Articles

  • article

    3D printing mathematics

    Saul Schleimer and Henry Segerman show off some of their beautiful 3D printed mathematical structures.
  • article

    The puzzle of time

    Why does time only ever move in one direction? We talk to philosophers of physics Jeremy Butterfield and David Wallace, as well as the eminent Roger Penrose about the puzzle time poses to physicists and what it has to do with the Big Bang and the second law of thermodynamics.
  • article
    fractal

    Do infinities exist in nature?

    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.
  • article

    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?
  • article

    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.
  • article

    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!
  • article

    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.
  • article

    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.
  • article
    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.
  • article

    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.
  • news
    icon

    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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    prime number
    number theory
    twin prime conjecture