Waves are all around us. There are sound waves, water waves, electromagnetic waves, and vibration waves to name just a few. When a wave meets an object in its path, it scatters off it in different directions. When many waves meet multiple objects, the scattering pattern soon becomes extremely complex, so complex that the mathematical techniques needed to understand and predict it are still being developed.

Multiple wave scattering, its mathematical theory and its applications are currently being studied at a research programme taking place at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge. This collection of content explores some of the mathematics and some of the applications being studied at the programme. From invisibility cloaks to mayonnaise, there's almost no end to the impact multiple wave scattering has on our lives.

Why you need maths to dance — Even a single sound wave emanating from your speaker can result in a fiendishly difficult mathematical problem .

Studying scattered waves — Find out about the purpose of the INI programme and some of the challenges that are being investigated.

Chocolate and mayonnaise — In this podcast Valerie Pinfield, co-organiser of the INI programme, tells us about her work and what is has to do with food, and has some useful advice for women early career researchers.

The lungs of the Earth — Ocean waves are the most obvious waves we see in the world around us. The work of Luke Bennetts, who co-organises the INI programme, focusses on the Southern Ocean. This article explores the role of mathematics in ocean science.

### Background and further reading

Why sine (and cosine) make waves — The sine function gives a mathematical representation of a perfect wave. But how do you go from right-angled triangles to waves?

**Invisibility cloaks** — Who wouldn't like to have one? Find out more about the maths behind the cloaks in *Invisibility cloaks* and *Now you see it, now you don't*.

Saving lives: The mathematics of tomography — Tomography involves passing waves through a person's body and constructing an image of its insides by seeing how these waves are scattered and absorbed. This article explores the mathematics behind this medical imaging technique.

Shining a light on gold — Apart from the human body, other materials too can be investigated by passing waves through them and seeing how they behave. Here is another example.

*This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here. *

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The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more. *