Marianne Freiberger

Like spirals and flowers? Then you'll love polar coordinates and the pretty pictures they allow you to draw!

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 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".

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?

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.

A clever statistical technique helped the Kepler mission to find the huge haul of new planets it announced last week.

What do you get when you add up all the natural numbers 1+2+3+4+ ... ? Not -1/12! We explore a strange result that has been making the rounds recently.