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.

The early 1950s were an experimental gold mine for physicists, with new particles produced in accelerators almost every week. Yet the strong nuclear force that acted between them defied theoretical description, sending physicists on a long and arduous journey that culminated in several Nobel prizes and the exotic concept of "asymptotic freedom".

The funeral of the great flamenco guitarist Paco de Lucía this week reminded us of the mathematical and musical reasons we love flamenco.

David Sloan calculates how likely it is that our Universe exists. He explains to us how, and why the answer can help shape our theories of physics.

Do the dramatic advances in cosmology in the last century herald a new golden age of philosophy? A new collaborative project between cosmologists and philosophers is leading the way.