Yitang Zhang

Yitang "Tom" Zhang (Chinese: 张益唐; pinyin: Zhāng Yìtáng)^[4] is a Chinese-born American mathematician working in the area of number theory. While working for the University of New Hampshire as a lecturer, Zhang submitted an article to the Annals of Mathematics in 2013 which established the first finite bound on gaps between prime numbers. This work led to a 2014 MacArthur award^[5] and his appointment as a professor.^[6][7]

Education

Zhang was born in Shanghai and lived there until he was 13 years old. At around the age of nine, he found a proof of the Pythagorean theorem.^[8] He first learned about Fermat’s last theorem and the Goldbach conjecture when he was 10.^[8] During the Cultural 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.^[8] After the Cultural Revolution ended, 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, the President of Peking University, and Professor Deng Donggao, Chair of the university's Math Department,^[9] Zhang was granted a full scholarship at Purdue University. Zhang arrived at Purdue in January 1985, studied there for seven years, and obtained his Ph.D. in mathematics 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 2013 interview with Nautilus 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 did not write me letters of recommendation." The reason behind this is that Zhang's research pointed out the mistakes made by his advisor Tzuong-Tsieng Moh's previous work. Moh was very unhappy with this and refused to write the job recommendation letter for Zhang.^[10] Zhang made this claim again in George Csicsery’s documentary film Counting From Infinity while discussing his difficulties at Purdue and in the years that followed.^[8] Tzuong-Tsieng Moh, his Ph.D. advisor at Purdue, said that Zhang never came back to him requesting recommendation letters.^[9] In a detailed profile published in The 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".^[7] After some years, Zhang managed to find a position as a lecturer 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] A profile published in the Quanta Magazine reports that Zhang used to live in his car during the initial job-hunting days.^[8] He served as lecturer at UNH from 1999^[11] until around January 2014, when UNH appointed him to a full professorship as a result of his breakthrough on prime numbers.^[12] In Fall 2015, Zhang accepted an offer of full professorship at the University of California, Santa Barbara.^[13][14]

Research

On April 17, 2013, Zhang announced a proof that states there are infinitely many pairs of prime numbers that differ by 70 million or less. This result implies the existence of an infinitely repeatable prime 2-tuple,^[3] thus establishing a theorem akin to the twin prime conjecture. Zhang's paper was accepted by Annals of Mathematics in early May 2013,^[6] his first publication since his last paper in 2001.^[15] The proof was refereed by leading experts in analytic number theory.^[7] Zhang's result set off a flurry of activity in the field, such as the Polymath8 project.

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.^[16][17] While these stronger conjectures remain unproven, a result due to James Maynard in November 2013, employing a different technique, showed that P(k) holds for some k ≤ 600.^[18] Subsequently, in April 2014, the Polymath project 8 lowered the bound to k ≤ 246.^[19] With current methods k ≤ 6 is the best attainable, and in fact k ≤ 12 and k ≤ 6 follow using current methods if the Elliott–Halberstam conjecture and its generalisation, respectively, hold.^[7][19]

Honors and awards

Zhang was awarded the 2013 Morningside Special Achievement Award in Mathematics,^[20] the 2013 Ostrowski Prize,^[21] the 2014 Frank Nelson Cole Prize in Number Theory,^[12][22] and the 2014 Rolf Schock Prize^[23] in Mathematics.

He is a recipient of the 2014 MacArthur award,^[24] and was elected as an Academia Sinica Fellow during the same year.^[1] He was an invited speaker at the 2014 International Congress of Mathematicians.

Political views

In 1989 Zhang joined a group interested in Chinese democracy (中国民联). In a 2013 interview, he affirmed that his political views on the subject hadn't changed since.^[7][25]

References

External links

• Alec Wilkinson, The Pursuit of Beauty, Yitang Zhang solves a pure-math mystery, The New Yorker, Profiles, February 2, 2015 issue
• Discover Magazine article by Steve Nadis, "Prime Solver"
• Gaps between Primes – Numberphile - University of Nottingham video (shorter version)
• Gaps between Primes (extra footage) – Numberphile (longer version)