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.
It is extraordinary to think that the diversity of the world we live in is based on a handful of elementary particles and a few fundamental forces. Peter Kalmus describes the combination of experimental and theoretical physics that has brought us to the understanding of today.
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.