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{{short description|Chinese-born American mathematician}}
{{short description|Chinese-born American mathematician}}
{{Use mdy dates|date=November 2022}}
{{family name hatnote|[[Zhang (surname)|Zhang]]|lang=Chinese}}
{{family name hatnote|[[Zhang (surname)|Zhang]]|lang=Chinese}}
{{Infobox scientist
{{Infobox scientist
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| caption = Zhang in 2014
| caption = Zhang in 2014
| birth_date = {{Birth date and age|1955|02|05}}
| birth_date = {{Birth date and age|1955|02|05}}
| birth_place = [[Pinghu]], [[Zhejiang]], China
| birth_place = Shanghai, China
| citizenship = United States
| citizenship = United States
| nationality =
| nationality =
| fields = [[Mathematics]], [[Number theory]]
| fields = [[Number theory]]
| workplaces = [[University of New Hampshire]]<br />[[University of California, Santa Barbara]]
| workplaces = [[University of New Hampshire]]<br />[[University of California, Santa Barbara]]
| alma_mater = [[Peking University]] ([[Bachelor of Science|BS]], [[Master of Arts|MA]])<br />[[Purdue University]] ([[Doctor of Philosophy|PhD]])
| alma_mater = [[Peking University]] ([[Bachelor of Science|BS]], [[Master of Arts|MA]])<br />[[Purdue University]] ([[PhD]])
| known_for = Establishing the existence of an infinitely repeatable [[Prime k-tuple|prime 2-tuple]]<ref name=quanta>{{cite news|last=Klarreich|first=Erica|title=Unheralded Mathematician Bridges the Prime Gap|url=https://www.simonsfoundation.org/quanta/20130519-unheralded-mathematician-bridges-the-prime-gap/|access-date=May 19, 2013|newspaper=Quanta Magazine|date=May 19, 2013}}</ref>
| known_for = Establishing the existence of an infinitely repeatable [[Prime k-tuple|prime 2-tuple]]<ref name=quanta>{{cite news|last=Klarreich|first=Erica|title=Unheralded Mathematician Bridges the Prime Gap|url=https://www.simonsfoundation.org/quanta/20130519-unheralded-mathematician-bridges-the-prime-gap/|access-date=May 19, 2013|newspaper=Quanta Magazine|date=May 19, 2013}}</ref>
| awards = [[Ostrowski Prize]] (2013)<br />[[Cole Prize]] (2014)<br />[[Rolf Schock Prize]] (2014)<br />[[MacArthur Fellowship]] (2014)
| awards = [[Ostrowski Prize]] (2013)<br />[[Cole Prize]] (2014)<br />[[Rolf Schock Prize]] (2014)<br />[[MacArthur Fellows Program|MacArthur Fellowship]] (2014)
| thesis_title = The Jacobian conjecture and the degree of field extension
| thesis_title = The Jacobian conjecture and the degree of field extension
| thesis_url = https://www.proquest.com/docview/303919798
| thesis_url = https://www.proquest.com/docview/303919798
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| doctoral_advisor = Tzuong-Tsieng Moh (莫宗堅)<ref>{{MathGenealogy|id=16848}}</ref>
| doctoral_advisor = Tzuong-Tsieng Moh (莫宗堅)<ref>{{MathGenealogy|id=16848}}</ref>
}}
}}
'''Yitang''' '''Zhang''' ({{zh|s=张益唐|p=}}; born February 5, 1955)<ref>{{cite book |last1=Zhang |first1=Yitang |title=The Jacobian conjecture and the degree of field extension |date=1991 |publisher=[[Purdue University]] |url=https://docs.lib.purdue.edu/dissertations/AAI9215703/ |access-date=4 March 2021}}</ref> is a Chinese American mathematician primarily working on [[number theory]] and a professor of mathematics at the [[University of California, Santa Barbara]] since 2015.<ref>{{Cite web |title=Yitang (Tom) Zhang {{!}} Department of Mathematics - UC Santa Barbara |url=https://www.math.ucsb.edu/people/yitang-tom-zhang |access-date=2022-10-19 |website=www.math.ucsb.edu}}</ref>
'''Yitang''' '''Zhang''' ({{zh|s=张益唐|p=}}; born February 5, 1955)<ref>{{cite book |last1=Zhang |first1=Yitang |title=The Jacobian conjecture and the degree of field extension |date=1991 |pages=1–24 |publisher=[[Purdue University]] |url=https://docs.lib.purdue.edu/dissertations/AAI9215703/ |access-date=March 4, 2021}}</ref> is a [[Chinese-American]] mathematician primarily working on [[number theory]] and a professor of mathematics at the [[University of California, Santa Barbara]] since 2015.<ref>{{Cite web |title=Yitang (Tom) Zhang {{!}} Department of Mathematics – UC Santa Barbara |url=https://www.math.ucsb.edu/people/yitang-tom-zhang |access-date=October 19, 2022 |website=math.ucsb.edu}}</ref>


