James Maynard (mathematician)

James Maynard (born 9 June 1987) is a British mathematician best known for his work on prime gaps.

Contents

• James maynard primes with missing digits
• James maynard small gaps between primes
• References

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 m there are infinitely many intervals of bounded length containing m prime numbers. This work can be seen as progress on the Hardy–Littlewood m -tuples conjecture as it establishes that "a positive proportion of admissible m -tuples satisfy the prime m -tuples conjecture for every m ." Maynard's approach yielded the upper bound

which improved significantly upon the best existing bounds due to the Polymath 8 project. (In other words, he showed that there are infinitely many prime gaps at most 600.) Subsequently, Polymath 8b was created, whose collaborative efforts have reduced the gap size to 252.

As of April 14, 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 its generalized form, the Polymath project wiki states that N 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.

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 2014, he was awarded the SASTRA Ramanujan Prize.