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Cormac O' Raifeartaigh recently made a surprising discovery – an unpublished paper by Albert Einstein that sheds light on how Einstein's thinking about the Universe changed as he tackled some of the big questions in cosmology at the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

In this, our second podcast from the AAA Meeting in Vancouver, Canada, we speak to Marcel Babin about using satellite images to measure the amount of organisms, such as phytoplankton, in the Arctic ocean and studies how this changing biological diversity can both indicate, and impact on, climate change.

From flattening the Earth to dining with the jellyfish, Plus chats about our first day at the AAAS meeting in Vancouver, Canada.

What's a multiverse? What's the future for intelligent life? And what happened 380,000 after the Big Bang. Find out in these interviews with the physicists David Spergel and Raphael Bousso, who we spoke to during Stephen Hawking's 70th birthday conference.

This is one of our podcasts from Stephen Hawking's 70th birthday conference, which took place in January 2012 in Cambridge. Rachel Thomas talks to Renata Kallosh from Stanford University about a theory that promises to unite the physics of the very small — quantum physics — and the physics of the very large — Einstein's theory of gravity.

"Astronomers are used to large numbers, but few are as large as the odds I'd have given this celebration today," is how Astronomer Royal Martin Rees started his presentation at Stephen Hawking's birthday symposium yesterday. He was talking about the 1960s when he first met Hawking who was then already suffering motor neurone disease. But Rees' prediction has been proved wrong. Hawking turned 70 yesterday and since the time of their first meeting he has made enormous contributions to cosmology and physics.

This podcast featuring Paul Davies, a theoretical physicist and cosmologist at Arizona State University and Director of BEYOND: Centre for Fundamental Concepts in Science, explores this difficult question and accompanies our What is time article.