Previously working at the [[University of New Hampshire]] as a lecturer, Zhang submitted a paper to the ''[[Annals of Mathematics]]'' in 2013 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often. This work led to a 2013 [[Ostrowski Prize]], a 2014 [[Cole Prize]], a 2014 [[Rolf Schock Prizes|Rolf Schock Prize]], and a 2014 [[MacArthur award]]. Zhang became a professor of mathematics at the University of California, Santa Barbara in fall 2015.<ref>[https://www.macfound.org/fellows/927/ Yitang Zhang, Mathematician], MacArthur Fellows Program, MacArthur Foundation, September 17, 2014</ref><ref name="bounded" /><ref name="New Yorker" /><ref>{{cite web|url=http://www.math.ucsb.edu/people/yitang-tom-zhang|title=Yitang (Tom) Zhang {{!}} Department of Mathematics - UC Santa Barbara|website=www.math.ucsb.edu|language=en|access-date=2018-02-15}}</ref>
Previously working at the [[University of New Hampshire]] as a lecturer, Zhang submitted a paper to the ''[[Annals of Mathematics]]'' in 2013 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often. This work led to a 2013 [[Ostrowski Prize]], a 2014 [[Cole Prize]], a 2014 [[Rolf Schock Prizes|Rolf Schock Prize]], and a 2014 [[MacArthur Fellows Program|MacArthur Fellowship]]. Zhang became a professor of mathematics at the University of California, Santa Barbara in fall 2015.<ref>[https://www.macfound.org/fellows/927/ Yitang Zhang, Mathematician], MacArthur Fellows Program, MacArthur Foundation, September 17, 2014</ref><ref name="bounded" /><ref name="New Yorker" /><ref>{{cite web|url=http://www.math.ucsb.edu/people/yitang-tom-zhang|title=Yitang (Tom) Zhang {{!}} Department of Mathematics – UC Santa Barbara|website=math.ucsb.edu|language=en|access-date=February 15, 2018}}</ref>


== Early life and education ==
== Early life and education ==
Zhang was born in [[Pinghu]], [[Zhejiang]], China, and lived there until he was 13 years old. At around the age of nine, he found a proof of the [[Pythagorean theorem]].<ref name=lin>{{cite news |url=https://www.quantamagazine.org/20150402-prime-proof-zhang-interview/ |title=After Prime Proof, an Unlikely Star Rises |author=Thomas Lin |work=Quanta Magazine |date=April 2, 2015}}</ref> He first learned about [[Fermat's Last Theorem]] and the [[Goldbach conjecture]] when he was 10.<ref name=lin/> During the [[Cultural Revolution]], he and his mother were sent to the countryside to work in the fields. He worked as a laborer for 10 years and was unable to attend high school.<ref name=lin/> After the Cultural Revolution ended, Zhang entered [[Peking University]] in 1978 as an undergraduate student and received a bachelor of science in mathematics in 1982. He became a graduate student of Professor Pan Chengbiao, a number theorist at Peking University, and obtained a master of science in mathematics in 1984.<ref name=sinica />
Zhang was born in Shanghai, China, with his [[ancestral home]] in [[Pinghu]], Zhejiang. He lived in Shanghai with his grandmother until he went to [[Peking University]]. At around the age of nine, he found a proof of the [[Pythagorean theorem]].<ref name=lin>{{cite news |url=https://www.quantamagazine.org/yitang-zhang-and-the-mystery-of-numbers-20150402/ |title=After Prime Proof, an Unlikely Star Rises |author=Thomas Lin |work=Quanta Magazine |date=April 2, 2015}}</ref> He first learned about [[Fermat's Last Theorem]] and the [[Goldbach conjecture]] when he was 10.<ref name=lin/> During the [[Cultural Revolution]], he and his mother were sent to the countryside to work in the fields. He worked as a laborer for 10 years and was unable to attend high school.<ref name=lin/> After the Cultural Revolution ended, Zhang entered [[Peking University]] in 1978 as an undergraduate student and received a Bachelor of Science in mathematics in 1982. He became a graduate student of Professor Pan Chengbiao, a number theorist at Peking University, and obtained a Master of Science in mathematics in 1984.<ref name=sinica>{{cite web |url=https://academicians.sinica.edu.tw/02.php?func=22.1&_op=?ID:M150&_session=UEp5yw3YPluQUZ98&_lang=en |title=Mathematics and Physical Sciences Yitang Zhang |date=2014 |website=sinica.edu.tw }}</ref>


After receiving his master's degree in mathematics, with recommendations from Professor [[Ding Shisun]], the President of Peking University, and Professor Deng Donggao, Chair of the university's Math Department,<ref name=ttm-recall>{{cite web|last=Moh|first=Tzuong-Tsieng|title=Zhang, Yitang's life at Purdue (Jan. 1985-Dec, 1991)|url=http://www.math.purdue.edu/~ttm/ZhangYt.pdf|access-date=May 24, 2013}}</ref> Zhang was granted a full scholarship at [[Purdue University]]. Zhang arrived at Purdue in January 1985, studied there for six and a half years, and obtained his PhD in mathematics in December 1991.
After receiving his master's degree in mathematics, with recommendations from Professor [[Ding Shisun]], the President of Peking University, and Professor Deng Donggao, chair of the university's Math Department,<ref name=ttm-recall>{{cite web|last=Moh|first=Tzuong-Tsieng|title=Zhang, Yitang's life at Purdue (Jan. 1985-Dec, 1991)|url=http://www.math.purdue.edu/~ttm/ZhangYt.pdf|access-date=May 24, 2013}}</ref> Zhang was granted a full scholarship at [[Purdue University]]. Zhang arrived at Purdue in January 1985, studied there for six and a half years, and obtained his PhD in mathematics in December 1991.


