There is a famous old joke about the farmer who hired mathematicians to help him increase his milk yield. He got their report back, and read its initial sentence: “Consider a spherical cow...” Ian Stewart quotes the joke in Mathematics of Life because it illustrates the disconnect between mathematics, the language of clear abstractions, and the life sciences, the domain of messy organic forms. For much of the history of science, biology and mathematics have barely been on speaking terms.
Ian Stewart says this is changing. He claims that for the next century the driving force behind mathematics will be biology, and that this marks a fundamental, and exciting, shift in how the sciences interrelate. “Mathematicians like nothing better than a rich source of new questions, – he writes – biologists, rightly, will be impressed only by the answers”.The versatility of the mathematical approach has proven ideal, as a vital tool, to find an intuitive solution just about every problem. Mathematics quantitatively describes everything from the shape of viruses to the structure and function of DNA, and helps to explain the evolutionary games that led to the diversity of life on Earth. Mathematics is one of the fastest propellers for advancing science, and is considered “one of the greatest creations of mankind”.
Ian Stewart, Britain's most prolific popularizer of mathematics, introduces us to a revolutionary approach to an array of bioscience subjects that may have been traditionally considered descriptive, qualitative and dull. Through a fascinating account on the historical exploration of biology, he portrays mathematics as the 'essential tension', promising a new revolutionary perspective that will advance our understanding of the mysteries of life. Such a mathematical approach determines all, from the shape of a flower to symmetrical viruses. Stewart leads us to believe that nature is much more interesting than most people ever imagined, telling us how biology is fun, through examples that include the story of how Japanese researchers claimed a Nobel Prize for demonstrating that slime molds can solve puzzles!
Stewart, like professor Thomas Kuhn, perceives the advances of life science as leaps caused by revolutions in approach, and proposes its five tension points were the invention of the microscope, the systematic classification of the living creatures, evolution, detection of genes, and discovery of the DNA structure. But he strongly believes that truly fundamental changes to the way we thought about biology will be advanced by looking through the lens of Mathematics. Disappointingly, the recent celebration of the human genome project's tenth anniversary ended. Scientists and the press are both blamed for creating false hopes for genomic research in human health. As the DNA era is running out of heat, biology is in desperate need of a fresh mathematical approach. Moreover, while the work of biological scientists is basic to the future leap forward of biological and medical sciences, any breakthrough that has been expected could not possibly deliver the awaited personalized drugs, and mass cure miracles, without the help of mathematical tools.
Stewart is a stalwart of the popular maths genre, having previously written accounts of mathematical subjects as diverse as chaos theory, symmetry and probability, and his engaging, accessible style is also present here. In fact, this book does not contain much mathematics in the shape of formulae and calculations; but this is precisely Stewart's point about mathematical biology: the puzzles should come from the biologists, rather than biology just being another area of application for existing mathematical results. It is a story of how scientists with contrasting backgrounds are coming together to solve real-life problems – important work that, in my opinion, cannot be emphasized enough.
As well an author, Stewart is also a researcher, and his work on how animals walk inevitably gets a mention, sandwiched between sections on the brain and leech heartbeats. The book's breadth, ambitiously aiming to give the reader the gist of many different corners within such a big research field, makes it an interesting read but inevitably creates a weakness too – in fact many topics are omitted or mentioned only too briefly. 
However, by including a solid biological backdrop for the problems he does cover, Stewart gives the book a nicely rounded feel, even if some chapters leave the reader wanting more. As an overview, it provides an entertaining and up-to-date insight into this exciting field.
Despite its title, this is a book for fans of biology as much as for those interested in mathematics. In many ways it reflects the increasingly blurred boundaries between the two subjects, and it gives an absorbing introduction to one of the fastest growing areas of modern science. According to Aristotle, “in all things of nature there is something of the marvellous”. Now mathematics can help us find it.
An enormous strength of the book is Stewart's dedication to challenging all-too-common misconceptions about evolution, often as a result of a very insular view about what constitutes habitable conditions. It's a fascinating tale, not least because of the ructions it caused for proving the bible wrong, but Stewart's main strength here is encapsulating the elegance and simplicity of Darwin's theory of natural selection. He also dismisses the reports of the appearance of allegedly oft-cited grey aliens as preposterous for being too obviously human-like (wannabee writers of science-fiction, please take note). Stewart considers what conditions might have to exist on other planets in order for life to be supported, and gives a potted history of the evolution of life on earth, from before oxygen was found in any great quantities in the atmosphere to the extraordinary biodiversity we see today. It's an exhilarating chapter to end on.
After reading The Mathematics of Life, you can look at the world through a mathematical lens and see the beauty and meaning that is revealed. Julie Rehmeyer, a math columnist for Science News, summarizes Stewart findings, “A surprising number of plants have spiral patterns in which each leaf, seed, or other structure follows the next at a particular angle called the golden angle. The golden angle is closely related to the celebrated golden ratio, which the ancient Greeks and others believed to have divine and mystical properties. Leonardo da Vinci believed that the human form displays the golden ratio. Scientists were puzzled over this pattern of plant growth for hundreds of years. Even though these numbers were introduced in 1202, Fibonacci numbers and the Fibonacci sequence are prime examples of how mathematics is connected to seemingly unrelated things”.
Scientists have not entirely solved the mystery, but a basic understanding of the process seems to be emerging. And the answers are sending botanists back to their electron microscopes to re-examine plants they thought they had already understood.
Mathematics of Life is a thoroughly readable book, full of interesting facts that should delight readers with a strong interest in science: in fact, the mathematics shouldn't put off lay readers; it's not easy, but it's challenging and enlightening. Ian Stewart has written a provocative narrative of passionately argued science: if you're interested in evolution, then this book will offer a fresh perspective, as well as providing a solid grounding in the history and important details of this hugely worthwhile subject.
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 speciality, 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».
Nicola De Nitti
