Yitang Zhang | |
|---|---|
 Zhang in 2014 | |
| Born | (1955-02-05)February 5, 1955 (age 70) Shanghai, China |
| Citizenship | United States |
| Alma mater | Peking University (BS,MA) Purdue University (PhD) |
| Known for | Establishing the existence of an infinitely repeatableprime 2-tuple[2] |
| Awards | Ostrowski Prize (2013) Cole Prize (2014) Rolf Schock Prize (2014) MacArthur Fellowship (2014) |
| Scientific career | |
| Fields | Number theory |
| Institutions | University of New Hampshire University of California, Santa Barbara Sun Yat-sen University |
| Thesis | The Jacobian conjecture and the degree of field extension (1992) |
| Doctoral advisor | Tzuong-Tsieng Moh (莫宗堅)[1] |
YitangZhang (Chinese:张益唐; born February 5, 1955)[3] is aChinese-American mathematician primarily working onnumber theory and a professor of mathematics at theUniversity of California, Santa Barbara since 2015.[4] In 2025, he was appointed a professor atSun Yat-sen University.[5]
Previously working at theUniversity of New Hampshire as a lecturer, Zhang submitted a paper to theAnnals 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 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.[6][7][8][9]
Zhang was born in Shanghai, China, with hisancestral home inPinghu, Zhejiang. 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.[10] He first learned aboutFermat's Last Theorem andGoldbach's conjecture when he was 10.[10] 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.[10] After the Cultural Revolution ended, Zhang enteredPeking 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.[11]
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,[12] 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.
Zhang's PhD work was on theJacobian conjecture. After graduation, Zhang had trouble finding an academic position. In a 2013 interview withNautilus 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."[13] Zhang made this claim again inGeorge Csicsery's documentary film "Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture"[14] while discussing his difficulties at Purdue and in the years that followed.[10] Moh claimed that Zhang never came back to him requesting recommendation letters.[12] In a detailed profile published inThe 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".[8] 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".[15]
After some years, Zhang managed to find a position as a lecturer at theUniversity of New Hampshire, where he was hired byKenneth 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 inKentucky and in aSubway sandwich shop.[2] A profile published inQuanta Magazine reports that Zhang used to live in his car during the initial job-hunting days.[10] He served as lecturer at UNH from 1999[16] until around January 2014, when UNH appointed him to a full professorship as a result of his breakthrough on prime numbers.[17] Zhang stayed for a semester at theInstitute for Advanced Study inPrinceton, NJ, in 2014, and he joined theUniversity of California, Santa Barbara in fall 2015.[18] He took a full-time position atSun Yat-sen University inGuangzhou, China on June 27, 2025.[19]
On April 17, 2013, Zhang announced a proof that there are infinitely many pairs ofprime numbers that 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 Mathematics in early May 2013,[7] his first publication since his last paper in 2001.[20] The proof was refereed by leading experts inanalytic number theory.[8] Researchers built off of Zhang's result, for example in thePolymath 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 forall even integersk.[21][22] While these stronger conjectures remain unproven, a result due toJames Maynard in November 2013, employing a different technique, showed thatP(k) holds for somek ≤ 600.[23] Subsequently, in April 2014, thePolymath project 8 lowered the bound tok ≤ 246.[24] If theElliott–Halberstam conjecture and its generalization, respectively, hold, thenk ≤ 12 andk ≤ 6 follow using current methods.[8][24]
Zhang was awarded the 2013Morningside Special Achievement Award in Mathematics,[25] the 2013Ostrowski Prize,[26] the 2014Frank Nelson Cole Prize in Number Theory,[17][27] and the 2014Rolf Schock Prize[28] in Mathematics.
He is a recipient of the 2014MacArthur award,[29] and was elected as anAcademia Sinica Fellow during the same year.[11] He was aninvited speaker at the 2014 International Congress of Mathematicians.
In 1989 Zhang joined a group interested inChinese democracy (中国民联). In a 2013 interview, he affirmed that his political views on the subject had not changed since.[8][30] Zhang cited the "political climate" of the United States as a reason for his return to China.[31]
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