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In this podcast we talk to Max Tegmark about his hypothesis that the Universe we live in is a mathematical structure.

Mathematics and theatre are both imagined things that need to be consistent. So what better way to explore mathematical ideas than through theatre? We talk to Marcus du Sautoy, Victoria Gould and Dermot Keany about their new show, X&Y.

*The universal machine* is a musical about Alan Turing, the mathematician and WWII code breaker who was convicted of homosexuality in the 1950s, chemically castrated as a result, and died young in mysterious circumstances. How do you turn such a story, and the maths in it, into a musical? We talked to writer and director David Byrne, Richard Delaney, who plays Turing, and Assistant Director Natalie York.

Is the Universe finite or infinite? Is there infinity inside a black hole? Is space infinitely divisible or is there a shortest length? Can infinity occur at all in the cosmos or is it a mathematical construct? Find out more in our podcast with Anthony Aguirre, John D. Barrow and George Ellis.

Mathematics does incredibly well at describing the world we live in. Could that be because the Universe itself is a mathematical structure? It's a suggestion that has been put forward by the cosmologist Max Tegmark. We talked to him to find out more.

*Travelling Salesman* is an unusual movie: despite almost every character being a mathematician there's not a mad person in sight. Moreover, the plot centres on one of the greatest unsolved problems in mathematics. We were lucky enough to speak to the writer/director Tim Lanzone about creating drama from mathematics.

How many dimensions are there? In the latest online poll of our *Science fiction, science fact* project you told us that you'd like an answer to this question. So we went to see theoretical physicist David Berman to find out more.

The 6th European Congress of Mathematics, which took place in Krakow at the beginning of July, wasn't just about mathematicians talking to each other. On the streets of Krakow maths buskers were entertaining the public, handcuffing innocent Krakowians, constructing emergency pentagons and reading minds. So what is maths busking all about? We caught up with Sara Santos, the director of the project, and one of her volunteers to find out.