== Career ==
== Career ==
Zhang's PhD work was on the [[Jacobian conjecture]]. After graduation, Zhang had trouble finding an academic position. In a 2013 interview with ''Nautilus'' magazine, Zhang said he did not get a job after graduation. "During that period it was difficult to find a job in academics. That was a job market problem. Also, my advisor [Tzuong-Tsieng Moh] did not write me letters of recommendation."<ref>{{cite web|url=http://nautil.us/issue/5/fame/the-twin-prime-hero|title=The Twin Prime Hero|work=Nautilus}}</ref> Zhang made this claim again in [[George Csicsery]]'s documentary film "Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture"<ref>[https://www.imdb.com/title/tt4363984/?ref_=nv_sr_srsg_0 Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture] on IMdB</ref> while discussing his difficulties at Purdue and in the years that followed.<ref name=lin/> Moh claimed that Zhang never came back to him requesting recommendation letters.<ref name=ttm-recall/> In a detailed profile published in ''[[The New Yorker]]'' magazine in February 2015, [[Alec Wilkinson]] wrote Zhang "parted unhappily" with Moh, and that Zhang "left Purdue without Moh's support, and, having published no papers, was unable to find an academic job".<ref name="New Yorker"/> In 2018, responding to reports of his treatment of Zhang, Moh posted an update on his website. Moh wrote that Zhang "failed miserably" in proving Jacobian conjecture, "never published any paper on algebraic geometry" after leaving Purdue, and "wasted 7 years of his [Zhang's] own life and my [Moh's] time".<ref>{{cite web|url=https://www.math.purdue.edu/~ttm/ZhangYt.pdf |title=Bio |publisher=www.math.purdue.edu |date=2013 |accessdate=2021-08-09}}</ref>
Zhang's PhD work was on the [[Jacobian conjecture]]. After graduation, Zhang had trouble finding an academic position. In a 2013 interview with ''Nautilus'' magazine, Zhang said he did not get a job after graduation. "During that period it was difficult to find a job in academics. That was a job market problem. Also, my advisor [Tzuong-Tsieng Moh] did not write me letters of recommendation."<ref>{{cite web|url=http://nautil.us/issue/5/fame/the-twin-prime-hero|title=The Twin Prime Hero|work=Nautilus}}</ref> Zhang made this claim again in [[George Csicsery]]'s documentary film "Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture"<ref>[https://www.imdb.com/title/tt4363984/?ref_=nv_sr_srsg_0 Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture] on IMdB</ref> while discussing his difficulties at Purdue and in the years that followed.<ref name=lin/> Moh claimed that Zhang never came back to him requesting recommendation letters.<ref name=ttm-recall/> In a detailed profile published in ''[[The New Yorker]]'' magazine in February 2015, [[Alec Wilkinson]] wrote Zhang "parted unhappily" with Moh, and that Zhang "left Purdue without Moh's support, and, having published no papers, was unable to find an academic job".<ref name="New Yorker"/> In 2018, responding to reports of his treatment of Zhang, Moh posted an update on his website. Moh wrote that Zhang "failed miserably" in proving the Jacobian conjecture, "never published any paper on algebraic geometry" after leaving Purdue, and "wasted seven years of his own life and my time".<ref>{{cite web|url=https://www.math.purdue.edu/~ttm/ZhangYt.pdf |title=Bio |publisher=math.purdue.edu |date=2013 |accessdate=August 9, 2021}}</ref>


