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.

Agreeing to pay £50,000 for something worth £2 wouldn't win you any haggling competitions. In mathematics, however, a similar result can bring you international acclaim. This is the case with recent progress towards the famous twin prime conjecture.

Remember how hard it was to fold maps? Mathematicians have struggled with map folding problems for ages but a recent insight suggests there might be another way to approach them, making an unlikely connection between combinatorics, origami and engineering.

In soccer a coin toss is used to decide who goes first in a penalty shootout and similarly in American football a coin decides who plays offence in overtime. But is this really fair? This article explores an alternative.

Cutting the threads of the spacetime fabric and reinstating the aether could lead to a theory of quantum gravity.

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.

The number pi can be expressed beautifully in terms of infinite sums. For practical purposes though, these sums are rather disappointing: they converge slowly, so you need to sum a large number of terms to get accurate estimates of pi. Here's a clever way to make them converge faster.

We've been dabbling a lot in the mysterious world of quantum physics lately, so to get back down to Earth we thought we'd bring you reminder of good old classical physics.

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.