We asked cosmologist Pau Figueras everything we’ve ever wanted to know about black holes. In this podcast he explains what black holes are, physically, and how we hope to observe them.

Is cosmology a science or a branch of philosophy? Mathematician and astronomer Bernard Carr gives some answers.

We talk to Shajay Bhooshan about his design for the new maths gallery at the Science Museum London.

In this podcast George Ellis explains why the study of the cosmos poses some deep philosophical questions.

If you're going to excel in maths it helps to start early — and that's what Peter Scholze certainly did.

Ingrid Daubechies, President of the International Mathematical Union, about the importance of community in mathematics.

Martin Grötschel, Secretary of the International Mathematical Union, about maths at school, integrating developing nations, and his dream of putting all maths that's ever been produced online.

Manjul Bhargava tells us why playing with maths in important in finding your own way of thinking.

Why doing maths is like being Lewis Carroll's Red Queen and how to keep going beyond the formidable age of 84.

Artur Avila tells us about taming chaos.

How burning paper can win you a prestigious maths prize.

Cormac O' Raifeartaigh recently made a surprising discovery – an unpublished paper by Albert Einstein that sheds light on how Einstein's thinking about the Universe changed as he tackled some of the big questions in cosmology at the time.

Fields medallist Cédric Villani talks to us about our solar system, chaos, and what it's like being a mathematical superstar.

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.

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.

At the beginning of July 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.

Imaginary is an interactive mathematics exhibition that inspires the imagination with beautiful images. And what is more exciting it allows anyone to step into the world of maths and play with beautiful mathematical surfaces, symmetry and much more. We went along to the Imaginary Barcelona conference, which brought together people involved in the original exhibition in Germany and its recent successful run throughout Spain.

Networks loomed large at the AAAS annual meeting in Vancouver, in particular the one you're looking at right now: the Internet. Plus went along to a session on web surveillance. It sounds sinister at first, but as we found out, it's not all about Big Brother breaching your privacy. Information on the web can help us catch terrorists and criminals and it can also identify a widespread practice called astroturfing.