British mathematician (born 1987)
James Alexander Maynard FRS analytic number theory and in particular the theory of prime numbers.[ 1] [ 2] [ 3] St John's College, Oxford . He was awarded theFields Medal in 2022[ 4] New Horizons in Mathematics Prize in 2023.
Early life and education [ edit ] Born on 10 June 1987 in Chelmsford, England,[ 1] [ 5] King Edward VI Grammar School, Chelmsford . After completing his bachelor's and master's degrees atQueens' College, Cambridge , in 2009, Maynard obtained his D.Phil. fromBalliol College, Oxford in 2013 under the supervision ofRoger Heath-Brown .[ 6] [ 1] Magdalen College, Oxford .[ 7]
For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at theUniversity of Montreal .[ 8]
In November 2013, Maynard gave a differentproof ofYitang Zhang 's theorem[ 9] primes , and resolved a longstandingconjecture by showing that for anym {\displaystyle m} m {\displaystyle m} [ 10] m {\displaystyle m} m {\displaystyle m} m {\displaystyle m} m {\displaystyle m} [ 11] upper bound , withp n {\displaystyle p_{n}} n {\displaystyle n}
lim inf n → ∞ ( p n + 1 − p n ) ≤ 600 , {\displaystyle \liminf _{n\to \infty }\left(p_{n+1}-p_{n}\right)\leq 600,} which improved significantly upon the best existing bounds due to thePolymath8 project.[ 12] [ 13] Polymath project wiki.[ 12] 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.[ 12]
In August 2014, Maynard (independently ofFord ,Green ,Konyagin andTao ) resolved alongstanding conjecture ofErdős on large gaps between primes, and received the largest Erdős prize ($10,000) ever offered.[ 14] [ 15]
In 2014, he was awarded theSASTRA Ramanujan Prize .[ 1] [ 16] Whitehead Prize [ 17] EMS Prize .[ 18]
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.[ 19] [ 20]
In 2019, together withDimitris Koukoulopoulos , he proved theDuffin–Schaeffer conjecture .[ 21] [ 22]
In 2020, in joint work withThomas Bloom , he improved the best-known bound forsquare-difference-free sets , showing that a setA ⊂ [ N ] {\displaystyle A\subset [N]} N ( log N ) c log log log N {\displaystyle {\frac {N}{(\log N)^{c\log \log \log N}}}} c > 0 {\displaystyle c>0} [ 23] [ 24]
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 inDiophantine approximation ".[ 25]
Maynard was elected aFellow of the Royal Society (FRS) in 2023.[ 26]
Maynard's partner is Eleanor Grant, a medical doctor. They have a son.[ 4] [ 27]
^a b c d Alladi, Krishnaswami ."James Maynard to Receive 2014 SASTRA Ramanujan Prize" (PDF) .qseries.org .Archived (PDF) from the original on 1 February 2017. Retrieved13 April 2017 .^ "James Maynard appointed Research Professor and receives a Wolfson Merit Award from the Royal Society" . 4 April 2018.Archived from the original on 4 April 2018. Retrieved4 April 2018 .^ "Professor James Maynard, St John's College, Oxford" .Archived from the original on 22 April 2022. Retrieved11 June 2022 .^a b Klarreich, Erica (June 2022)."A Solver of the Hardest Easy Problems About Prime Numbers" .Quanta Magazine Archived from the original on 5 July 2022. Retrieved5 July 2022 .^ "James Maynard" .Heidelberg Laureate Forum . Retrieved23 September 2025 .^ James Maynard at theMathematics Genealogy Project ^ "James Maynard: Prime Numbers" .Archived from the original on 16 April 2021. Retrieved11 June 2022 .^ "Dr James Maynard" .Magdalen College, Oxford . Archived fromthe original on 20 May 2018. Retrieved17 April 2014 .^ Zhang, Yitang (2014)."Bounded gaps between primes" Annals of Mathematics .179 (3). Princeton University and the Institute for Advanced Study:1121– 1174.doi :10.4007/annals.2014.179.3.7 Archived from the original on 22 January 2014. Retrieved16 August 2013 . ^ Klarreich, Erica (19 November 2013)."Together and Alone, Closing the Prime Gap" .Quanta Magazine .Archived from the original on 5 December 2019. Retrieved5 December 2019 . ^ Maynard, James (20 November 2013). "Small Gaps Between Primes".arXiv :1311.4600 math.NT ]. ^a b c "Bounded gaps between primes" .Polymath Project .Archived from the original on 28 February 2020. Retrieved21 July 2013 .^ Tao, Terence (19 November 2013)."Polymath8b: Bounded intervals with many primes, after Maynard" .Archived from the original on 8 May 2021. Retrieved17 April 2014 .^ Klarreich, Erica (10 December 2014)."Prime Gap Grows After Decades-Long Lull" .Quanta Magazine .Archived from the original on 15 July 2017. Retrieved10 December 2014 . ^ Maynard, James (21 August 2014). "Large gaps between primes".arXiv :1408.5110 math.NT ]. ^ Alladi, Krishnaswami (December 2014),"Maynard Awarded 2014 SASTRA Ramanujan Prize" (PDF) , Mathematics People,Notices of the AMS 61 (11): 1361,ISSN 1088-9477 ,archived (PDF) from the original on 30 November 2020, retrieved28 April 2021 ^ "2015 Whitehead Prize" .Clay Mathematics Institute . 8 July 2015.Archived from the original on 20 August 2019. Retrieved6 July 2022 .^ "History of prizes awarded at European Congresses of Mathematics" .European Mathematical Society .Archived from the original on 9 February 2015. Retrieved6 July 2022 .^ Grechuk, Bogdan (2021).Landscape of 21st Century Mathematics: Selected Advances, 2001–2020 ISBN 978-3-030-80627-9 Archived from the original on 7 July 2022. Retrieved6 July 2022 . ^ Maynard, J.:Invent. math. (2019) 217: 127.https://doi.org/10.1007/s00222-019-00865-6 Archived 7 July 2022 at theWayback Machine ^ Sloman, Leila (16 September 2019)."New Proof Solves 80-Year-Old Irrational Number Problem" .Scientific American .Archived from the original on 24 May 2022. Retrieved6 July 2022 . ^ Koukoulopoulos, Dimitris; Maynard, James (1 July 2020)."On the Duffin-Schaeffer conjecture" .Annals of Mathematics .192 (1).arXiv :1907.04593 doi :10.4007/annals.2020.192.1.5 .ISSN 0003-486X .S2CID 195874052 .Archived from the original on 7 July 2022. Retrieved6 July 2022 . ^ Bloom, T.; Maynard, J. (2020). "A new upper bound for sets with no square differences".arXiv :2011.13266 math.NT ]. ^ Doyle, John R.; Rice, Alex (5 September 2021). "Multivariate Polynomial Values in Difference Sets". p. 3.arXiv :2006.15400 math.NT ]. ^ "The Fields Medal 2022. James Maynard" (PDF) . International Mathematical Union.Archived (PDF) from the original on 5 July 2022. Retrieved6 July 2022 .^ "James Maynard" .royalsociety.org . Retrieved14 May 2023 .^ Winning the Fields Medal (with James Maynard) - Numberphile , retrieved14 October 2023
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