What's the integral of x^k? If you're up to speed with your calculus, you can probably rattle the answer off by heart. But can you prove it? Chris Sangwin introduces an ingenious method for deriving the integral from first principles.

David Spiegelhalter explains that waiting for an infinite number of monkeys to produce the complete works of Shakespeare is not just a probabilistic certainty, it also gives us an insight into how long we can expect to wait for a rare event to happen.

Genes normally evolve by tiny mutations, but every now and then something more radical occurs and entire genes along a chromosome get flipped. Understanding gene flipping boils down to solving a problem from pure maths. Colva Roney-Dougal and Vincent Vatter explain, taking us on a journey from waiters sorting pancakes, via one of the richest men in the world, to the genetic similarities of mice and humans.

Stats, damn stats and genetics

One in nine women will get breast cancer in her lifetime, and it seems sensible to screen women for breast cancer to treat them as early as possible. But, as David Spiegelhalter explains, screening is a controversial issue.