This post is based on a book review I recently wrote on The Mathematics of Life, by Ian Stewart. A final version of the review will appear in a future issue of SIGACT News. Please feel free to download a pdf version of the full preprint, or just read an abbreviated version of it here, in blog format.

**Introduction**

Ian Stewart is one of the premier popularizers of mathematics. He has written over twenty books about math for lay audiences. He has also co-authored science fiction, and books on the science of science fiction (three books on “the science of discworld”). In his newest effort, *The Mathematics of Life*, Stewart focuses his talents on the mathematics of biology, and the result is superb. In an easy, flowing read, with dozens of diagrams and scholarly footnotes — but without a single formula — he introduces the reader to a wide range of interactions between mathematicians and biologists. I heartily recommend this book.

**Turing’s morphogenesis in the modern day
**

*The Mathematics of Life* contains 19 chapters. Chapter 8, “The Book of Life,” focuses on the Human Genome Project, and algorithmic challenges of DNA sequencing. However, as this possibly the area most familiar to SIGACT News readers, I will only mention it briefly, and, instead, focus on chapters that introduced me to areas of mathematical biology I had not previously encountered.

Perhaps the most direct connection to (the roots of) theoretical computer science comes in Chapter 13, “Spots and Stripes,” where Stewart considers Alan Turing’s famous paper, The Chemical Basis of Morphogenesis, and sketches the development of biological thought about animal markings since Turing’s groundbreaking proposal. As Stewart says:

For half a century, mathematical biologists have built on Turing’s ideas. His specific model, and the biological theory of pattern-formation that motivated it, turns out to be too simple to explain many details of animal markings, but it captures many important features in a simple context, and points the way to models that are biologically realistic.

Turing proposed “reaction-diffusion” equations to model the creation of patterns on animals during embryonic development. As noted by Stewart, Hans Meinhardt, in The Algorithmic Beauty of Seashells, has shown that the patterns on many seashells match the predictions of variations of Turing’s equations. The mathematician James Murray extended Turing’s ideas with wave systems, and proved the following theorem: *a spotted animal can have a striped tail, but a striped animal cannot have a spotted tail*. Intuitively, this is because “the smaller diameter of the tail leaves less room for stripes to become unstable, whereas this instability is more likely on the larger-diameter body.”

**Teaser for full review**

In the pdf I also discuss Stewart’s presentation of evolutionary game theory to model biological evolution, and the use of high-dimensional geometry to model the self-assembly of chemical virus coats. Beyond that, there is much more great material in Stewart’s book that I did not mention at all. The prose style is friendly and clear throughout, without talking down to the reader.

I consider this to be an excellent introduction to the mathematics of biology, for both amateurs and professionals. Seasoned researchers are likely to learn “teasers” about areas unfamiliar to them, and smart people “afraid of math” can read the book and enjoy the material. Highly recommended. I will conclude this review with the same words Stewart used to conclude the book:

Instead of isolated clusters of scientists, obsessed with their own narrow specialty, today’s scientific frontiers increasingly require teams of people with diverse, complementary interests. Science is changing from a collection of villages to a worldwide community. And if the story of mathematical biology shows anything, it is that interconnected communities can achieve things that are impossible for their individual members.

Welcome to the global ecosystem of tomorrow’s science.

Ian Stewart (2011). The Mathematics of Life Book: ISBN 0465022383

All life is programmed, software, in their genes. Certain genes control the development of cells into complex “body” parts which function to keep the body living and to enable it to survive. An example is the “master eye gene”

which is programmed to construct a complete eye anywhere on the body of a living organism that has eyes. I am sure that mathematics has a part in the program that constructs a complete eye that can see.

Reference the discovery of Dr. Walter Gehring of Switzerland.