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.

Ocean waves are not moving walls of water. Instead, it's some kind of energy that moves along. But then, what happens to the water itself? This isn't just an idle question to ponder while watching the ocean — its answer may help protect us from it too. And it requires some sophisticated maths.

Few things in nature are as dramatic, and potentially dangerous, as ocean waves. The impact they have on our daily lives extends from shipping to the role they play in driving the global climate. From a theoretical viewpoint water waves pose rich challenges: solutions to the equations that describe fluid motion are elusive, and whether they even exist in the most general case is one of the hardest unanswered questions in mathematics.

It's not just evil villians who can blow smoke rings, it seems peat moss has been doing it for millennia.

Andy Green, Royal Air force pilot and Oxford maths graduate, is gearing up to break his own land speed record in Bloodhound SSC, a supersonic car designed to reach speeds of up to 1000mph. He tells Plus about the challenges — and the maths — behind this engineering adventure.

Alexis Wajsbrot is a visual effects specialist who has worked on a number of high-profile films including Harry Potter and the Half-blood Prince, Harry Potter and the Order of Phoenix, Tim Burton's Sweeney Todd, and also on some of those visually stunning commercials you see while waiting for your film to start. His speciality is anything that behaves like a fluid: water, smoke, fire, even fur or cloth. Plus went to see him to find out more.

Describing the motion of fluids is a huge and unsolved mathematical problem. There are equations that seem to describe it well, but their complete solution is way beyond reach. But could there be a simpler method? The physicist Jerry Gollub tells Plus about a new discovery which combines experiment with sophisticated maths.

Penguin eggs are not something you'd normally associate with maths, but they are right there on the archives of the Smith Institute, an organisation helping businesses use maths to solve their problems. Claudia Centazzo tells us about her role at the institute, selling maths to unsuspecting business people.