James Maynard (mathematician)

James Maynard
Born	June 10, 1987 Chelmsford, England[1]
Nationality	British
Fields	Mathematics
Institutions	University of Montreal, University of Oxford
Alma mater	University of Cambridge, University of Oxford
Doctoral advisor	Roger Heath-Brown[2]
Known for	Work on prime gaps
Notable awards	SASTRA Ramanujan Prize (2014) Whitehead Prize (2015) EMS Prize (2016)

James Maynard (born 10 June 1987) is a British mathematician best known for his work on prime gaps.^[1]

In November 2013, Maynard gave a different proof of Yitang Zhang's theorem^[3] 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.^[4] 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 $m$."^[5] Maynard's approach yielded the upper bound

$\liminf _{{n\to \infty }}\left(p_{{n+1}}-p_{n}\right)\leq 600,$

which improved significantly upon the best existing bounds due to the Polymath 8 project.^[6] (In other words, he showed that there are infinitely many prime gaps at most 600.) Subsequently, Polymath 8b was created,^[7] whose collaborative efforts have reduced the gap size to 252.^[6]

As of April 14, 2014, one year after Zhang's announcement, according to the Polymath project wiki, N has been reduced to 246.^[6] 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.^[6]

In August 2014, Maynard^[8] (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.^[9]

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.^[1] For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at the University of Montreal.^[10]

In 2014, he was awarded the SASTRA Ramanujan Prize.^[11]

References

1. James Maynard to Receive 2014 SASTRA Ramanujan Prize, Krishnaswami Alladi
2. James Maynard at the Mathematics Genealogy Project
3. Zhang, Yitang (2014). "Bounded gaps between primes". Annals of Mathematics. Princeton University and the Institute for Advanced Study. 179 (3): 1121. doi:10.4007/annals.2014.179.3.7. Retrieved August 16, 2013.
4. Klarreich, Erica (19 November 2013). "Together and Alone, Closing the Prime Gap". Quanta Magazine (Simons Institute).
5. Maynard, James (2013). "Small Gaps Between Primes". arXiv:1311.4600 [math.NT].
6. "Bounded gaps between primes". Polymath. Retrieved 2013-07-21.
7. "Polymath8b: Bounded intervals with many primes, after Maynard".
8. Maynard, James (2014). "Large gaps between primes". arXiv:1408.5110 [math.NT].
9. "Mathematicians Make a Major Discovery About Prime Numbers". Wired. Retrieved 2015-07-27.
10. "Oxford Webpage".
11. Alladi, Krishnaswami (December 2014), "Maynard Awarded 2014 SASTRA Ramanujan Prize" (PDF), Mathematics People, Notices of the AMS, 61 (11): 1361, ISSN 1088-9477.