Can we always find order in systems that are disordered? If so, just how large does a system have to be to contain a certain amount of order?

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

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".

As your cereal tumbled into your bowl this morning, were you daydreaming of sand dunes or snowy mountains? It wouldn't be surprising given the drab grey skies outside. But now you have another excuse: the cereal, sand and snow can all be examples of granular flows.

There's no doubt that information is power, but could it be converted into physical energy you could heat a room with or run a machine on? In the 19th century James Clerk Maxwell invented a hypothetical being — a "demon" — that seemed to be able to do just that. The problem was that the little devil blatantly contravened the laws of physics. What is Maxwell's demon and how was it resolved?

How a cute 18th century puzzle laid the foundations for one of the most modern areas of maths: network theory.

Data from BICEP2 gathered in the South Pole reveals swirls in the CMB, the first image of gravitational waves and evidence for inflation.

A Gömböc is a strange thing. It wriggles and rolls around with an apparent will of its own. Until quite recently, no-one knew whether Gömböcs even existed. Even now, Gábor Domokos, one of their discoverers, reckons that in some sense they barely exists at all.

How chickens' eyes solve a subtle maths problem.