Why there are only three regular polygons you can tile a wall with.
What does packing balls in higher dimensions have to do with getting your message across?
What is dark matter and how can the LHC find it?
How the maths that is used to predict earthquakes can help fight gang crime.
Using maths to simulate the behaviour of criminals.
How a special kind of curve can keep your data safe.
Fermat's little theorem and fake primes.