Yitang Zhang

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] and shared the 2014 Frank Nelson Cole Prize in Number Theory ^[6][7] for his work on bounded gaps between primes.

Research

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.^[8] The proof was refereed by leading experts in analytic number theory.^[9]

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

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,^[9] 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 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."^[9] 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^[13] until around January 2014, when UNH appointed him to a full professorship.^[7]

References

External links

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

• Gaps between Primes – Numberphile, the shorter version.
• Gaps between Primes (extra footage) – Numberphile, the longer version.