After some years, Zhang managed to find a position as a lecturer at the [[University of New Hampshire]], where he was hired by [[Kenneth Appel]] in 1999. Prior to getting back to academia, he worked for several years as an accountant and a delivery worker for a New York City restaurant. He also worked in a motel in Kentucky and in a [[Subway (restaurant)|Subway]] sandwich shop.<ref name=quanta /> A profile published in the [[Quanta Magazine]] reports that Zhang used to live in his car during the initial job-hunting days.<ref name=lin/> He served as lecturer at UNH from 1999<ref>{{cite news |url=http://www.unionleader.com/article/20131215/NEWS04/131219488/0/SANTAFUND |work=New Hampshire Union Leader |date=December 14, 2013 |first=Gretyl |last=Macalaster |title=Math world stunned by UNH lecturer's find}}</ref> until around January 2014, when UNH appointed him to a full professorship as a result of his breakthrough on prime numbers.<ref name=prizebooklet/> Zhang stayed for a semester at [[The Institute For Advanced Study]] in Princeton, NJ in 2014, and he joined the [[University of California, Santa Barbara]] in fall 2015.<ref>{{Cite web|url=https://dailynexus.com/2015-09-17/celebrity-mathematician-joins-ucsb-faculty/|title=Celebrity Mathematician Joins UCSB Faculty &#124; The Daily Nexus|date=September 17, 2015}}</ref>
After some years, Zhang managed to find a position as a lecturer at the [[University of New Hampshire]], where he was hired by [[Kenneth Appel]] in 1999. Prior to getting back to academia, he worked for several years as an accountant and a delivery worker for a New York City restaurant. He also worked in a motel in [[Kentucky]] and in a [[Subway (restaurant)|Subway]] sandwich shop.<ref name=quanta /> A profile published in the [[Quanta Magazine]] reports that Zhang used to live in his car during the initial job-hunting days.<ref name=lin/> He served as lecturer at UNH from 1999<ref>{{cite news |url=http://www.unionleader.com/article/20131215/NEWS04/131219488/0/SANTAFUND |work=New Hampshire Union Leader |date=December 14, 2013 |first=Gretyl |last=Macalaster |title=Math world stunned by UNH lecturer's find}}</ref> until around January 2014, when UNH appointed him to a full professorship as a result of his breakthrough on prime numbers.<ref name=prizebooklet/> Zhang stayed for a semester at the [[Institute for Advanced Study]] in [[Princeton University|Princeton]], NJ, in 2014, and he joined the [[University of California, Santa Barbara]] in fall 2015.<ref>{{Cite web|url=https://dailynexus.com/2015-09-17/celebrity-mathematician-joins-ucsb-faculty/|title=Celebrity Mathematician Joins UCSB Faculty &#124; The Daily Nexus|date=September 17, 2015}}</ref>


== Research ==
== Research ==
{{See also|Prime gap}}
{{See also|Prime gap}}


On April 17, 2013, Zhang announced a proof that there are infinitely many pairs of [[prime number]]s that differ by less than 70 million. This result implies the existence of an infinitely repeatable [[Prime k-tuple|prime 2-tuple]],<ref name=quanta/> thus establishing a theorem akin to the [[twin prime conjecture]]. Zhang's paper was accepted by ''Annals of Mathematics'' in early May 2013,<ref name=bounded>{{cite journal | title = Bounded gaps between primes | first = Yitang | last = Zhang | journal = Annals of Mathematics | volume = 179 | year = 2014 | pages = 1121–1174 | doi=10.4007/annals.2014.179.3.7 | issue=3 | mr=3171761 | zbl=1290.11128}} {{subscription required}}</ref> his first publication since his last paper in 2001.<ref>{{cite web| url=http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.html | title= The Beauty of Bounded Gaps | author= Jordan Ellenberg | date=22 May 2013 | publisher=Slate | access-date=23 January 2017}}</ref> The proof was refereed by leading experts in [[analytic number theory]].<ref name="New Yorker">{{cite magazine | url = http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty | title = The Pursuit of Beauty | first = Alec | last = Wilkinson | magazine = [[The New Yorker]] | issue = February 2, 2015}}</ref> Zhang's result set off a flurry of activity in the field, such as the [[Polymath project#Polymath8|Polymath8 project]].
On April 17, 2013, Zhang announced a proof that there are infinitely many pairs of [[prime number]]s that differ by less than 70 million. This result implies the existence of an infinitely repeatable [[Prime k-tuple|prime 2-tuple]],<ref name=quanta/> thus establishing a theorem akin to the [[twin prime conjecture]]. Zhang's paper was accepted by ''[[Annals of Mathematics]]'' in early May 2013,<ref name=bounded>{{cite journal | title = Bounded gaps between primes | first = Yitang | last = Zhang | journal = Annals of Mathematics | volume = 179 | year = 2014 | pages = 1121–1174 | doi=10.4007/annals.2014.179.3.7 | issue=3 | mr=3171761 | zbl=1290.11128| doi-access = free }} {{subscription required}}</ref> his first publication since his last paper in 2001.<ref>{{cite web| url=http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.html | title= The Beauty of Bounded Gaps | author= Jordan Ellenberg | date=May 22, 2013 | publisher=Slate | access-date=January 23, 2017}}</ref> The proof was refereed by leading experts in [[analytic number theory]].<ref name="New Yorker">{{cite magazine | url = http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty | title = The Pursuit of Beauty | first = Alec | last = Wilkinson | magazine = [[The New Yorker]] | issue = February 2, 2015}}</ref> Researchers built off of Zhang's result like in [[Polymath project#Polymath8|Polymath8 project]].


