What's the point of the Fields Medal and other maths prizes? Who decides who gets one? And when will we have the first female medallist? Rachel talks to László Lovász, current president of the International Mathematical Union (IMU), Martin Grötschel, the IMU's secretary, and Ragni Piene, the new chair of the Abel Prize committee about all this and more.

We talk to Simon Singh, winner of the Leelavati Prize for public outreach in maths, at the International Congress of Mathematicians 2010.

We talk to Brendan Mackay, who spoke at the ICM, about how he debunked the bible codes.

We were lucky enough to interview Stas Smirnov at the ICM in Hyderabad, India. As well as being very pleased at winning the Fields Medal and being recognised by his colleagues, Stas reminded us that mathematicians don't do research to win medals. They do it because of curiosity and he personally can't wait to get back to his theorems.

Here's the full and uncut version of our interview with Fields Medallist Cédric Villani. We'll publish a slightly more polished version when we get the time, with more explanations, but thought you'd like the chance to listen to the whole thing.

By cleverly cross-referencing different databases it can be possible for evil adversaries to reveal intimate information about individuals. Given that it's hard these days to keep your details off these databases, what can be done to protect privacy? We talk to Cynthia Dwork from Microsoft, whose talk at the ICM showcases some mathematical tools to keep our details safe.

We're at the massive conference dinner, talking to Alex Bellos, author of best-selling popular maths book Alex's adventures in numberland, mathematician Colva Roney-Dougal,  other delegates and ourselves.

A very tired Marianne and Rachel discuss the atmosphere at the first day of the ICM when the Fields medals were awarded...