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.

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.

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.

Prestigious mathematics prize goes to group theorists

Conversations across science and art

It's easier than you think

Bonuses are a fact of business life. Last year the Guardian newspaper calculated that the cash rewards paid to London's financial chiefs comfortably outstripped the UK's entire transport budget. With such large sums at stake, envy is bound to raise its ugly head, nver a good thing for company morale. So how should you decide who gets how much? Steven J. Brams suggests a method that's not only fair, but also encourages honesty.

Lewis Dartnell turns the universe into a matrix to model traffic, forest fires and sprawling cities.

According to Darwin, natural selection is the driving force of evolution. It's a beautifully simple idea, but given the thousands of years that are involved, nobody has ever seen it in action. So how can we tell whether or not natural selection occurs and which of our traits are a result of it? In this article Charlotte Mulcare uses milk to show how maths and stats can provide genetic answers.