James Alexander Maynard FRS (born 10 June 1987) is an English mathematician working in analytic number theory and in particular the theory of prime numbers.

[2] Maynard is a fellow[3] of St John's College, Oxford.

He was awarded the Fields Medal in 2022[4] and the New Horizons in Mathematics Prize in 2023.

After completing his bachelor's and master's degrees at Queens' College, Cambridge, in 2009, Maynard obtained his D.Phil.

[6] For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at the University of Montreal.

[7] In November 2013, Maynard gave a different proof of Yitang Zhang's theorem[8] that there are bounded gaps between primes, and resolved a longstanding conjecture by showing that for any

'th prime number, which improved significantly upon the best existing bounds due to the Polymath8 project.

Subsequently, Polymath8b was created,[12] whose collaborative efforts have reduced the gap size to 246, according to an announcement on 14 April 2014 by the Polymath project wiki.

[11] 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.

[11] 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.

[22][23] Maynard was awarded the Fields Medal 2022 for "contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation".

[24] Maynard was elected a Fellow of the Royal Society (FRS) in 2023.