James A. Maynard: Difference between revisions

James Maynard
FRS
James Maynard FRS
	Maynard in 2013
Born	James Alexander Maynard; 10 June 1987 (age 37); Chelmsford, Essex, England
Alma mater	Queens' College, Cambridge (BA, MPhil); Balliol College, Oxford (DPhil);
Known for	Work on prime gaps
Awards	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);
	Scientific career
Fields	Number theory
Institutions	University of Montreal; University of Oxford;
Thesis	Topics in analytic number theory (2013)
Doctoral advisor	Roger Heath-Brown

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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.^[1] In 2017, he was appointed Research Professor at Oxford.^[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.

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.^[5]^[1] He then became a Fellow by Examination at Magdalen College, Oxford.^[6]

Career

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 $m$ there are infinitely many intervals of bounded length containing $m$ prime numbers.^[9] 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 $m$ ."^[10] Maynard's approach yielded the upper bound, with $p_{n}$ denoting the $n$ 'th prime number,

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

which improved significantly upon the best existing bounds due to the Polymath8 project.^[11] (In other words, he showed that there are infinitely many prime gaps with size of at most 600.) 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.^[13]^[14]

In 2014, he was awarded the SASTRA Ramanujan Prize.^[1]^[15] In 2015, he was awarded a Whitehead Prize^[16] and in 2016 an EMS Prize.^[17]

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.^[18]^[19]

In 2019, together with Dimitris Koukoulopoulos, he proved the Duffin–Schaeffer conjecture.^[20]^[21]

In 2020, in joint work with Thomas Bloom, he improved the best-known bound for square-difference-free sets, showing that a set $A\subset [N]$ with no square difference has size at most ${\frac {N}{(\log N)^{c\log \log \log N}}}$ for some $c>0$ .^[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.^[25]

Personal life

Maynard was born on 10 June 1987 in Chelmsford, England.^[1] His partner is Eleanor Grant, a medical doctor. They have a son.^[4]^[26]

References

^ ^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. Retrieved 13 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. Retrieved 4 April 2018.
^ "Professor James Maynard, St John's College, Oxford". Archived from the original on 22 April 2022. Retrieved 11 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. Retrieved 5 July 2022.
^ James A. Maynard at the Mathematics Genealogy Project
^ "James Maynard: Prime Numbers". Archived from the original on 16 April 2021. Retrieved 11 June 2022.
^ "Dr James Maynard". Magdalen College, Oxford. Archived from the original on 20 May 2018. Retrieved 17 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. Retrieved 16 August 2013.
^ Klarreich, Erica (19 November 2013). "Together and Alone, Closing the Prime Gap". Quanta Magazine. Archived from the original on 5 December 2019. Retrieved 5 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. Retrieved 21 July 2013.
^ Tao, Terence (19 November 2013). "Polymath8b: Bounded intervals with many primes, after Maynard". Archived from the original on 8 May 2021. Retrieved 17 April 2014.
^ Klarreich, Erica (10 December 2014). "Prime Gap Grows After Decades-Long Lull". Quanta Magazine. Archived from the original on 15 July 2017. Retrieved 10 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, retrieved 28 April 2021
^ "2015 Whitehead Prize". Clay Mathematics Institute. 8 July 2015. Archived from the original on 20 August 2019. Retrieved 6 July 2022.
^ "History of prizes awarded at European Congresses of Mathematics". European Mathematical Society. Archived from the original on 9 February 2015. Retrieved 6 July 2022.
^ Grechuk, Bogdan (2021). Landscape of 21st Century Mathematics: Selected Advances, 2001–2020. Springer Nature. p. 14. ISBN 978-3-030-80627-9. Archived from the original on 7 July 2022. Retrieved 6 July 2022.
^ Maynard, J.: Invent. math. (2019) 217: 127. https://doi.org/10.1007/s00222-019-00865-6 Archived 7 July 2022 at the Wayback 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. Retrieved 6 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. Retrieved 6 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. Retrieved 6 July 2022.
^ "James Maynard". royalsociety.org. Retrieved 14 May 2023.
^ Winning the Fields Medal (with James Maynard) - Numberphile, retrieved 14 October 2023

External links

[K_A_SASTRA-1] Alladi, Krishnaswami. "James Maynard to Receive 2014 SASTRA Ramanujan Prize" (PDF). qseries.org. Archived (PDF) from the original on 1 February 2017. Retrieved 13 April 2017.

