Mathematics of Life (2011)

Preface

Mathematical theory and practice have always gone hand in hand, from the time primitive humans scratched marks on bones to record the phases of the Moon to the current search for the Higgs boson using the Large Hadron Collider. Isaac Newton’s calculus informed us about the heavens, and over the past three centuries its successors have opened up the whole of mathematical physics: heat, light, sound, fluid mechanics, and later relativity and quantum theory. Mathematical thinking has become the central paradigm of the physical sciences.

Until very recently, the life sciences were different. There, mathematics was at best a servant. It was used to perform routine calculations and to test the significance of statistical patterns in data. It didn’t contribute much conceptual insight or understanding. It didn’t inspire great theories or great experiments. Most of the time, it might as well not have existed.

Today, this picture is changing. Modern discoveries in biology have opened up a host of important questions, and many of them are unlikely to be answered without significant mathematical input. The variety of mathematical ideas now being used in the life sciences is enormous, and the demands of biology are stimulating the creation of entirely new mathematics, specifically aimed at living processes. Today’s mathematicians and biologists are working together on some of the most difficult scientific problems that the human race has ever tackled – including the nature and origin of life itself.

Biology will be the great mathematical frontier of the twenty-first century.

Mathematics of Life celebrates the rich variety of connections between mathematics and biology that already exist, from the Human Genome Project, through the structure of viruses and the organisation of the cell, to the form and behaviour of entire organisms and their interaction in the global ecosystem. It will also show how mathematics can shed new light on difficult issues concerning evolution, where many important processes take too long to observe, or happened hundreds of millions of years ago and have left only cryptic traces.

Initially, biology was about plants and animals. Then it was about cells. Now it is mostly about complex molecules. To reflect these changes in scientific thinking about the enigma of life, the book starts from the everyday human level, and follows the historical path that led biologists to focus ever more sharply on the microscopic structure of living creatures, culminating in DNA, the ‘molecule of life’.

Most of the material discussed in the first third of the book is therefore about biology. However, mathematics makes an early appearance, tracing questions about the geometry of plants from Victorian times to the present day, to illustrate how new mathematical ideas have been motivated by biology. Once the biological background has been established, mathematics comes to centre stage as we build up from the atomic scale, back to the level with which we feel most comfortable, the one on which we all live. The world of grass, trees, sheep, cows, cats, dogs . . . and people.

The mathematics involved is far-ranging: probability, dynamics, chaos theory, symmetry, networks, mechanics, elasticity – even knot theory. Most of the applications discussed here are to mainstream mathematical biology: the structure and function of the complex molecules that co-ordinate the complex processes of life, the shapes of viruses, the evolutionary games that led to the huge diversity of life on this planet and are still happening today, the workings of the nervous system and the brain, the dynamics of ecosystems. I’ve also included chapters on the nature of life and the possible existence of alien life forms.

The interaction between mathematics and biology is one of the hottest areas of science. It has already come a long way in a very short time. Only the future will show just how far it can go. But one thing I guarantee: it’s going to be an exciting ride.