What are mathematical invariants and why are they useful?

A lattice may seem like a simple regular grid of points, but it leads to fascinating new research in maths and cryptography!

Ingenious maths keeps your credit card details safe when you shop online and underlies the security of the internet.  Find out how in this easy introduction.

Whenever you smell the lovely smell of fresh coffee or drop a tea bag into hot water you're benefiting from diffusion. Find a quick introduction to the concept here.

Random walks are great for modelling anything that moves, from particles to people. They're also fun, versatile and beautiful!

Even simple rules can lead to interesting processes. Play with Conway's famous cellular automaton to see life-like patterns unfold. 

Worried about your population of bugs? A branching process can help you understand it.

What exactly do we mean when we say group theory is the study of symmetry? Group actions make precise what it means for a group to act by symmetries on an object.

How many ways can you write a number as the sum of smaller numbers?  

How does artificial intelligence manage to produce reliable outputs? Stochastic gradient descent has the answer!