Is the Universe finite or infinite? Is there infinity inside a black hole? Is space infinitely divisible or is there a shortest length? We talk to philosophers and physicists to find out.

A commonly held belief about medieval Europe is that academic pursuits had fallen into a dark age. The majority of scholars were churchmen, and their enquiry often related to some principle of church practice. But is there a value to respecting the tenacity of historic mathematicians?

Is poker a game of psychology and cunning rather than strategy? We investigate the maths of bluffing.

This is the second article in our four-part series exploring quantum electrodynamics. After successfully applying quantum mechanics to the electromagnetic field, physicists faced a problem of boundless proportions: every calculation they made returned infinity as the answer.

You may have heard of quantum theory and you probably know what a field is. But what is quantum field theory? This article traces the development of quantum electrodynamics in the first half of the 20th century. Hair raising difficulties, heroic struggle and illustrious characters — this story has it all!

This is the third article in our four-part series exploring quantum electrodynamics. After struggling with a theory plagued by unwieldy infinities an ingenious trick put QED back on track.

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.

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.