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    Monsters, moonshine and shadows

    Rachel Thomas

    Monsters, moonshine and shadows sound like the ingredients for an excellent fairy tale. They are also part of a fascinating mathematical story that brings together some of our favourite things – number theory, group theory, string theory and even quantum gravity – as well as some of our favourite mathematicians.

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    Not just the ingredients for a fairy tale...

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    Folding fractions

    Folding a piece of paper in half might be easy, but what about into thirds, fifths, or thirteenths? Here is a simple and exact way for fold any fraction, all thanks to the maths of triangles.
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    Who's looking at you?

    Observers are, of course, vital in physics: we test our theories by comparing them to our observations. But in cosmology, as Jim Hartle explains, we could be one of many possible observers in the Universe and knowing which one we are is vital in testing our theories.
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    Steady on, Einstein

    To celebrate the release of more English translations of Einstein's papers, we revisit one of his previously unknown models of the Universe.
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    From dust to us

    Where planets are born is not necessarily where they will stay…