The Isaac Newton Institute: Creating eureka moments

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.