"I think I'll stop here." This is how, on 23rd June 1993, Andrew Wiles ended his series of lectures at the Isaac Newton Institute (INI), our neighbour here at the Centre for Mathematical Sciences. The applause, so witnesses report, was thunderous. Wiles had just announced a proof that had eluded mathematicians for over 350 years: the proof of Fermat's Last Theorem.

Wiles' announcement, 30 years ago today, was a thrilling moment in mathematical history. But Fermat's Last Theorem is not just the story of one person. Jack Thorne, who works on new mathematics that builds on Wiles' proof, told us that it is actually a story of people talking to each other over a period of centuries.

To celebrate 30 years since that exciting moment, we were lucky enough to speak with Andrew Wiles and Jack Thorne, and also to Tom Körner, who was there the day Wiles announced the proof.

This is a special joint episode with the INI's Living Proof podcast, made in collaboration with our friend Dan Aspel, from the INI.

You can find out more about Fermat's Last Theorem in the article that accompanies this podcast, and in this collection of further reading.

This podcast 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.

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.