). “. . . assembled with the careful scholarship that cussing these applications. Devlin some- has become Rossiter’s hallmark. Once again, the times stops short, for fear of becoming too Born To Rebel: Birth Order, Family quantity of material researched is enormous and hard, before he has really become compre- Dynamics and Creative Lives my caveats are few. . . . I found the book heavier hensible. Inevitably, some of the topics are by Frank J. Sulloway going than its predecessor, with fewer of the light familiar in the genre, while others are new, Abacus, £9.99 touches of irony and humour that I had enjoyed but even the old ones are deservedly popular. “Born To Rebel contains a treasure-trove of so much before”, June Goodfield, Nature 380, Even mathematics has only so many greatest information . . . . I doubt that anyone will ever 306 (1996). hits. But it would be a churlish reader who again claim that the variable of birth order has did not find that mathematics is much more been shown to be unimportant”, Howard Imagined Worlds diverse than might be suspected, and much Gardner, Nature 384, 125 (1996). by Freeman Dyson more useful in all sorts of ways. Harvard University Press, $14, £8.50 As with his earlier book, Devlin pushes The Ovary of Eve: Egg and Sperm “Dyson has a startlingly profound imagination, a the quick definition that mathematics is the and Preformation willingness to take ideas as far as they can science of patterns. Readers may not be per- by Clara Pinto-Correia possibly go. . . . I think Dyson could write a better suaded, but they should certainly come away University of Chicago Press, $17.50, £13.95 book about the future than this one. I think he thinking that mathematicians have some- “Her engrossing book is likely to remain for could write a better book about the future than thing attractive to say about their subject, many years the most readable and informative — almost anyone; I wish he would”, Oliver Morton, and about many others besides. Sadly, they certainly the most enjoyable — account of the Nature 387, 361 (1997). will not find notes and a bibliography docu- early scientific efforts to explain human menting where all this information came conception . . . . It is a strength of The Ovary of Charles Darwin’s Letters: from, nor are they provided with suggestions Eve that it succeeds in fully appropriating the A Selection 1825–1859 for further reading. view-point of the scientists of the past, and edited by Frederick Burkhardt Jeremy Gray is in the Faculty of Mathematics and makes the reader realize the nobility, the Cambridge University Press, £9.95, $12.95 Computing, Open University, Milton Keynes MK7 6AA, UK. 428 Nature © Macmillan Publishers Ltd 1998 NATURE | VOL 396 | 3 DECEMBER 1998 | www.nature.com