James Maynard (mathematician)
James Maynard (born 10 June 1987) is a British mathematician best known for his work on prime gaps. In 2017, he was appointed Research Professor at Oxford. Biography. After completing his bachelor's and master's degrees at University of Cambridge in 2009, Maynard obtained his D.Phil. from University of Oxford at Balliol College in 2013 under the supervision of Roger Heath-Brown. For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at the University of Montreal. In November 2013, Maynard gave a different proof of Yitang Zhang's theorem that there are bounded gaps  between primes, and resolved a longstanding conjecture by showing that for any formula_1 there are infinitely many intervals of bounded length containing formula_1 prime numbers. This work can be seen as progress on the Hardy–Littlewood formula_1-tuples conjecture as it establishes that "a positive proportion of admissible formula_1-tuples satisfy the prime formula_1-tuples conjecture for every formula_1." Maynard's approach yielded the upper bound, with formula_7 denoting the formula_8'th prime number, which improved significantly upon the best existing bounds due to the Polymath8 project. (In other words, he showed that there are infinitely many prime gaps with size  of at most 600.) Subsequently, Polymath8b was created, whose collaborative efforts have reduced the gap size to 246, according to an announcement on 14 April 2014 by the Polymath project wiki. Further, assuming the Elliott–Halberstam conjecture and, separately, its generalised form, the Polymath project wiki states that the gap size has been reduced to 12 and 6, respectively. In August 2014, Maynard (independently of Ford, Green, Konyagin and Tao) resolved a longstanding conjecture of Erdős on large gaps between primes, and received the largest Erdős prize ($10,000) ever offered. In 2014, he was awarded the SASTRA Ramanujan Prize . In 2015, he was awarded a Whitehead prize and in 2016 an EMS Prize. In 2016, he showed that, for any given decimal digit, there are infinitely many prime numbers that do not have that digit in their decimal expansion. In 2019, together with Dimitris Koukoulopoulos, he proved the Duffin–Schaeffer conjecture.