Yitang Zhang

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Yitang Zhang
Born 1955 (age 58–59)
Residence United States
Nationality United States
Fields Mathematics
Institutions University of New Hampshire
Alma mater Purdue University
Peking University
Thesis The Jacobian Conjecture And The Degree Of Field Extension (1992)
Doctoral advisor Tzuong-Tsieng Moh[1]
Known for Work with twin primes[2]
Notable awards 2013 Morningside Special Achievement Award in Mathematics
2013 Ostrowski Prize
2014 Frank Nelson Cole Prize in Number Theory
2014 Rolf Schock Prize in Mathematics

Yitang "Tom" Zhang (Romanized form: Yitang Zhang, Chinese: 张益唐, Zhāng Yìtáng)[3] is a Chinese-American mathematician working in the area of number theory. While working as a lecturer unknown to the research community, Zhang stunned the mathematical world by submitting an article establishing the first finite bound on gaps between prime numbers.

This discovery, previously believed to be unattainable by current methods, received wide attention and lifted Zhang from obscurity to public fame overnight. Zhang has been awarded the 2013 Morningside Special Achievement Award in Mathematics,[4] the 2013 Ostrowski Prize,[5] the 2014 Frank Nelson Cole Prize in Number Theory,[6][7] and the 2014 Rolf Schock Prize[8] in Mathematics.

Research[edit]

On April 17, 2013, Zhang announced a proof that there are infinitely many pairs of prime numbers which 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.[9] The proof was refereed by leading experts in analytic number theory.[citation needed]

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). The classical form of the twin prime conjecture is equivalent to P(2); and in fact it has been conjectured that P(k) for all even integers k.[10][11] 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.[12]

Education[edit]

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 1985. Several articles (in Chinese) by his former classmates have all confirmed that Zhang was a top student among his peers. 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,[13] 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[edit]

Zhang's Ph.D. work was on the Jacobian conjecture. After graduation, Zhang had a hard time finding an academic position. In a recent article, Zhang's thesis advisor, Professor Tzuong-Tsieng Moh, recalled that "Sometimes I regretted not fixing him a job" and "He never came back to me requesting recommendation letters."[13] He managed to find a position as a lecturer after many years, at the University of New Hampshire, where he was hired by Kenneth Appel back 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] He served as a lecturer at UNH from 1999[14] until around January 2014, when UNH appointed him to a full professorship.[7]

References[edit]

  1. ^ Yitang Zhang at the Mathematics Genealogy Project
  2. ^ a b Klarreich, Erica (May 19, 2013). "Unheralded Mathematician Bridges the Prime Gap". Quanta Magazine. Retrieved May 19, 2013. 
  3. ^ "UNH Mathematician’s Proof Is Breakthrough Toward Centuries-Old Problem". University of New Hampshire. May 1, 2013. Retrieved May 20, 2013. 
  4. ^ "ICCM 2013: Morningside Awards". 
  5. ^ "The 2013 Ostrowski Prize". 
  6. ^ "Yitang Zhang Receives 2014 AMS Cole Prize in Number Theory". 
  7. ^ a b "January 2014 AMS-MAA Prize booklet". p. 7. 
  8. ^ "The 2014 Rolf Schock Prize". 
  9. ^ Zhang, Yitang. "Bounded gaps between primes". Annals of Mathematics (Princeton University and the Institute for Advanced Study). Retrieved March 11, 2014.  (subscription required)
  10. ^ McKee, Maggie (May 14, 2013). "First proof that infinitely many prime numbers come in pairs". Nature. Retrieved May 21, 2013. 
  11. ^ Chang, Kenneth (May 20, 2013). "Solving a Riddle of Primes". The New York Times. Retrieved May 21, 2013. 
  12. ^ Klarreich, Erica (2013-11-20). "Together and Alone, Closing the Prime Gap". Retrieved 2013-11-20. 
  13. ^ a b Moh, Tzuong-Tsieng. "Zhang, Yitang’s life at Purdue (Jan. 1985-Dec, 1991)". Retrieved May 24, 2013. 
  14. ^ Macalaster, Gretyl (December 14. 2013). "Math world stunned by UNH lecturer's find". New Hampshire Union Leader. 

External links[edit]

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