Ellen Porteus By Vicky Neale IT WAS the British mathematician G.H. Hardy who popularised the idea that youthful brains do the best maths. “I do not know of a major mathematical advance initiated by a man past fifty”, he wrote in A Mathematician’s Apology, a lament for the decline of his own creativity that he published in 1940 at the age of 62. “If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.” If blooming youth is the rule, Yitang Zhang is a definite exception. For the best part of a decade after completing his PhD, he wasn’t even working as a mathematician, instead doing odd accounting jobs around Kentucky. At one point he did a stint working in a Subway fast-food restaurant. When he announced a mathematical breakthrough that had eluded his peers for a couple of centuries, he was 57. What Zhang made public in 2013 wasn’t a proof of the hallowed “twin primes conjecture”, but it was a significant step towards one. And even if things haven’t quite panned out in the years since, he has inspired work that is promising new insights into the prime numbers, the most beguiling numbers of all. Primes are those numbers greater than 1 that are divisible only by 1 and themselves. The sequence begins 2, 3, 5, 7, 11, 13, 17, 19 and goes on… well, as long as you like. Primes underpin modern cryptography,