Artur Avila is being honoured for "formidable technical power, the ingenuity and tenacity of a master problem-solver, and an unerring sense for deep and
significant questions."

It's one of the most beautiful sights in nature: fireflies illuminating the night with their synchronised flashing. Mathematicians have just solved a 40 year-old problem behind this striking phenomenon.

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.

If you thought that billiards was a harmless game to play in the pub, think again. It's a breeding ground for chaos!

Fields medallist Cédric Villani talks to us about our solar system, chaos, and what it's like being a mathematical superstar.

The ability to see order in chaos has won the mathematician Yakov G. Sinai the 2014 Abel Prize.

Struggling to solve today's sudoku? Is your tried and tested method hitting a brick wall and you feel like you are going around in circles? New research might make you feel a bit better: you might not necessarily be stuck... perhaps you are just in a patch of transient chaos on your way to the solution.

If you are prone to forgetting your passwords, you're not alone. To make sure we remember all our passwords, many of us take measures that defeat the purpose. These include, as studies have shown, using the same password for everything or writing them down on post-it notes and sticking them to our computer. But such sloppiness makes easy work for evil agents out to steal our data and identities. Now physicists from the US and Germany have devised a safer way of using passwords that takes account of the human need for memorability.

This article is part of a series of two articles exploring two ways in which mathematics comes into food, and especially into food safety and health. In this article we will take a dive into the rather smelly business of digesting food, and how a crazy application of chaos theory shows the best way to digest a medicinal drug.

Controlled chaos produces realistic behaviour in robotic cockroach

Not if their predictions are made clearer...

Describing the motion of fluids is a huge and unsolved mathematical problem. There are equations that seem to describe it well, but their complete solution is way beyond reach. But could there be a simpler method? The physicist Jerry Gollub tells Plus about a new discovery which combines experiment with sophisticated maths.