What's so funny 'bout applied mathematics? Modelling, theory, and methods -- Do you want to know a secret? Turkeys, giants, and atomic bombs -- Do you believe in models? Simplicity and complexity -- Do you know the way to solve equations? Spinning tops and chaotic rabbits -- What's the frequency, Kenneth? Waves, quakes, and solitons -- Can you picture that? X-rays, DNA, and photos -- Mathematics, what is it good for? Quaternions, knots and more DNA -- Where are we going? Networks and the brain.

Mathematics is playing an increasingly important role in society and the sciences, enhancing our ability to use models and handle data. While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world in which we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields. This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics and engineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.