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The problem with infinity

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.
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Let me take you down, cos we're going to ... quantum fields

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!
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Taming QED

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.
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Quantum pictures

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.
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Operas, revolutions and nature's tricks: a conversation with Freeman Dyson

In February this year we were lucky enough to interview Freeman Dyson at the Institute for Advanced Studies in Princeton, USA. Dyson is now 89 and still does physics every day in his first floor office at the Institute. Here is an edited version of our interview that we hope conveys his generous nature, wit and intellect.
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Cognition, brains and Riemann

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.

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Maths inspires a rollercoaster ride

Rollercoasters, the London Eye, planes, bikewheels and boomerangs - no it's not our plans for the summer holidays, it's just a normal afternoon at a Maths Inspiration gig.
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Twins move within reach

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.
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A very old problem turns 20

An "electric atomosphere" is not what you expect at a maths lecture. But it is what prevailed when Andrew Wiles announced his proof of a 350-year-old-old problem, Fermat's last theorem, exactly 20 years ago.
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Putting Turing on stage

Alan Turing was a mathematician and WWII code breaker who was convicted of homosexuality in the 1950s, chemically castrated as a result, died young in mysterious circumstances and still hasn't received all the recognition he deserves. His life clearly makes great material for a play — but a musical? We talk to the directors and lead actor of The Universal Machine.
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Exploring the financial ecosystem

Deciding who is to blame and who should pay for the financial crisis will be a hot topic at the G8 next week. Financial mathematics received a lot of bad press in the aftermath of the crunch and many believe that it was the popularity of mathematical models – often borrowed from physics — that put the financial system at risk. But now models borrowed from biology are helping us understand how this risk might be reduced.
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Folding the future: From origami to engineering

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.