In this issue...

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.

What's the integral of xk? 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.

Coming to think of it, is the standard formula for the integral of xk really the best one? Chris Sangwin makes an interesting case that it is not.

Want to impress an audience? Then why not become a lightning calculator by learning Burkard Polster and Marty Ross' method for working out the day on which someone was born from their birthday really fast.

Genomics is one of the fastest moving areas of science and Gavin Harper, a mathematician and statistician, has put himself right at its centre. He works for Oxford Nanopore Technologies, a company which is developing new technology for analysing molecules and sequencing DNA. With 75 employees from 18 different countries and all sorts of scientific backgrounds, Gavin's work environment is nothing like the solitary paper-and-pencil affair traditionally associated with mathematics.

Maths is all about patterns and rhythms, so it's no surprise that there's plenty of maths in art. Whether it's the visual or the performing arts, maths can be a tool, an inspiration, or simply something that's naturally contained within the structures and patterns.

How do you judge the risks and benefits of a new medical treatments? With a finite health care budget, how do you decide which treatments should be made freely available on the NHS? Over recent decades the approach to answering these questions has become increasingly rational. Statistics and maths are used not just to test new treatments, but also to figure out which treatments provide most "health for money". To explore these difficult questions, have a look at our recently published package of articles, podcasts and a classroom activity.