## 54

*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.

**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.

**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.

**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.