This year's Nobel Prize for Physics brings together the physics of materials with one of our favourite areas of maths – topology. This is the second in a series of articles where we asked Fiona Burnell to explain the maths behind the work, and how it may help lead to quicker and smaller electronics, and even the elusive quantum computer.

This year's Nobel Prize for Physics brings together the physics of materials with one of our favourite areas of maths – topology.

Find out how some black holes are bigger on the inside than they are on the outside.

How "forced experimentation" can lead to economic benefits.

How crinkly is crinkly?

A Klein bottle can't hold any liquid because it doesn't have an inside. How do you construct this strange thing and why would you want to?

Why doing maths is like being Lewis Carroll's Red Queen and how to keep going beyond the formidable age of 84.

Maryam Mirzakhani is being honoured for her "rare combination of superb technical ability, bold ambition, far-reaching vision, and deep curiosity".

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.

How to make a hard problem easy by changing the way you look at it.

The London Underground turns 150 today! It's probably the most famous rail network in the world and much of that fame is due to the iconic London Underground map. But what makes this map so special?

Progress in pure mathematics has its own tempo. Major questions may remain open for decades, even centuries, and once an answer has been found, it can take a collaborative effort of many mathematicians in the field to check that it is correct. The New Contexts for Stable Homotopy Theory programme, held at the Institute in 2002, is a prime example of how its research programmes can benefit researchers and its lead to landmark results.