Why are English Premier League football shirt patterns very similar to animal coat markings? And what do invasive species have in common with cancer cells in the body? Mathematical biology develops models which answer these questions, as they are applied to processes from the spread of a gene in a population, to predator-prey dynamics in an ecosystem, to the growth of tumors.

In this Very Short Introduction Philip K. Maini describes the art of modeling, what it is, why we do it, and illustrates how the abstract way of thinking that is the essence of mathematics enables us to transfer knowledge from one area of research to another. Using numerous examples, he explains how the same fundamental ideas have been used in different fields, and shows how mathematics is the language of science. The author also points to cases in science where the traditional scientific modelling approach—verbal reasoning—is incorrect and shows how mathematics can uncover, and correct, such flawed reasoning while, at the same time, enhance our intuition. This book provides a guide to the trajectory of mathematical biology from a niche subject in the 1970s to a well-established, popular subject that is truly inter-disciplinary, and points to exciting future challenges.