[2] "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. Retrieved 4 April 2018.

[3] "Professor James Maynard, St John's College, Oxford". Archived from the original on 22 April 2022. Retrieved 11 June 2022.

[harest-easy-4] Klarreich, Erica (June 2022). "A Solver of the Hardest Easy Problems About Prime Numbers". Quanta Magazine. Archived from the original on 5 July 2022. Retrieved 5 July 2022.

[MathGenealogy-5] James A. Maynard at the Mathematics Genealogy Project

[6] "James Maynard: Prime Numbers". Archived from the original on 16 April 2021. Retrieved 11 June 2022.

[7] "Dr James Maynard". Magdalen College, Oxford. Archived from the original on 20 May 2018. Retrieved 17 April 2014.

[8] 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. Retrieved 16 August 2013.

[9] Klarreich, Erica (19 November 2013). "Together and Alone, Closing the Prime Gap". Quanta Magazine. Archived from the original on 5 December 2019. Retrieved 5 December 2019.

[10] Maynard, James (20 November 2013). "Small Gaps Between Primes". arXiv:1311.4600 [math.NT].

[polymath-11] "Bounded gaps between primes". Polymath Project. Archived from the original on 28 February 2020. Retrieved 21 July 2013.

[12] Tao, Terence (19 November 2013). "Polymath8b: Bounded intervals with many primes, after Maynard". Archived from the original on 8 May 2021. Retrieved 17 April 2014.

[Prime_Gap_Grows_After_Decades-Long_Lull-13] Klarreich, Erica (10 December 2014). "Prime Gap Grows After Decades-Long Lull". Quanta Magazine. Archived from the original on 15 July 2017. Retrieved 10 December 2014.

[Large_gaps_between_primes-14] Maynard, James (21 August 2014). "Large gaps between primes". arXiv:1408.5110 [math.NT].

[15] 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, retrieved 28 April 2021

[16] "2015 Whitehead Prize". Clay Mathematics Institute. 8 July 2015. Archived from the original on 20 August 2019. Retrieved 6 July 2022.

[17] "History of prizes awarded at European Congresses of Mathematics". European Mathematical Society. Archived from the original on 9 February 2015. Retrieved 6 July 2022.

[18] Grechuk, Bogdan (2021). Landscape of 21st Century Mathematics: Selected Advances, 2001–2020. Springer Nature. p. 14. ISBN 978-3-030-80627-9. Archived from the original on 7 July 2022. Retrieved 6 July 2022.

[19] Maynard, J.: Invent. math. (2019) 217: 127. https://doi.org/10.1007/s00222-019-00865-6 Archived 7 July 2022 at the Wayback Machine

[20] Sloman, Leila (16 September 2019). "New Proof Solves 80-Year-Old Irrational Number Problem". Scientific American. Archived from the original on 24 May 2022. Retrieved 6 July 2022.

[21] 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. Retrieved 6 July 2022.

[22] Bloom, T.; Maynard, J. (2020). "A new upper bound for sets with no square differences". arXiv:2011.13266 [math.NT].

[23] Doyle, John R.; Rice, Alex (5 September 2021). "Multivariate Polynomial Values in Difference Sets". p. 3. arXiv:2006.15400 [math.NT].

[24] "The Fields Medal 2022. James Maynard" (PDF). International Mathematical Union. Archived (PDF) from the original on 5 July 2022. Retrieved 6 July 2022.

[25] "James Maynard". royalsociety.org. Retrieved 14 May 2023.

