You meet an old friend on holiday, you find your colleague shares your birthday, you win the lottery. Exactly how rare are these rare events? David Spiegelhalter investigates in his regular column on uncertainty and risk.

When the famous diagram fails

Phil Trinh discovers how maths helps solve the mysteries of flight and love.

José-Manuel Rey revisits a scene of the film A beautiful Mind.

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.

Liz Newton finds that having a small brain doesn't stop you doing great things.

Peter Macgregor explores the beautiful world of the infinite.

Alan Turing is the father of computer science and contributed significantly to the WW2 effort, but his life came to a tragic end. Stefan Kopieczek explores his story.

The primes are the building blocks of our number system, but there's no general formula that will give you all of them. If you want them, you have to hunt them down one by one. Abigail Kirk investigates a method that does just that.

Not so long ago, if you had a medical complaint, doctors had to open you up to see what it was. These days they have a range of sophisticated imaging techniques at their disposal, saving you the risk and pain of an operation. Chris Budd and Cathryn Mitchell look at the maths that isn't only responsible for these medical techniques, but also for much of the digital revolution.

Josefina Alvarez describes the workings of the most famous search engine of them all. You'll need some linear algebra for this one, but it's worth the while!