If ''P''(''N'') stands for the proposition that there is an infinitude of pairs of prime numbers (not necessarily consecutive primes) that differ by exactly ''N'', then Zhang's result is equivalent to the statement that there exists at least one even integer ''k'' < 70,000,000 such that ''P''(''k'') is true. The classical form of the twin prime conjecture is equivalent to ''P''(2); and in fact it has been conjectured that ''P''(''k'') holds for ''all'' even integers ''k''.<ref name=nature>{{cite news|last=McKee|first=Maggie|title=First proof that infinitely many prime numbers come in pairs|url=http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989|access-date=May 21, 2013|newspaper=[[Nature (journal)|Nature]]|date=May 14, 2013}}</ref><ref name=nytimes>{{cite news|last=Chang|first=Kenneth|title=Solving a Riddle of Primes|url=https://www.nytimes.com/2013/05/21/science/solving-a-riddle-of-primes.html|access-date=May 21, 2013|newspaper=[[The New York Times]]|date=May 20, 2013}}</ref> While these stronger conjectures remain unproven, a result due to [[James Maynard (mathematician)|James Maynard]] in November 2013, employing a different technique, showed that ''P''(''k'') holds for some ''k'' ≤ 600.<ref name="Polymath8">{{cite web|url=https://www.simonsfoundation.org/quanta/20131119-together-and-alone-closing-the-prime-gap/ |title=Together and Alone, Closing the Prime Gap | access-date=2013-11-20 | date=2013-11-20 | last=Klarreich | first=Erica}}</ref> Subsequently, in April 2014, the [[Polymath project|Polymath project 8]] lowered the bound to ''k'' ≤ 246.<ref name="polymath">{{cite web|url=http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes|title=Bounded gaps between primes|publisher=Polymath}}</ref> With current methods ''k'' ≤ 6 is the best attainable, and in fact ''k'' ≤ 12 and ''k'' ≤ 6 follow using current methods if the [[Elliott–Halberstam conjecture]] and its generalization, respectively, hold.<ref name="New Yorker"/><ref name="polymath"/>
If ''P''(''N'') stands for the proposition that there is an infinitude of pairs of prime numbers (not necessarily consecutive primes) that differ by exactly ''N'', then Zhang's result is equivalent to the statement that there exists at least one even integer ''k'' < 70,000,000 such that ''P''(''k'') is true. The classical form of the twin prime conjecture is equivalent to ''P''(2); and in fact it has been conjectured that ''P''(''k'') holds for ''all'' even integers ''k''.<ref name=nature>{{cite news|last=McKee|first=Maggie|title=First proof that infinitely many prime numbers come in pairs|url=http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989|access-date=May 21, 2013|newspaper=[[Nature (journal)|Nature]]|date=May 14, 2013}}</ref><ref name=nytimes>{{cite news|last=Chang|first=Kenneth|title=Solving a Riddle of Primes|url=https://www.nytimes.com/2013/05/21/science/solving-a-riddle-of-primes.html|access-date=May 21, 2013|newspaper=[[The New York Times]]|date=May 20, 2013}}</ref> While these stronger conjectures remain unproven, a result due to [[James Maynard (mathematician)|James Maynard]] in November 2013, employing a different technique, showed that ''P''(''k'') holds for some ''k'' ≤ 600.<ref name="Polymath8">{{cite web|url=https://www.simonsfoundation.org/quanta/20131119-together-and-alone-closing-the-prime-gap/ |title=Together and Alone, Closing the Prime Gap | access-date=November 20, 2013 | date=November 20, 2013 | last=Klarreich | first=Erica}}</ref> Subsequently, in April 2014, the [[Polymath project|Polymath project 8]] lowered the bound to ''k'' ≤ 246.<ref name="polymath">{{cite web|url=http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes|title=Bounded gaps between primes|publisher=Polymath}}</ref> If the [[Elliott–Halberstam conjecture]] and its generalization, respectively, hold, then ''k'' ≤ 12 and ''k'' ≤ 6 follow using current methods.<ref name="New Yorker"/><ref name="polymath"/>


== Honors and awards ==
== Honors and awards ==
Zhang was awarded the 2013 Morningside Special Achievement Award in Mathematics,<ref>{{cite web|url=http://iccm.tims.ntu.edu.tw/#@MorningsideAwards | title=ICCM 2013: Morningside Awards}}</ref> the 2013 [[Ostrowski Prize]],<ref>{{cite web|url=http://www.ostrowski.ch/index_e.php?ifile=home | title=The 2013 Ostrowski Prize}}</ref> the 2014 [[Cole Prize|Frank Nelson Cole Prize]] in Number Theory,<ref name=prizebooklet>{{cite web|url=http://www.ams.org/profession/prizes-awards/prizebooklet-2014.pdf|title=January 2014 AMS-MAA Prize booklet|page=7}}</ref><ref>{{cite web|url=http://www.ams.org/news?news_id=2082 | title=Yitang Zhang Receives 2014 AMS Cole Prize in Number Theory}}</ref> and the 2014 [[Rolf Schock Prize]]<ref>{{cite web|url=http://www.kva.se/en/Prizes/Rolf-Shock-prizes | title=The 2014 Rolf Schock Prize}}</ref> in Mathematics.
Zhang was awarded the 2013 [[Morningside Medal|Morningside Special Achievement Award in Mathematics]],<ref>{{cite web|url=http://iccm.tims.ntu.edu.tw/#@MorningsideAwards | title=ICCM 2013: Morningside Awards}}</ref> the 2013 [[Ostrowski Prize]],<ref>{{cite web|url=http://www.ostrowski.ch/index_e.php?ifile=home | title=The 2013 Ostrowski Prize}}</ref> the 2014 [[Cole Prize|Frank Nelson Cole Prize]] in Number Theory,<ref name=prizebooklet>{{cite web|url=http://www.ams.org/profession/prizes-awards/prizebooklet-2014.pdf|title=January 2014 AMS-MAA Prize booklet|page=7}}</ref><ref>{{cite web|url=http://www.ams.org/news?news_id=2082 | title=Yitang Zhang Receives 2014 AMS Cole Prize in Number Theory}}</ref> and the 2014 [[Rolf Schock Prize]]<ref>{{cite web|url=http://www.kva.se/en/Prizes/Rolf-Shock-prizes | title=The 2014 Rolf Schock Prize}}</ref> in Mathematics.


