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Yitang Zhang

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Yitang Zhang
Born1955 (age 68–69)
Shanghai, China
NationalityUnited States
Alma materPurdue University (PhD 1991)
Peking University (B.A. 1982; M.A. 1984) [1]
Known forWork with twin primes[3]
AwardsOstrowski Prize (2013)
Cole Prize (2014)
Rolf Schock Prize (2014)
MacArthur Fellowship (2014)
Academia Sinica Fellow (2014) [1]
Scientific career
FieldsMathematics
InstitutionsUniversity of New Hampshire (Lecturer 1999-2013; Professor 2014-present)
Thesis The Jacobian Conjecture And The Degree Of Field Extension  (1992)
Doctoral advisorTzuong-Tsieng Moh[2]

Yitang "Tom" Zhang (Romanized form: Yitang Zhang, Chinese: 张益唐, Zhāng Yìtáng)[4] is a Chinese-born American mathematician working in the area of number theory. While working as a lecturer, Zhang submitted an article establishing the first finite bound on gaps between prime numbers.[5]

Education

Zhang entered Peking University in 1978 as an undergraduate student and received his B.Sc. degree in mathematics in 1982. He became a graduate student of Professor Pan Chengbiao, a number theorist at Peking University, and obtained his M.Sc. degree in mathematics in 1984.[1] After receiving his master's degree in mathematics, with recommendations from Professor Ding Shisun, President of Peking University and Professor Deng Donggao, Chair of the Math Department of Peking University,[6] Zhang was granted a full scholarship by Purdue University, where he arrived in January 1985 and studied for seven years. He obtained his Ph.D. in mathematics from Purdue in December 1991.

Career

Zhang's Ph.D. work was on the Jacobian conjecture. After graduation, Zhang had a hard time finding an academic position. In an interview with Nautilus magazine, Zhang said he didn't get a job after graduation because "during that period it was difficult to find a job in academics. "[7] In an article that appeared on his advisor's website, professor Tzong-Tsieng Moh, after Zhang's twin-prime breakthrough, Moh recalled that "(Zhang) never came back to me requesting recommendation letters," and "Sometimes I regretted not fixing him a job."[6] Zhang managed to find a position as a lecturer after some years 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.[3] He served as a lecturer at UNH from 1999[8] until around January 2014, when UNH appointed him to a full professorship.[9]

Research

On April 17, 2013, Zhang announced a proof that there are infinitely many pairs of prime numbers that differ by 70 million or less. This proof is the first to establish the existence of a finite bound for prime gaps, resolving a weak form of the twin prime conjecture. Zhang's paper was accepted by Annals of Mathematics in early May 2013.[5] The proof was refereed by leading experts in analytic number theory.[10]

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.[11][12] While these stronger conjectures remain unproven, a recent result due to James Maynard, employing a different technique, has shown that P(k) for some k ≤ 600.[13] Subsequently, the Polymath_project lowered the bound to P(246).[14] P(6) is thought to be the best attainable with current methods, and in fact P(12) and P(6) follow using current methods if also the Elliott–Halberstam conjecture and its generalisation holds.[15][14]

Honors and awards

Zhang was awarded the 2013 Morningside Special Achievement Award in Mathematics,[16] the 2013 Ostrowski Prize,[17] the 2014 Frank Nelson Cole Prize in Number Theory,[18][9] and the 2014 Rolf Schock Prize[19] in Mathematics. He is a 2014 recipient of the MacArthur "Genius" Award,[20] and elected to Academia Sinica Fellow (2014).[1]

References

  1. ^ a b c d "Mathematics and Physical Sciences Yitang Zhang". sinica.edu.tw. 2014.
  2. ^ Yitang Zhang at the Mathematics Genealogy Project
  3. ^ a b Klarreich, Erica (May 19, 2013). "Unheralded Mathematician Bridges the Prime Gap". Quanta Magazine. Retrieved May 19, 2013.
  4. ^ "UNH Mathematician's Proof Is Breakthrough Toward Centuries-Old Problem". University of New Hampshire. May 1, 2013. Retrieved May 20, 2013.
  5. ^ a b Zhang, Yitang (2014). "Bounded gaps between primes". Annals of Mathematics. 179. Princeton University and the Institute for Advanced Study: 1121–1174. doi:10.4007/annals.2014.179.3.7. Retrieved March 11, 2014. (subscription required)
  6. ^ a b Moh, Tzuong-Tsieng. "Zhang, Yitang's life at Purdue (Jan. 1985-Dec, 1991)" (PDF). Retrieved May 24, 2013.
  7. ^ "The Twin Prime Hero". Nautilus.
  8. ^ Macalaster, Gretyl (December 14, 2013). "Math world stunned by UNH lecturer's find". New Hampshire Union Leader.
  9. ^ a b "January 2014 AMS-MAA Prize booklet" (PDF). p. 7.
  10. ^ Wilkinson, Alec. "The Pursuit of Beauty". The New Yorker. No. February 2, 2015. p. p. 26. {{cite magazine}}: |page= has extra text (help)
  11. ^ McKee, Maggie (May 14, 2013). "First proof that infinitely many prime numbers come in pairs". Nature. Retrieved May 21, 2013.
  12. ^ Chang, Kenneth (May 20, 2013). "Solving a Riddle of Primes". The New York Times. Retrieved May 21, 2013.
  13. ^ Klarreich, Erica (2013-11-20). "Together and Alone, Closing the Prime Gap". Retrieved 2013-11-20.
  14. ^ a b "Bounded gaps between primes". Polymath. Retrieved 2013-07-21.
  15. ^ Wilkinson, Alec (2 February 2015). "The Pursuit of Beauty". The New Yorker: 22-28.
  16. ^ "ICCM 2013: Morningside Awards".
  17. ^ "The 2013 Ostrowski Prize".
  18. ^ "Yitang Zhang Receives 2014 AMS Cole Prize in Number Theory".
  19. ^ "The 2014 Rolf Schock Prize".
  20. ^ Lee, Felicia R. (September 17, 2014). "MacArthur Awards Go to 21 Diverse Fellows". The New York Times.

Zhang Yitang's proof has been the subject of two explanatory videos by physicists at the University of Nottingham.

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