It might not be as familiar as the circle or parabola, but it's definitely worth getting to know the hyperbola!

What makes a number a constant of nature?

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."

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.

By the 1970s physicists had successfully tamed three of the fundamental forces using a sophisticated construct called quantum field theory. The trouble was that the framework seemed to fall apart when you looked at very high or very low energy scales. So how could these be thought of as valid theories? It's a question physicists are still grappling with today.