Spheres within spheres: A journey through many dimensions

We guide you through an exciting recent breakthrough in the world of topology, involving something called the telescope conjecture.

Spheres within spheres: Simplicity and failure

We continue our exploration of the telescope conjecture.

Maths in a minute: Homotopy

The concept of homotopy is a great example of how the language of maths can make intuition precise.

What is symplectic geometry?

This beautiful version of geometry was developed to keep track of things that move! Here's a very brief introduction.

A very old problem turns 30!

Andrew Wiles's proof of Fermat's Last Theorem solved a centuries-old problem by opening a door onto the future of mathematics.

Celebrating 30 years of Andrew Wiles and Fermat's Last Theorem

"Find problems you enjoy, and just work on them. It doesn't matter if you never solve them." We speak to Andrew Wiles on the 30th anniversary of his announcing the proof of Fermat's Last Theorem.

A practical guide to writing about anything for anyone!

Some practical tips to help you when you need it most – when you are sitting at the keyboard, ready (or perhaps not so ready) to put your ideas on the page!

Why you need maths to dance

When sound waves leave your speaker they wreak havoc with mathematics.

Studying scattered waves

Ice, food, and invisibility cloaks — meet the maths that links them together!

Revolutionising the power of blood tests using AI

The BloodCounts! project is gearing up towards one of the largest-scale applications yet of machine learning in medicine and healthcare.

Maths in a minute: Optimisation

Maths can help you make the best of things!

The lungs of the Earth

How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?