# Mathematics of Life: Unlocking the Secrets of Existence

Ian Stewart

PROFILE BOOKS 2011, 368 PAGES

PRICE £20.00 (HARDBACK) ISBN 978-1-846-68198-1

*‘Biology will be the great mathematical frontier of the twenty-first century.’ *So says Ian Stewart, Emeritus Professor of Mathematics at Warwick University (and undoubtedly well known to all readers of this magazine). In the *Mathematics of Life* he suggests that, historically, there have been five revolutions that have changed the way scientists think about life and that a sixth – the mathematical solution of biological problems – is on its way.

The early chapters concentrate on the first five revolutions: the microscope; the Linnaeus classification system; the theory of evolution; genetics and the structure of DNA. These concentrate on the biology, which he explains very clearly, but, of course, he throws in some mathematics and historical sketches of the people involved as well.

Perhaps because the author is a mathematician not a biologist, he takes great care to explain the biology carefully, assuming the reader is basically ignorant of the field (certainly a correct assumption in my case!). So, for example, not only does he describe, say, the difference between prokaryotes and eukaryotes in terms of their structure, but he also gives examples: bacteria are prokaryotes; amoebas and tigers are eukaryotes. I found his explanation of genetic inheritance, in his discussion of Mendel’s experiments in the chapter called ‘In a Monastery Garden’, particularly enlightening.

When talking of genetics he emphasises the fact that, though DNA may be seen as a ‘blueprint’ for life, you need much more than a blueprint of something to understand how to make it or to predict all of its capabilities. This is especially true of biological systems.

The book contains several snippets of the ‘not a lot of people know that’ kind. For example, did you know that DNA was first discovered by Friedrich Miescher, a Swiss doctor, when analysing pus in bandages that had been discarded after use in surgery? Also, slime mould placed on a map of the area around Tokyo, with food sources placed at the locations of 36 cities, managed to produce a network of tubes connecting the food sources that closely matched the actual rail network connecting those cities! And the structure of certain viruses are best modelled using four-dimensional geometry (the author quotes the work of Reidun Twarock, which also forms the basis of one of the IMA’s Mathematics Matters articles, *Fighting Infections with Symmetry*, which was reproduced in the April 2011 issue of *Mathematics Today* and is also available on the IMA website.

Professor Stewart provides several thought-provoking discussions on a range of topics from genetically modified foods to alien life-forms and what we mean by the word ‘life’ itself. He has strangely little to say explicitly about his sixth revolution, but he does note: *‘I doubt that mathematics will ever dominate biological thinking in the way it now does for physics, but its role is becoming essential’*, and *‘By the time we get to the twenty-second century mathematics and biology will have changed each other out of all recognition, just as mathematics and physics did in the nineteenth and twentieth centuries.’*

The book is a fascinating read and I highly recommend it.

**Alan Stevens CMath FIMA**

Book review published directly onto IMA website (April 2013)