Patterns and structures lie at the heart of mathematics, some even say they are mathematics. But how do they help us do mathematics?

Many materials around us are oxides – such as rocks, window glass and some of the materials used in your computer. These materials may seem hard and rigid, but mathematics reveals a hidden flexibility that can explain many of their properties.

The paths of billiard balls on a table can be long and complicated. To understand them mathematicians use a beautiful trick, turning tables into surfaces.

Mathematics is incredibly good at describing the world we live in. So much so that some people have argued that maths is not just a tool for describing the world, but that the world is itself a mathematical structure. Does his claim stand up to scrutiny?

Physicists love symmetry, but they get even more excited about symmetry breaking. They even believe that many of the features of the world we live in are a result of it. What do they mean by that?

Imagine a circle with radius 1 cm rolling completely along the circumference of a circle with radius 4 cm. How many rotations did the smaller circle make? Be prepared for a surprise!

We might have found the Higgs boson, but the search for new physics at the LHC isn't over yet.

One thing that makes TV game shows fun to watch is that there's usually an element of luck involved. But how (un)lucky is (un)lucky? We look at the probabilities of two popular examples.

Why does time have a direction?

To create energy from information you would need to break the second law of thermodynamics — that's impossible in the real world, but could theories that do break it shed light on why nature is the way it is?

Like spirals and flowers? Then you'll love polar coordinates and the pretty pictures they allow you to draw!