Prestigious mathematics prize goes to group theorists

Squares do it, triangles do it, even hexagons do it — but pentagons don't. They just won't fit together to tile a flat surface. So are there any tilings based on fiveness? Craig Kaplan takes us through the five-fold tiling problem and uncovers some interesting designs in the process.

A Beautiful Mathematical Method for Modelling Viruses

Mathematicians pin down symmetry

A new liquid breaks the laws of physics

Winner of the general public category. Enormous is the right word: this theorem's proof spans over 10,000 pages in 500 journal articles and no-one today understands all its details. So what does the theorem say? Richard Elwes has a short and sweet introduction.

Everyone knows what symmetry is, and the ability to spot it seems to be hard-wired into our brains. Mario Livio explains how not only shapes, but also laws of nature can be symmetrical, and how this aids our understanding of the universe.

The work of Donald Coxeter, who died on 31 March 2003, will continue to inspire both mathematicians and artists.

Some molecules - thalidomide, for example - come in both left and right handed versions, while others are indistinguishable from their reflections. Plus finds out about the role of mathematical symmetry in chemistry.

Eugen Jost is a Swiss artist whose work is strongly influenced by mathematics. He sent us this Postcard from Italy, telling us about his work and the important roles that nature and numbers play in it.