[26] Winning the Fields Medal (with James Maynard) - Numberphile, retrieved 14 October 2023

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@@ Line 1: / Line 1: @@
-{{Short description|British mathematician}}
+{{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             = 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            = Mathematics
+| fields            = [[Number theory]]
 | workplaces        = {{ubl|[[University of Montreal]] | [[University of Oxford]]}}
-| alma_mater        = {{ubl|[[University of Cambridge]] | [[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_title      = Topics in analytic number theory
-| thesis_year = 2013
+| thesis_year       = 2013
-| thesis_url = http://www.worldcat.org/oclc/885436217
+| thesis_url        = http://www.worldcat.org/oclc/885436217
 | doctoral_students =
 | known_for         = Work on [[prime gap]]s
-| awards            = {{plainlist|class=nowrap|
+| awards            = {{plainlist|
 * [[SASTRA Ramanujan Prize]] (2014)
 * [[Whitehead Prize]] (2015)
 * [[EMS Prize]] (2016)
-* [[Cole Prize]] in Number Theory (2020)
+* [[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 |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 ==
-'''James Alexander Maynard''' (born 10 June 1987) is a British 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 Jams 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 |url=https://www.quantamagazine.org/number-theorist-james-maynard-wins-the-fields-medal-20220705/ |title=A Solver of the Hardest Easy Problems About Prime Numbers |first=Erica |last=Klarreich |magazine=[[Quanta Magazine]] |date=1 June 2020 |accessdate=5 July 2022 |archive-date=5 July 2022 |archive-url=https://web.archive.org/web/20220705072059/https://www.quantamagazine.org/number-theorist-james-maynard-wins-the-fields-medal-20220705/ |url-status=live}}</ref>
+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>
-== Biography ==
+== 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>
-Maynard attended [[King Edward VI Grammar School, Chelmsford]] in [[Chelmsford]], England. After completing his bachelor's and master's degrees at [[Queens' College]], [[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]].<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/ |title=James Maynard: Prime Numbers |access-date=11 June 2022 |archive-date=16 April 2021 |archive-url=https://web.archive.org/web/20210416070215/https://www.magd.ox.ac.uk/research/jrf/maynard/ |url-status=live }}</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,
-For the 2013–2014 year, Maynard was a CRM-ISM postdoctoral researcher at the [[University of Montreal]].<ref>{{cite web |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-url=https://web.archive.org/web/20180520013033/http://www.magd.ox.ac.uk/member-of-staff/james-maynard/ |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-date=22 January 2014 |archive-url=https://web.archive.org/web/20140122004120/http://annals.math.princeton.edu/articles/7954 |url-status=live }}</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 |title=Together and Alone, Closing the Prime Gap |url=https://www.quantamagazine.org/mathematicians-team-up-on-twin-primes-conjecture-20131119/ |url-status=live |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}}</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 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|date=19 November 2013|access-date=17 April 2014|archive-date=8 May 2021|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}}</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" />
+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>
@@ Line 48: / Line 52: @@
 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 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>
-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 journal |last1=Doyle |first1=John R. |last2=Rice |first2=Alex |date=5 September 2021 |title=Multivariate Polynomial Values in Difference Sets |url=http://arxiv.org/abs/2006.15400 |pages=3 |arxiv=2006.15400 |journal= |access-date=6 July 2022 |archive-date=17 August 2020 |archive-url=https://web.archive.org/web/20200817143129/https://arxiv.org/abs/2006.15400 |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>
-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 |title=The Fields Medal 2022. James Maynard |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Maynard_citation.pdf |archive-url=https://web.archive.org/web/20220705165532/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Maynard_citation.pdf |access-date=6 July 2022 |publisher=International Mathematical Union |archive-date=5 July 2022 |url-status=live}}</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.<ref name=harest-easy/>
+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==
@@ Line 61: / Line 67: @@
 ==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=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]
+* [https://www.youtube.com/watch?v=1LoSV1sjZFI Maynard interviewed by Brady Haran on the completion of the Duffin-Schaeffer Conjecture]
 * {{Google scholar id}}
@@ Line 73: / Line 79: @@
 [[Category:1987 births]]
 [[Category:Living people]]
-[[Category:British mathematicians]]
+[[Category:English mathematicians]]
-[[Category:Alumni of the University of Cambridge]]
+[[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]]

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