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## 张益唐## 华人数学家大会## 孪生素数## 晨兴数学金奖 |

# A summary of interview with Zhang Yitang by Lizhen Ji and Ping-Zen Ong

in Taipei, in the evening of July 13, 2013.

A detailed (Chinese) version transcribing the 2 hour interview will appear later.

This is the first face-to-face interview with Zhang by mathematicians.

1. Right after the big typhoon, we (Ji and Ong) interviewed him at the math dept of Tai Da.

2. About His name. Tang is his mother's last name, it also means the whole Chinese people as in Tang people. Yi also means "Number 1". This name was picked by his grand father, who was a school teacher and wrote beautiful words.

3. at the age of 10, he read the popular book series "1000 why" (10个 万 为什么 ). volume 8 deals with math. He read "Goldbach conjecture" and "Riemann hypothesis" in this volume, but "Twin prime conjecture" was not mentioned there.

4. He did not get normal education (middle or high school education), and at the age of 15, he went to the countryside with his parents to Hubei. He read a book by Xia Daoxing called "\pi and e", which inspired him. He might still have this book. He was intrigued why \pi and e are irrational numbers. He could easily understand about e, but it was more difficult about \pi. Then later he read a book by Hua "Introduction to Number theory" and understood better. His pure interest motivated him to study mathematics on his own.

5. He took the entrance exam to university twice. He did not do so well at the first time, but did very well the second time. He was very happy that he did well in Chinese. When he entered college, he decided to study mathematics. His interest has always been interested in number theory. His reason is that in number theory, problems are simple to state, but it is often difficult to solve. He also emphasized that he was not encouraged by the success of Chen Jinrun, especially the report about Chen around 1978. In 1973 at the age of 18, before he learned calculus, he read the paper of Chen Jinrun without fully understanding it.

6. When asked if he had any mathematics hero, he said that when he was young, Gauss was his hero, but later he had none and felt that he was as good as great mathematicians (he can do as well as them). But he admired two people Andrew Wiles and Grigori Perelman.

7. In his work on the twin prime numbers, people
all read that he had a breakthrough on July 3, 2012. The big idea
he got on July 3 last year was that he realized that the problem
could be reduced to several cases. He felt that he could handle
them, especially one case was simple to be proved. But he was not
completely right. The simplest case turned out to the most
complicated.

8. He learnt basic techniques in analytic number theory from his teacher Pan at Bei Da. This has been crucial to his work on the twin prime problem, From his Ph. D. adviser Mu, he also learned to do explicit computation in algebraic geometry.

9. Zhang emphasized that it is important to learn new things, a broad vision, a high goal, and combine various things. During the 8 year period from getting Ph.D. degree until he worked at University of New Hampshire, he tried to read and learnt many new things. Though he was busy with work (he worked for his friend, who had several business), he can always find time to do mathematics. Though he did not have access to a math library, he made copies of things he needed.

10. He is now working on another big problem, the Siegel zero problem and is making substantial progress. A Siegel zero is a type of potential counterexample to the generalized Riemann hypothesis. It was named after Carl Ludwig Siegel because of his work in 1930s. Its existence or non-existence will have a huge impact on many problems in number theory.

11. Teaching is important for Zhang and he still remembers vividly the effective and inspiring teaching of two excellent teachers in college.He has been thinking about writing a book on analytic number theory.It will not be in the usual format "Definition, Theorem, Lemma, Proposition ..." Instead he will explain how problems arise, why we should consider them, the essential points ..., i.e., emphasizing the more global picture side. For example, he does not agree with some people who plan to read his paper on twin primes line by line to fully understand it (or all the details).