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

We continue our exploration of the telescope conjecture.

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

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

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

"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.

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!

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

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

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

Maths can help you make the best of things!

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