Mathematician Yitang Zhang’s Pursuit of the Landau-Siegel Zeros Conjecture

Yitang (Tom) Zhang, a Chinese-American mathematician, recently disclosed in an online salon organized by the Peking University Alumni Association that he has proven the longstanding Landau-Siegel zeros conjecture. This finding is related to the Riemann hypothesis, a formula for the distribution of prime numbers that has remained unsolved for more than a century. Behind an aura of many achievements is Zhang’s lifetime of focusing on mathematics like a hermit.

Before making his great achievements, his legendary status, which was built up throughout the past 67 years, was widely relished – a mathematical genius of Peking University, a down-and-out Subway employee, and an unknown university lecturer in his fifties who has now become a world-renowned mathematician in one fell swoop.

Zhang was born in Shanghai in 1955 and obtained a bachelor’s degree from the Mathematics Department at Peking University in 1982. From 1982 to 1985, he studied for a master’s degree under the famous mathematician and Professor Pan Chengbiao of Peking University. He then graduated from Purdue University in the US in 1992 with a doctorate.

Zhang went to Purdue University to study at his own expense. In 1984, Professor Tzuong-Tsieng Moh from Purdue University visited Peking University and wanted to invite several students to study abroad. Ding Shisun, the president of Peking University at that time, recommended Zhang, who was interested in number theory, one of the branches of pure mathematics. However, Ding believed that a group of practical talents should be trained to benefit China’s development, and he hoped Zhang could study algebraic geometry abroad.

Zhang agreed. When studying for a doctorate in his thirties, it took Zhang only two years to complete part of the results of his doctoral thesis, but it took him seven years to obtain his doctorate.

After graduating from Purdue University, Zhang found that it seemed unrealistic to return to China to teach, due to political factors. Invited by friends, he went to work in a Subway in Kentucky. But he was not pursuing a better material life. He just wanted to have a pure place to return to the research of number theory.

In 1999, on the recommendation of a friend at Peking University, Zhang came to the University of New Hampshire in the northeastern United States as a temporary lecturer. This was the first time he had approached academic work since graduation, although there were only four courses per semester, paid on a daily basis and with no research funds. At the age of 50, Zhang was officially hired as a formal lecturer by the school.

Twenty years later, in 2013, Zhang published “Bounded Gaps Between Primes in The Annals of Mathematics,” which proved that there are infinitely many pairs of prime numbers that differ by less than 70 million. This result implies the existence of an infinitely repeatable prime 2-tuple, thus establishing a theorem akin to the twin prime conjecture. Based on this, Zhang’s academic position in the history of mathematics was firmly established.

In 2016, Zhang was made a tenured professor of mathematics at the University of California, Santa Barbara. But he didn’t have many teaching tasks, and he just liked to stay at the school and think. He also had no research pressure, because he didn’t need to publish papers continuously to receive more funds.

In fact, after becoming famous, loneliness was Zhang’s normal state, but he still maintains strong concentration and acumen. He dedicated all his remaining time to the major problem he had been determined to work on since his youth – the Landau-Siegel zeros conjecture.

SEE ALSO: Mathematician Yitang Zhang Claims to Have Proven Riemann Hypothesis Problem

The Landau-Siegel zeros conjecture is a type of potential counterexample to the generalized Riemann hypothesis. Zhang said at an alumni association meeting that solving the problem “feels like a person was hit by lightning twice!” Solving the last bottleneck of Landau-Siegel zeros conjecture is due to a “broad vision,” he added.

In his academic career, Zhang has actually published only three papers. In addition to a paper about prime conjecture in 2013, there were two other articles published in the Duke Mathematical Journal and Acta Mathematica Sinica, both of which were related to the Riemann hypothesis.

When asked in an interview with Renwu what kind of person he would have liked to become if he didn’t have a talent for mathematics, Zhang said that perhaps he would have wished for a happier life.