James Maynard (mathematician)


James Maynard is a British mathematician best known for his work on prime gaps. 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 2017, he was appointed Research Professor at Oxford.

Work

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 there are infinitely many intervals of bounded length containing prime numbers. This work can be seen as progress on the Hardy–Littlewood -tuples conjecture as it establishes that "a positive proportion of admissible -tuples satisfy the prime -tuples conjecture
for every." Maynard's approach yielded the upper bound
which improved significantly upon the best existing bounds due to the Polymath8 project. Subsequently, Polymath8b was created, whose collaborative efforts have reduced the gap size to 246.
On 14 April 2014, one year after Zhang's announcement, according to the Polymath project wiki, N had been reduced to 246. Further, assuming the Elliott–Halberstam conjecture and, separately, its generalised form, the Polymath project wiki states that N has been reduced to 12 and 6, respectively.
In August 2014, Maynard resolved a longstanding conjecture of Erdős on large gaps between primes, and received the largest Erdős prize 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.