View source for James A. Maynard

{{Short description|British mathematician (born 1987)}}
{{Use British English|date=July 2022}}
{{Use dmy dates|date=July 2022}}
{{Infobox scientist
| name              = James Maynard
| honorific_suffix  = {{post-nominals|country=GBR|FRS|size=100}}
| image             = James Maynard MFO 2013.jpg
| image_size        = 
| caption           = Maynard in 2013
| birth_name        = James Alexander Maynard
| birth_date        = {{Birth date and age|df=y|1987|6|10}}
| birth_place       = [[Chelmsford]], Essex, England
| death_date        = 
| death_place       = 
| fields            = [[Number theory]]
| workplaces        = {{ubl|[[University of Montreal]] | [[University of Oxford]]}}
| alma_mater        = {{ubl|[[Queens' College, Cambridge]] ([[Bachelor of Arts|BA]], [[MPhil]])| [[Balliol College, Oxford]] ([[DPhil]])}}
| doctoral_advisor  = [[Roger Heath-Brown]]
| thesis_title      = Topics in analytic number theory
| thesis_year       = 2013
| thesis_url        = http://www.worldcat.org/oclc/885436217
| doctoral_students = 
| known_for         = Work on [[prime gap]]s
| awards            = {{plainlist|
* [[SASTRA Ramanujan Prize]] (2014)
* [[Whitehead Prize]] (2015)
* [[EMS Prize]] (2016)
* [[Cole Prize]] (2020)
* [[Fields Medal]] (2022)
* [[New Horizons in Mathematics Prize]] (2023)
* [[Fellow of the Royal Society]] (2023)
}}
}}
'''James Alexander Maynard''' {{post-nominals|country=GBR|FRS}} (born 10 June 1987) is an English mathematician working in [[analytic number theory]] and in particular the theory of prime numbers.<ref name="K_A_SASTRA" /> In 2017, he was appointed Research Professor at Oxford.<ref>{{cite web|date=4 April 2018|title=James Maynard appointed Research Professor and receives a Wolfson Merit Award from the Royal Society|url=https://www.maths.ox.ac.uk/node/26989|access-date=4 April 2018|archive-date=4 April 2018|archive-url=https://web.archive.org/web/20180404202247/https://www.maths.ox.ac.uk/node/26989|url-status=live}}</ref> Maynard is a fellow<ref>{{cite web |url=https://www.sjc.ox.ac.uk/discover/people/professor-james-maynard/ |title=Professor James Maynard, St John's College, Oxford |access-date=11 June 2022 |archive-date=22 April 2022 |archive-url=https://web.archive.org/web/20220422183936/https://www.sjc.ox.ac.uk/discover/people/professor-james-maynard/ |url-status=live }}</ref> of [[St John's College, Oxford]]. He was awarded the [[Fields Medal]] in 2022<ref name="harest-easy">{{cite magazine |last=Klarreich |first=Erica |authorlink=Erica Klarreich |date=June 2022 |title=A Solver of the Hardest Easy Problems About Prime Numbers |url=https://www.quantamagazine.org/number-theorist-james-maynard-wins-the-fields-medal-20220705/ |url-status=live |magazine=[[Quanta Magazine]] |archive-url=https://web.archive.org/web/20220705072059/https://www.quantamagazine.org/number-theorist-james-maynard-wins-the-fields-medal-20220705/ |archive-date=5 July 2022 |accessdate=5 July 2022}}</ref> and the [[New Horizons in Mathematics Prize]] in 2023.

== Education ==
Maynard attended [[King Edward VI Grammar School, Chelmsford]] in [[Chelmsford]], England. After completing his bachelor's and master's degrees at [[Queens' College, Cambridge]], in 2009, Maynard obtained his D.Phil. from [[Balliol College, Oxford]], in 2013 under the supervision of [[Roger Heath-Brown]].<ref name="MathGenealogy">{{MathGenealogy|id=178890}}</ref><ref name="K_A_SASTRA" /> He then became a Fellow by Examination at [[Magdalen College, Oxford]].<ref>{{cite web |url=https://www.magd.ox.ac.uk/research/jrf/maynard/ |archive-url=https://web.archive.org/web/20210416070215/https://www.magd.ox.ac.uk/research/jrf/maynard/ |title=James Maynard: Prime Numbers |access-date=11 June 2022 |archive-date=16 April 2021 |url-status=live }}</ref>

