## group theory

When things go round and round, a cyclic group may be just what you need!

Groups occur all over mathematics, so it makes sense to find a common language to talk about them all.

A journey into the maths of card shuffling gives us a great insight into how mathematicians work.

Henry Wilton has won a Whitehead Prize for work that combines geometry and algebra.

We speak to Cheryl Praeger about her mathematics and encouraging the next generation of mathematicians.

Mathematicians are busy tidying up the largest proof in history.

An impossible equation, two tragic heroes and the mathematical study of symmetry.

In 1982 Dan Shechtman discovered a crystal that would revolutionise chemistry. He has just been awarded the 2011 Nobel Prize in Chemistry for his discovery — but has the Nobel committee missed out a chance to honour a mathematician for his role in this revolution as well?

Topologists famously think that a doughnut is the same as a coffee cup because one can be deformed into the other without tearing or cutting. In other words, topology doesn't care about exact measurements of quantities like lengths, angles and areas. Instead, it looks only at the overall shape of an object, considering two objects to be the same as long as you can morph one into the other without breaking it. But how do you work with such a slippery concept? One useful tool is what's called the fundamental group of a shape.