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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.

*Plus*went to the European Congress of Mathematics in Krakow! Around 1,000 mathematicians came together there for a week-long programme of talks and seminars. To give you an idea of what it was like we chatted to several of them during one of the coffee breaks.

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.

In the latest poll of our Science fiction, science fact project you told us that you wanted to know if infinity exists. In this interview the cosmologist John D. Barrow gives us an overview on the question, from Aristotle's ideas to Cantor's never-ending tower of mathematical infinities, and from shock waves to black holes.

This podcast comes to you from a conference on the nature of time. We talk to philosophers of physics Jeremy Butterfield and David Wallace, as well as the eminent Roger Penrose about the puzzle time poses to physicists and what it has to do with the Big Bang and the second law of thermodynamics.