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Keywords: Mathematics, biography, history of ideas Title: Calculus Gems Author: George F. Simmons Publisher: The Mathematical Association of America ISBN: 0883855615 Media: Book Verdict: Recommended

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This is a book in two halves, as is made clear from the subtitle: 'Brief Lives and Memorable Mathematics'. For those afraid that this is actually some kind of calculus book under the covers, relax, this isn't a text book, nor even a populist introduction to the subject. Instead the author treats us to a series of brief biographical sketches of a number of leading mathematical thinkers, followed by an examination of some interesting mathematical topics.

For those who are fascinated by genius, this is a great little book. Starting from the ancient world of Thales, Pythagoras and Archimedes and moving on through to the middle ages and then on and into the 19th century with Gauss, Chebyshev and Riemann we are treated to 33 quick biographies of some truly remarkable individuals. George Simmons focuses on the personalities as well as on the mathematics, producing pen portraits that are engaging and readable. The mathematics is explained in terms of historical context, placing the person and the work into the broader story of the advances in the subject from the early beginnings in Ancient Greece.

Simmons has decided views on his subjects, for example ranking Euler, Gauss and Riemann as the greatest mathematicians of modern times. Or in declaring Euclid's Elements as one of the dullest books ever written. But this engagement with his subjects and the pleasure he derives in writing about their lives and works is evident throughout. It's a pleasure to read, even if your mathematics is of the shaky and barely remembered kind.

The second part of the book deals much less in personalities and more in mathematics. Here Simmons looks at a number of the problems in diverse areas of mathematics that he has found interesting during a long and successful lecturing career. These range from number theory to geometry to physics. It's a mixed bag, but a useful diversion for those studying maths and who want to get away from their textbooks without leaving the subject completely.

There are a couple of points worth noting. The first is that although this is a new issue of the book, it has not been updated. Therefore it does not mention the Andrew Wiles proof of Fermat's Last Theorem, so that it is still referred to as being unsolved. It is also worth mentioning that the mathematical lives only extend to the end of the 19th century and that some of the great mathematicians of the last century (such as Hilbert, Ramanujan, von Neumann, Erdos and others) are not included.

However, for many readers who aren't interested in the second part of the book, the brief lives in the first section are an absolute delight and make this a book that is easy to recommend.