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Yitang Zhang

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In thisChinese name,thefamily nameisZhang.
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 repeatableprime 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 ( mạc tông kiên )[1]

YitangZhang(Chinese:Trương ích đường;born February 5, 1955)[3]is aChinese-Americanmathematician primarily working onnumber theoryand a professor of mathematics at theUniversity of California, Santa Barbarasince 2015.[4]

Previously working at theUniversity of New Hampshireas a lecturer, Zhang submitted a paper to theAnnals of Mathematicsin 2013 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often. This work led to a 2013Ostrowski Prize,a 2014Cole Prize,a 2014Rolf Schock Prize,and a 2014MacArthur 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[edit]

Zhang was born in Shanghai, China, with hisancestral homeinPinghu,Zhe gian g. He lived in Shanghai with his grandmother until he went toPeking University.At around the age of nine, he found a proof of thePythagorean theorem.[9]He first learned aboutFermat's Last Theoremand theGoldbach conjecturewhen he was 10.[9]During theCultural 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 enteredPeking Universityin 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 ProfessorDing Shisun,the President of Peking University, and Professor Deng Donggao, chair of the university's Math Department,[11]Zhang was granted a full scholarship atPurdue 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[edit]

Zhang's PhD work was on theJacobian conjecture.After graduation, Zhang had trouble finding an academic position. In a 2013 interview withNautilusmagazine, 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 inGeorge 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 inThe New Yorkermagazine in February 2015,Alec Wilkinsonwrote 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 theUniversity of New Hampshire,where he was hired byKenneth Appelin 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 inKentuckyand in aSubwaysandwich shop.[2]A profile published in theQuanta Magazinereports 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 theInstitute for Advanced StudyinPrinceton,NJ, in 2014, and he joined theUniversity of California, Santa Barbarain fall 2015.[17]

Research[edit]

See also:Prime gap

On April 17, 2013, Zhang announced a proof that there are infinitely many pairs ofprime numbersthat differ by less than 70 million. This result implies the existence of an infinitely repeatableprime 2-tuple,[2]thus establishing a theorem akin to thetwin prime conjecture.Zhang's paper was accepted byAnnals of Mathematicsin early May 2013,[6]his first publication since his last paper in 2001.[18]The proof was refereed by leading experts inanalytic number theory.[7]Researchers built off of Zhang's result like inPolymath8 project.

IfP(N) stands for the proposition that there is an infinitude of pairs of prime numbers (not necessarily consecutive primes) that differ by exactlyN,then Zhang's result is equivalent to the statement that there exists at least one even integerk< 70,000,000 such thatP(k) is true. The classical form of the twin prime conjecture is equivalent toP(2); and in fact it has been conjectured thatP(k) holds foralleven integersk.[19][20]While these stronger conjectures remain unproven, a result due toJames Maynardin November 2013, employing a different technique, showed thatP(k) holds for somek≤ 600.[21]Subsequently, in April 2014, thePolymath project 8lowered the bound tok≤ 246.[22]If theElliott–Halberstam conjectureand its generalization, respectively, hold, thenk≤ 12 andk≤ 6 follow using current methods.[7][22]

Honors and awards[edit]

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

He is a recipient of the 2014MacArthur award,[27]and was elected as anAcademia SinicaFellow during the same year.[10]He was aninvited speakerat the 2014 International Congress of Mathematicians.

Political views[edit]

In 1989 Zhang joined a group interested inChinese democracy(Trung Quốc dân liên). In a 2013 interview, he affirmed that his political views on the subject had not changed since.[7][28]

Publications[edit]

  • 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[edit]

  1. ^Yitang Zhangat theMathematics Genealogy Project
  2. ^abcKlarreich, Erica (May 19, 2013)."Unheralded Mathematician Bridges the Prime Gap".Quanta Magazine.RetrievedMay 19,2013.
  3. ^Zhang, Yitang (1991).The Jacobian conjecture and the degree of field extension.Purdue University.pp. 1–24.RetrievedMarch 4,2021.
  4. ^"Yitang (Tom) Zhang | Department of Mathematics – UC Santa Barbara".math.ucsb.edu.RetrievedOctober 19,2022.
  5. ^Yitang Zhang, Mathematician,MacArthur Fellows Program, MacArthur Foundation, September 17, 2014
  6. ^abZhang, Yitang (2014)."Bounded gaps between primes".Annals of Mathematics.179(3): 1121–1174.doi:10.4007/annals.2014.179.3.7.MR3171761.Zbl1290.11128.(subscription required)
  7. ^abcdeWilkinson, 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.RetrievedFebruary 15,2018.
  9. ^abcdeThomas Lin (April 2, 2015)."After Prime Proof, an Unlikely Star Rises".Quanta Magazine.
  10. ^ab"Mathematics and Physical Sciences Yitang Zhang".sinica.edu.tw.2014.
  11. ^abMoh, Tzuong-Tsieng."Zhang, Yitang's life at Purdue (Jan. 1985-Dec, 1991)"(PDF).RetrievedMay 24,2013.
  12. ^"The Twin Prime Hero".Nautilus.
  13. ^Counting from Infinity: Yitang Zhang and the Twin Prime Conjectureon IMdB
  14. ^"Bio"(PDF).math.purdue.edu. 2013.RetrievedAugust 9,2021.
  15. ^Macalaster, Gretyl (December 14, 2013)."Math world stunned by UNH lecturer's find".New Hampshire Union Leader.
  16. ^ab"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.RetrievedJanuary 23,2017.
  19. ^McKee, Maggie (May 14, 2013)."First proof that infinitely many prime numbers come in pairs".Nature.RetrievedMay 21,2013.
  20. ^Chang, Kenneth (May 20, 2013)."Solving a Riddle of Primes".The New York Times.RetrievedMay 21,2013.
  21. ^Klarreich, Erica (November 20, 2013)."Together and Alone, Closing the Prime Gap".RetrievedNovember 20,2013.
  22. ^ab"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. ^"Trương ích đường hỏi đáp lục"(in Chinese). July 1, 2013.RetrievedJune 30,2015.

External links[edit]

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