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

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.

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!

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.

From the complexity of the snowflake, to the London tube map and the spiralling Andromeda galaxy, imagery has always been a vitally important ingredient of science. This week, Plus talks to John Barrow, professor of mathematics at Cambridge University and author of the new book Cosmic Imagery, about the images that have changed science, and how we have viewed science, over the centuries.

The Enigma machine was once considered unbreakable, and the cracking of the "unbreakable code" by the allies changed the course of World War 2. This week, Plus talks to Nadia Baker from the Enigma Project about the history of codes and code-breaking, why the Enigma machine was considered unbreakable, the mathematics behind codes, and how it was finally cracked. The Enigma Project travels all over the United Kingdom and abroad, visiting over 100 schools and organisations, reaching over 12,000 people of all ages every year.

Bacon sandwiches, drinking while pregnant, obesity - health risks are a favourite with the media. But behind the simple numbers quoted in the headlines lies a huge and sophisticated body of statistical research. We talk to Professor Sheila Bird of the Biostatistics Unit in Cambridge about her work in public health and its impact on policy, and discuss bias in pharmaceutical studies, as recently highlighted by the controversy around antidepressants.

Prestigious mathematics prize goes to group theorists

Conversations across science and art

It's easier than you think