Remember the graph paper you used at school, the kind that’s covered with tiny squares? It’s the perfect illustration of what mathematicians call a “periodic tiling of space”, with shapes covering an ...

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems. For more than 50 years, mathematicians have ...

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape. We are fond of saying things are symmetric, but what does ...

Moving pictures: microscope image of a quasicrystal two days after release. The right half has been colour coded. (Courtesy: Po-Yuan Wang and Thomas Mason/Nature) A quasicrystal made from tiny Penrose ...