This is the last article in a four-part series exploring quantum electrodynamics. After a breakthrough that tamed QED in theory, the stick-like drawings known as Feynman diagrams, policed by a young Freeman Dyson, made the theory useable.

Are number, space and time features of the outside world or a result of the brain circuitry we have developed to live in it? Some interesting parallels between modern neuroscience and the mathematics of 19th century mathematician Bernard Riemann.

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.

Superposition, an audio-visual performance written by Ryoji Ikeda, is not for the faint hearted. We certainly wouldn't ever be tempted to listen to the sound track on its own. But despite its challenging nature, it is a wonderful experience which evoked a sense of beauty from chaos, mathematics, and physics, carried across by visual art and music.

Space is the stage on which physics happens. It's unaffected by what happens in it and it would still be there if everything in it disappeared. This is how we learn to think about space at school. But the idea is as novel as it is out-dated.

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.

Would you stake your fortune on a 100 to 1 outsider? Probably not. But what if, somewhere in a parallel universe, the straggling nag does come in first? Would the pleasure you feel in that universe outweigh the pain you feel in the one in which you've lost? Questions not dissimilar to this one occupy physicists and for entirely respectable reasons.

Are there parallel universes? Universes in which, rather than reading this article, you are still asleep; in which you are happier, unhappier, richer, poorer, or even dead? The answer is "possibly". It's a controversial claim but one that has won more and more followers over the last few decades.

Hugh Everett III is the father of the many-worlds interpretation of quantum mechanics. He published the idea in his PhD thesis but died before it gained the recognition it deserves. This article gives an insight into Everett's difficult life.

In the previous article we explored how a clever argument involving gambling makes the idea that there are parallel universes more credible. But does it really?

On the face of it the Universe is a fairly complex place. But could mathematics ultimately lead to a simple description of it? In fact, should simplicity be a defining feature of a "theory of everything"? We ponder the answers.

In this, the second part of this series, we look at a mathematical notion of complexity and wonder whether the Universe is just too complex for our tiny little minds to understand.