The natural numbers, 1, 2, 3, 4, ..., are nice. So what could be nicer than discovering interesting patterns within them?

At last month's Cambridge Science Festival we had great fun trying out a hands-on (or rather feet-on) activity based on one of our favourite puzzles – the bridges of Königsberg. We were really pleased with how it went, so we thought we'd share our game for others to put on at their own science or maths event.

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

The search for the missing Malaysia Airlines' flight MH370 was dramatically narrowed last week due to a mathematical analysis of satellite signals from the plane. Careful analysis of just a handful of data points has focussed the search on an area in the southern Indian Ocean.

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.

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.