He is a recipient of the 2014 [[MacArthur Fellows Program|MacArthur award]],<ref>{{cite news|last1=Lee|first1=Felicia R.|title=MacArthur Awards Go to 21 Diverse Fellows|url=https://www.nytimes.com/2014/09/17/arts/macarthur-awards-go-to-21-diverse-fellows.html|work=The New York Times|date=September 17, 2014}}</ref> and was elected as an [[Academia Sinica]] Fellow during the same year.<ref name=sinica /> He was an [[invited speaker at the International Congress of Mathematicians|invited speaker]] at the 2014 International Congress of Mathematicians.
He is a recipient of the 2014 [[MacArthur Fellows Program|MacArthur award]],<ref>{{cite news|last1=Lee|first1=Felicia R.|title=MacArthur Awards Go to 21 Diverse Fellows|url=https://www.nytimes.com/2014/09/17/arts/macarthur-awards-go-to-21-diverse-fellows.html|work=The New York Times|date=September 17, 2014}}</ref> and was elected as an [[Academia Sinica]] Fellow during the same year.<ref name=sinica /> He was an [[invited speaker at the International Congress of Mathematicians|invited speaker]] at the 2014 International Congress of Mathematicians.


== Political views ==
== Political views ==
In 1989 Zhang joined a group interested in [[Chinese democracy movement|Chinese democracy]] ({{lang|zh|中国民联}}). In a 2013 interview, he affirmed that his political views on the subject had not changed since.<ref name="New Yorker"/><ref>{{cite web|title=张益唐问答录|url=http://beijingspring.com/bj2/2010/240/201378202613.htm|access-date=Jun 30, 2015|date=Jul 1, 2013|language=zh}}</ref>
In 1989 Zhang joined a group interested in [[Democracy movements of China|Chinese democracy]] ({{lang|zh|中国民联}}). In a 2013 interview, he affirmed that his political views on the subject had not changed since.<ref name="New Yorker"/><ref>{{cite web|title=张益唐问答录|url=http://beijingspring.com/bj2/2010/240/201378202613.htm|access-date=June 30, 2015|date=July 1, 2013|language=zh}}</ref>

== Publications ==
* {{cite arXiv |eprint=0705.4306 |last1=Zhang |first1=Yitang |title=On the Landau-Siegel Zeros Conjecture |year=2007 |class=math.NT }}
* {{cite journal |doi=10.4007/annals.2014.179.3.7 |title=Bounded gaps between primes |year=2014 |last1=Zhang |first1=Yitang |journal=Annals of Mathematics |volume=179 |issue=3 |pages=1121–1174 |doi-access=free }}
* {{cite arXiv |eprint=2211.02515 |last1=Zhang |first1=Yitang |title=Discrete mean estimates and the Landau-Siegel zero |year=2022 |class=math.NT }}


== References ==
== References ==
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== External links ==
== External links ==
*{{aut|Alec Wilkinson}}, [http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty The Pursuit of Beauty, Yitang Zhang solves a pure-math mystery], ''[[The New Yorker]]'', Profiles, February 2, 2015 issue
*{{aut|Alec Wilkinson}}, [http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty The Pursuit of Beauty, Yitang Zhang solves a pure-math mystery], ''[[The New Yorker]]'', Profiles, February 2, 2015, issue
*[http://discovermagazine.com/bonus/prime-solver ''Discover Magazine'' article by Steve Nadis, "Prime Solver"]
*[http://discovermagazine.com/bonus/prime-solver ''Discover Magazine'' article by Steve Nadis, "Prime Solver"]
*[https://www.youtube.com/watch?v=vkMXdShDdtY ''Gaps between Primes – Numberphile''] - [[University of Nottingham]] video (shorter version)
*[https://www.youtube.com/watch?v=vkMXdShDdtY ''Gaps between Primes – Numberphile''] – [[University of Nottingham]] video (shorter version)
*[https://www.youtube.com/watch?v=D4_sNKoO-RA ''Gaps between Primes (extra footage) – Numberphile''] (longer version)
*[https://www.youtube.com/watch?v=D4_sNKoO-RA ''Gaps between Primes (extra footage) – Numberphile''] (longer version)


