The Isaac Newton Institute: Creating eureka moments

Fractals are a treat for your eyes, but what about your ears? Dmitry Kormann, a composer/keyboardist from São Paulo, Brazil, explains how he integrates fractal-like patterns in the very structure of his music, to obtain beautiful results.

"It's a match!" cries the CSI. At first glance it might seem that if the police have matched a suspect's DNA to evidence from the crime scene, then the case is closed. But some statistical thinking is required to understand exactly what a match is, and importantly, how juries should assess this as part of the evidence in a trial.

Neil Pieprzak tells the fascinating story of Andrew Wiles who, with intense devotion and in secret, proved a deceptively simple-looking conjecture that had defeated mathematicians for almost 400 years.

Not so long ago, if you had a medical complaint, doctors had to open you up to see what it was. These days sophisticated imaging techniques save you the risk and pain of an operation. Chris Budd and Cathryn Mitchell look at the maths that is responsible for these medical techniques, and also for much of the digital revolution.

String theory is a theory of everything in which everything's made of strings — but why strings? What do they do? Find out in our equation-free introduction for beginners.

Winner of the general public category. Enormous is the right word: this theorem's proof spans over 10,000 pages in 500 journal articles and no-one today understands all its details. So what does the theorem say? Richard Elwes has a short and sweet introduction.