Mathematical Biology

Abstract Mathematical Biology: A Very Short Introduction explores how mathematical models uncover patterns in nature, such as animal coat markings (and their remarkable similarity to football shirt designs). It shows how biological ideas can be translated into the language of mathematics, where they can be integrated and studied in detail, generating results which can then be interpreted biologically. It introduces the key basic mathematical concepts used to analyse the models that arise from this procedure. It explains how the same mathematical principles apply across biological systems, from invasive species to cancer cells. This VSI illustrates how abstract mathematical thinking transfers knowledge between disciplines, improving scientific understanding. It demonstrates why mathematics is the language of science, challenging traditional approaches that rely solely on verbal reasoning. It shows that mathematical models can be used to test existing biological hypotheses and generate new hypotheses. Through numerous examples, it shows how modelling refines research in biology, medicine, ecology, and epidemiology, revealing insights that conventional methods often overlook. It also highlights what are the key future challenges in the field.