As an electronic musician Oli Freke has always been fascinated by sine waves, so much so that he's created a song based on them for the Geekpop festival, which is currently taking place on the Web. In this article he explores his song, touching on ancient Greek mythology, strange piano tunings and Johann Sebastian Bach.

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.

The prime numbers are the atoms amongst the integers, and while we know that there are infinitely many of them, there's no general formula that generates them all. Julian Havil looks at a little-known algorithm that sieves out all primes up to a given number, and which is astonishing in its simplicity.

Why length matters

In 1979 decorating work in a house in Vienna revealed a set of medieval frescoes depicting a cycle of songs by a 13th century poet, who was particularly fond of satirising the erotic relationships between knights and peasant maidens. The frescoes are of great historical significance, but they are badly damaged. In this article Carola Schönlieb explores how mathematicians use the heat equation to fill in the gaps.

In the light of recent events, it may appear that attempting to model the behaviour of financial markets is an impossible task. However, there are mathematical models of financial processes that, when applied correctly, have proved remarkably effective. Angus Brown looks at one of these, a simple model for option pricing, and explains how it takes us on the road to the famous Black-Scholes equation of financial mathematics, which won its discoverers the 1997 Nobel Prize in Economics.

With the credit crunch dominating the news, columnists have been wailing about "chaos in the markets", and "turbulent" share prices. But what does move the markets? Are they deterministic, or a result of chance? Colva Roney-Dougal explores the maths, from chaos to group theory.

Mathematics takes to the stage with A disappearing number, a work by Complicite, inspired by the mathematical collaboration of Hardy and Ramanujan. Rachel Thomas went to see the play, and explains some of the maths. You can also read her interview with Victoria Gould about how the show was created.

We live in a world full of information and it's a statistician's job to make sense of it. In this article Dianne Cook explores ways of analysing data and shows how they can be applied to anything from investigating diners' tipping behaviour to understanding climate change and genetics.

When it comes to describing natural phenomena, mathematics is amazingly — even unreasonably — effective. In this article Mario Livio looks at an example of strings and knots, taking us from the mysteries of physical matter to the most esoteric outpost of pure mathematics, and back again.