== Career ==
For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at the [[University of Montreal]].<ref>{{cite web |archive-url=https://web.archive.org/web/20180520013033/http://www.magd.ox.ac.uk/member-of-staff/james-maynard/ |url=http://www.magd.ox.ac.uk/member-of-staff/james-maynard/ |title=Dr James Maynard |publisher=[[Magdalen College, Oxford]] |access-date=17 April 2014 |archive-date=20 May 2018 |url-status=dead }}</ref>

In November 2013, Maynard gave a different [[mathematical proof|proof]] of [[Yitang Zhang]]'s theorem<ref>{{cite journal |url=http://annals.math.princeton.edu/articles/7954 |title=Bounded gaps between primes |first=Yitang |last=Zhang |journal=Annals of Mathematics |volume=179 |issue=3 |pages=1121–1174 |publisher=Princeton University and the Institute for Advanced Study |accessdate=16 August 2013 |doi=10.4007/annals.2014.179.3.7 |year=2014 |archive-url=https://web.archive.org/web/20140122004120/http://annals.math.princeton.edu/articles/7954 |url-status=live |archive-date=22 January 2014 |doi-access=free }}</ref> that there are bounded gaps between [[prime number|primes]], and resolved a longstanding [[conjecture]] by showing that for any <math> m</math> there are infinitely many intervals of bounded length containing <math> m</math> prime numbers.<ref>{{cite magazine |last=Klarreich |first=Erica |date=19 November 2013 |archive-url=https://web.archive.org/web/20191205222609/https://www.quantamagazine.org/mathematicians-team-up-on-twin-primes-conjecture-20131119/ |archive-date=5 December 2019 |access-date=5 December 2019 |magazine=Quanta Magazine |title=Together and Alone, Closing the Prime Gap |url=https://www.quantamagazine.org/mathematicians-team-up-on-twin-primes-conjecture-20131119/ |url-status=live }}</ref> This work can be seen as progress on the Hardy–Littlewood <math> m</math>-tuples conjecture as it establishes that "a positive proportion of admissible <math> m</math>-tuples satisfy the prime <math> m</math>-tuples conjecture for every <math> m</math>."<ref>{{cite arXiv |eprint=1311.4600 |title=Small Gaps Between Primes |last1=Maynard |first1=James |class=math.NT |date=20 November 2013}}</ref> Maynard's approach yielded the [[upper and lower bounds|upper bound]], with <math>p_n</math> denoting the <math>n</math>'th prime number,

:<math>\liminf_{n\to\infty}\left(p_{n+1}-p_n\right)\leq 600,</math>

which improved significantly upon the best existing bounds due to the [[Polymath Project#Polymath8|Polymath8]] project.<ref name="polymath">{{cite web |url=http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes |title=Bounded gaps between primes |publisher=[[Polymath Project]] |accessdate=21 July 2013 |archive-date=28 February 2020 |archive-url=https://web.archive.org/web/20200228120914/http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes |url-status=live}}</ref> (In other words, he showed that there are infinitely many prime gaps with size of at most 600.) Subsequently, Polymath8b was created,<ref>{{cite web |url=https://terrytao.wordpress.com/2013/11/19/polymath8b-bounded-intervals-with-many-primes-after-maynard/ |title=Polymath8b: Bounded intervals with many primes, after Maynard|first=Terence|last=Tao|authorlink=Terence Tao |archive-url=https://web.archive.org/web/20210508020614/https://terrytao.wordpress.com/2013/11/19/polymath8b-bounded-intervals-with-many-primes-after-maynard/|url-status=live|date=19 November 2013|access-date=17 April 2014|archive-date=8 May 2021}}</ref> whose collaborative efforts have reduced the gap size to 246, according to an announcement on 14 April 2014 by the [[Polymath project]] wiki.<ref name="polymath" /> 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.<ref name="polymath" />

