"The beauty of the wave equation manifests itself in several ways," says Ian Stewart of the University of Warwick in the UK. "It is mathematically simple and elegant. It has an interesting range of solutions with pleasant mathematical features."

The wave equation describes how waves propagate. It applies to all kinds of waves, from water waves to sound and vibrations, and even light and radio waves.

It has a remarkable history, says Stewart.

It began with a simple model of a vibrating violin string, and developed into something used to study a diverse range of phenomena, from earthquakes to oil prospecting and even safety on ships. Its link to music helped explain how our ears hear sound, and why some combinations are harmonious while others are jarring.

"It is a poster child for the idea that mathematical principles developed in one area, or for their own sake, can have vital applications in other areas," says Stewart. "Its beauty comes from the combination of these attributes: elegance, surprise, intellectual depth, utility."

Read more: What is the most beautiful equation?