Latest revision as of 15:04, 14 May 2024

In this Chinese name, the family name is Zhang.
Yitang Zhang
Zhang in 2014
Born (1955-02-05) February 5, 1955 (age 69)
Shanghai, China
CitizenshipUnited States
Alma materPeking University (BS, MA)
Purdue University (PhD)
Known forEstablishing the existence of an infinitely repeatable prime 2-tuple[2]
AwardsOstrowski Prize (2013)
Cole Prize (2014)
Rolf Schock Prize (2014)
MacArthur Fellowship (2014)
Scientific career
FieldsNumber theory
InstitutionsUniversity of New Hampshire
University of California, Santa Barbara
ThesisThe Jacobian conjecture and the degree of field extension (1992)
Doctoral advisorTzuong-Tsieng Moh (莫宗堅)[1]

Yitang Zhang (Chinese: 张益唐; born February 5, 1955)[3] is a Chinese-American mathematician primarily working on number theory and a professor of mathematics at the University of California, Santa Barbara since 2015.[4]

Previously working at the University of New Hampshire as a lecturer, Zhang submitted a paper to the Annals of Mathematics in 2013 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often. This work led to a 2013 Ostrowski Prize, a 2014 Cole Prize, a 2014 Rolf Schock Prize, and a 2014 MacArthur Fellowship. Zhang became a professor of mathematics at the University of California, Santa Barbara in fall 2015.[5][6][7][8]

Early life and education

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Zhang was born in Shanghai, China, with his ancestral home in Pinghu, Zhejiang. He lived in Shanghai with his grandmother until he went to Peking University. At around the age of nine, he found a proof of the Pythagorean theorem.[9] He first learned about Fermat's Last Theorem and the Goldbach conjecture when he was 10.[9] During the Cultural Revolution, he and his mother were sent to the countryside to work in the fields. He worked as a laborer for 10 years and was unable to attend high school.[9] After the Cultural Revolution ended, Zhang entered Peking University in 1978 as an undergraduate student and received a Bachelor of Science in mathematics in 1982. He became a graduate student of Professor Pan Chengbiao, a number theorist at Peking University, and obtained a Master of Science in mathematics in 1984.[10]

After receiving his master's degree in mathematics, with recommendations from Professor Ding Shisun, the President of Peking University, and Professor Deng Donggao, chair of the university's Math Department,[11] Zhang was granted a full scholarship at Purdue University. Zhang arrived at Purdue in January 1985, studied there for six and a half years, and obtained his PhD in mathematics in December 1991.

Career

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Zhang's PhD work was on the Jacobian conjecture. After graduation, Zhang had trouble finding an academic position. In a 2013 interview with Nautilus magazine, Zhang said he did not get a job after graduation. "During that period it was difficult to find a job in academics. That was a job market problem. Also, my advisor [Tzuong-Tsieng Moh] did not write me letters of recommendation."[12] Zhang made this claim again in George Csicsery's documentary film "Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture"[13] while discussing his difficulties at Purdue and in the years that followed.[9] Moh claimed that Zhang never came back to him requesting recommendation letters.[11] In a detailed profile published in The New Yorker magazine in February 2015, Alec Wilkinson wrote Zhang "parted unhappily" with Moh, and that Zhang "left Purdue without Moh's support, and, having published no papers, was unable to find an academic job".[7] In 2018, responding to reports of his treatment of Zhang, Moh posted an update on his website. Moh wrote that Zhang "failed miserably" in proving the Jacobian conjecture, "never published any paper on algebraic geometry" after leaving Purdue, and "wasted seven years of his own life and my time".[14]

After some years, Zhang managed to find a position as a lecturer at the University of New Hampshire, where he was hired by Kenneth Appel in 1999. Prior to getting back to academia, he worked for several years as an accountant and a delivery worker for a New York City restaurant. He also worked in a motel in Kentucky and in a Subway sandwich shop.[2] A profile published in the Quanta Magazine reports that Zhang used to live in his car during the initial job-hunting days.[9] He served as lecturer at UNH from 1999[15] until around January 2014, when UNH appointed him to a full professorship as a result of his breakthrough on prime numbers.[16] Zhang stayed for a semester at the Institute for Advanced Study in Princeton, NJ, in 2014, and he joined the University of California, Santa Barbara in fall 2015.[17]

Research

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See also: Prime gap

On April 17, 2013, Zhang announced a proof that there are infinitely many pairs of prime numbers that differ by less than 70 million. This result implies the existence of an infinitely repeatable prime 2-tuple,[2] thus establishing a theorem akin to the twin prime conjecture. Zhang's paper was accepted by Annals of Mathematics in early May 2013,[6] his first publication since his last paper in 2001.[18] The proof was refereed by leading experts in analytic number theory.[7] Researchers built off of Zhang's result like in Polymath8 project.