In August 2014, Maynard (independently of [[Kevin Ford (mathematician)|Ford]], [[Ben Green (mathematician)|Green]], [[Sergei Konyagin|Konyagin]] and [[Terence Tao|Tao]]) resolved a [[Prime gap#Lower bounds|longstanding conjecture]] of [[Paul Erdős|Erdős]] on large gaps between primes, and received the largest Erdős prize ($10,000) ever offered.<ref name="Prime Gap Grows After Decades-Long Lull">{{cite magazine |url=https://www.quantamagazine.org/mathematicians-prove-conjecture-on-big-prime-number-gaps-20141210/ |title=Prime Gap Grows After Decades-Long Lull |magazine=Quanta Magazine |accessdate=10 December 2014 |first=Erica |last=Klarreich |date=10 December 2014 |archive-date=15 July 2017 |archive-url=https://web.archive.org/web/20170715103523/https://www.quantamagazine.org/mathematicians-prove-conjecture-on-big-prime-number-gaps-20141210 |url-status=live}}</ref><ref name="Large gaps between primes">{{cite arXiv |eprint=1408.5110 |title=Large gaps between primes |last1=Maynard |first1=James |class=math.NT |date=21 August 2014}}</ref>

In 2014, he was awarded the [[SASTRA Ramanujan Prize]].<ref name="K_A_SASTRA">{{cite web |url=http://qseries.org/sastra-prize/2014.pdf |title=James Maynard to Receive 2014 SASTRA Ramanujan Prize |first=Krishnaswami |last=Alladi |authorlink=Krishnaswami Alladi |website=qseries.org |accessdate=13 April 2017 |archive-date=1 February 2017 |archive-url=https://web.archive.org/web/20170201171909/http://qseries.org/sastra-prize/2014.pdf |url-status=live }}</ref><ref>{{citation |url=https://www.ams.org/notices/201411/rnoti-p1359.pdf |department=Mathematics People |title=Maynard Awarded 2014 SASTRA Ramanujan Prize |journal=[[Notices of the AMS]] |page=1361 |date=December 2014 |volume=61 |issue=11 |first=Krishnaswami |last=Alladi |authorlink=Krishnaswami Alladi |issn=1088-9477 |access-date=28 April 2021 |archive-date=30 November 2020 |archive-url=https://web.archive.org/web/20201130173519/http://www.ams.org/notices/201411/rnoti-p1359.pdf |url-status=live}}</ref> In 2015, he was awarded a [[Whitehead Prize]]<ref>{{Cite web |date=8 July 2015 |title=2015 Whitehead Prize |url=https://www.claymath.org/events/news/2015-whitehead-prize |access-date=6 July 2022 |website=Clay Mathematics Institute |archive-date=20 August 2019 |archive-url=https://web.archive.org/web/20190820170750/http://www.claymath.org/events/news/2015-whitehead-prize |url-status=live }}</ref> and in 2016 an [[EMS Prize]].<ref>{{Cite web |title=History of prizes awarded at European Congresses of Mathematics |url=https://euro-math-soc.eu/history-prizes-awarded-european-congresses-mathematics |access-date=6 July 2022 |website=European Mathematical Society |archive-date=9 February 2015 |archive-url=https://web.archive.org/web/20150209183245/https://euro-math-soc.eu/history-prizes-awarded-european-congresses-mathematics |url-status=live }}</ref>

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.<ref>{{Cite book |last=Grechuk |first=Bogdan |url=https://books.google.com/books?id=qElEEAAAQBAJ |title=Landscape of 21st Century Mathematics: Selected Advances, 2001–2020 |date=2021 |publisher=Springer Nature |isbn=978-3-030-80627-9 |pages=14 |access-date=6 July 2022 |archive-date=7 July 2022 |archive-url=https://web.archive.org/web/20220707010821/https://books.google.com/books?id=qElEEAAAQBAJ |url-status=live }}</ref><ref>Maynard, J.: [[Inventiones Mathematicae|Invent. math.]] (2019) 217: 127. https://doi.org/10.1007/s00222-019-00865-6 {{Webarchive|url=https://web.archive.org/web/20220707010823/https://link.springer.com/article/10.1007/s00222-019-00865-6 |date=7 July 2022 }}</ref>

