Articles

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    The lost mathematicians: Numbers in the (not so) dark ages

    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?
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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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    Dyson

    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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    Twins move within reach

    Marianne Freiberger

    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. Mathematics can be a lot like haggling: if you can't get the answer you want, you try to get as close as possible. In the case of the famous twin prime conjecture the answer you want is 2. Recent results claim to have managed just over 50,000, but they are causing quite a stir. That's because the gap between 2 and 50,000 is a whole lot smaller than the gap between 50,000 and infinity.

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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.
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    Why you shouldn't use a toss for overtime

    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.
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    Ripping apart Einstein

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