If P(N) stands for the proposition that there is an infinitude of pairs of prime numbers (not necessarily consecutive primes) that differ by exactly N, then Zhang's result is equivalent to the statement that there exists at least one even integer k < 70,000,000 such that P(k) is true. The classical form of the twin prime conjecture is equivalent to P(2); and in fact it has been conjectured that P(k) holds for all even integers k.[19][20] While these stronger conjectures remain unproven, a result due to James Maynard in November 2013, employing a different technique, showed that P(k) holds for some k ≤ 600.[21] Subsequently, in April 2014, the Polymath project 8 lowered the bound to k ≤ 246.[22] If the Elliott–Halberstam conjecture and its generalization, respectively, hold, then k ≤ 12 and k ≤ 6 follow using current methods.[7][22]

Honors and awards

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Zhang was awarded the 2013 Morningside Special Achievement Award in Mathematics,[23] the 2013 Ostrowski Prize,[24] the 2014 Frank Nelson Cole Prize in Number Theory,[16][25] and the 2014 Rolf Schock Prize[26] in Mathematics.

He is a recipient of the 2014 MacArthur award,[27] and was elected as an Academia Sinica Fellow during the same year.[10] He was an invited speaker at the 2014 International Congress of Mathematicians.

Political views

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In 1989 Zhang joined a group interested in Chinese democracy (中国民联). In a 2013 interview, he affirmed that his political views on the subject had not changed since.[7][28]

Publications

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  • Zhang, Yitang (2007). "On the Landau-Siegel Zeros Conjecture". arXiv:0705.4306 [math.NT].
  • Zhang, Yitang (2014). "Bounded gaps between primes". Annals of Mathematics. 179 (3): 1121–1174. doi:10.4007/annals.2014.179.3.7.
  • Zhang, Yitang (2022). "Discrete mean estimates and the Landau-Siegel zero". arXiv:2211.02515 [math.NT].

References

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  1. ^ Yitang Zhang at the Mathematics Genealogy Project
  2. ^ a b c Klarreich, Erica (May 19, 2013). "Unheralded Mathematician Bridges the Prime Gap". Quanta Magazine. Retrieved May 19, 2013.
  3. ^ Zhang, Yitang (1991). The Jacobian conjecture and the degree of field extension. Purdue University. pp. 1–24. Retrieved March 4, 2021.
  4. ^ "Yitang (Tom) Zhang | Department of Mathematics – UC Santa Barbara". math.ucsb.edu. Retrieved October 19, 2022.
  5. ^ Yitang Zhang, Mathematician, MacArthur Fellows Program, MacArthur Foundation, September 17, 2014
  6. ^ a b Zhang, Yitang (2014). "Bounded gaps between primes". Annals of Mathematics. 179 (3): 1121–1174. doi:10.4007/annals.2014.179.3.7. MR 3171761. Zbl 1290.11128. (subscription required)
  7. ^ a b c d e Wilkinson, Alec. "The Pursuit of Beauty". The New Yorker. No. February 2, 2015.
  8. ^ "Yitang (Tom) Zhang | Department of Mathematics – UC Santa Barbara". math.ucsb.edu. Retrieved February 15, 2018.
  9. ^ a b c d e Thomas Lin (April 2, 2015). "After Prime Proof, an Unlikely Star Rises". Quanta Magazine.
  10. ^ a b "Mathematics and Physical Sciences Yitang Zhang". sinica.edu.tw. 2014.
  11. ^ a b Moh, Tzuong-Tsieng. "Zhang, Yitang's life at Purdue (Jan. 1985-Dec, 1991)" (PDF). Retrieved May 24, 2013.
  12. ^ "The Twin Prime Hero". Nautilus.
  13. ^ Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture on IMdB
  14. ^ "Bio" (PDF). math.purdue.edu. 2013. Retrieved August 9, 2021.
  15. ^ Macalaster, Gretyl (December 14, 2013). "Math world stunned by UNH lecturer's find". New Hampshire Union Leader.
  16. ^ a b "January 2014 AMS-MAA Prize booklet" (PDF). p. 7.
  17. ^ "Celebrity Mathematician Joins UCSB Faculty | The Daily Nexus". September 17, 2015.
  18. ^ Jordan Ellenberg (May 22, 2013). "The Beauty of Bounded Gaps". Slate. Retrieved January 23, 2017.
  19. ^ McKee, Maggie (May 14, 2013). "First proof that infinitely many prime numbers come in pairs". Nature. Retrieved May 21, 2013.
  20. ^ Chang, Kenneth (May 20, 2013). "Solving a Riddle of Primes". The New York Times. Retrieved May 21, 2013.
  21. ^ Klarreich, Erica (November 20, 2013). "Together and Alone, Closing the Prime Gap". Retrieved November 20, 2013.
  22. ^ a b "Bounded gaps between primes". Polymath.
  23. ^ "ICCM 2013: Morningside Awards".
  24. ^ "The 2013 Ostrowski Prize".
  25. ^ "Yitang Zhang Receives 2014 AMS Cole Prize in Number Theory".
  26. ^ "The 2014 Rolf Schock Prize".
  27. ^ Lee, Felicia R. (September 17, 2014). "MacArthur Awards Go to 21 Diverse Fellows". The New York Times.
  28. ^ "张益唐问答录" (in Chinese). July 1, 2013. Retrieved June 30, 2015.
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