In 2019, together with [[Dimitris Koukoulopoulos]], he proved the [[Duffin–Schaeffer conjecture]].<ref>{{Cite web |last=Sloman |first=Leila |date=16 September 2019 |title=New Proof Solves 80-Year-Old Irrational Number Problem |url=https://www.scientificamerican.com/article/new-proof-solves-80-year-old-irrational-number-problem/ |access-date=6 July 2022 |website=Scientific American |language=en |archive-date=24 May 2022 |archive-url=https://web.archive.org/web/20220524051820/https://www.scientificamerican.com/article/new-proof-solves-80-year-old-irrational-number-problem/ |url-status=live }}</ref><ref>{{Cite journal |last1=Koukoulopoulos |first1=Dimitris |last2=Maynard |first2=James |date=1 July 2020 |title=On the Duffin-Schaeffer conjecture |url=https://projecteuclid.org/journals/annals-of-mathematics/volume-192/issue-1/On-the-Duffin-Schaeffer-conjecture/10.4007/annals.2020.192.1.5.full |journal=Annals of Mathematics |volume=192 |issue=1 |doi=10.4007/annals.2020.192.1.5 |arxiv=1907.04593 |s2cid=195874052 |issn=0003-486X |access-date=6 July 2022 |archive-date=7 July 2022 |archive-url=https://web.archive.org/web/20220707010822/https://projecteuclid.org/journals/annals-of-mathematics/volume-192/issue-1/On-the-Duffin-Schaeffer-conjecture/10.4007/annals.2020.192.1.5.short |url-status=live}}</ref>

In 2020, in joint work with [[Thomas Bloom]], he improved the best-known bound for [[square-difference-free set]]s, showing that a set <math>A \subset [N]</math> with no square difference has size at most  <math>\frac{N}{(\log N)^{c\log \log\log N}}</math> for some <math>c > 0</math>.<ref>{{cite arXiv |first1=T. |last1=Bloom |first2=J. |last2=Maynard |title=A new upper bound for sets with no square differences |year=2020 |class=math.NT |eprint=2011.13266}}</ref><ref>{{Cite arXiv |last1=Doyle |first1=John R. |last2=Rice |first2=Alex |date=5 September 2021 |title=Multivariate Polynomial Values in Difference Sets |pages=3 |class=math.NT |eprint=2006.15400 }}</ref>

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]]".<ref>{{Cite web  |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Maynard_citation.pdf |title=The Fields Medal 2022. James Maynard  |access-date=6 July 2022 |publisher=International Mathematical Union |archive-url=https://web.archive.org/web/20220705165532/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Maynard_citation.pdf |archive-date=5 July 2022 |url-status=live}}</ref>

Maynard was elected a [[Fellow of the Royal Society]] (FRS) in 2023.<ref>{{Cite web |title=James Maynard |url=https://royalsociety.org/people/james-maynard-36190/ |access-date=2023-05-14 |website=royalsociety.org}}</ref>

==Personal life==
Maynard was born on 10 June 1987 in Chelmsford, England.<ref name="K_A_SASTRA" /> His partner is Eleanor Grant, a medical doctor. They have a son.<ref name=harest-easy/><ref>{{Citation |title=Winning the Fields Medal (with James Maynard) - Numberphile |url=https://www.youtube.com/watch?v=eupAXdWPvX8 |access-date=2023-10-14 |language=en}}</ref>

==References==
{{reflist}}

==External links==
* [https://www.youtube.com/watch?v=QKHKD8bRAro Maynard interviewed by Brady Haran on the Twin Prime Conjecture]
* [https://www.youtube.com/watch?v=1LoSV1sjZFI Maynard interviewed by Brady Haran on the completion of the Duffin-Schaeffer Conjecture]
* {{Google scholar id}}

{{Fields medalists}}
{{Recipients of SASTRA Ramanujan Prize winners|state=collapsed}}

{{Authority control}}

{{DEFAULTSORT:Maynard, James}}
[[Category:1987 births]]
[[Category:Living people]]
[[Category:English mathematicians]]
[[Category:Alumni of Queens' College, Cambridge]]
[[Category:Alumni of the University of Oxford]]
[[Category:Whitehead Prize winners]]
[[Category:People educated at King Edward VI Grammar School, Chelmsford]]
[[Category:Fields Medalists]]
[[Category:Fellows of the Royal Society]]