A post appeared recently on popular online Chinese Q&A platform Zhihu, stating that “mathematician Yitang [Tom] Zhang has published a new paper, ‘Discrete Mean Estimates and the Landau-Siegel Zero.’ What are the achievements and significance of this research?” This question has aroused extensive discussion, and Zhang himself posted a long article in response on November 10.
In the article, Zhang first commented on some deep mathematical questions raised by other respondents for the paper and research. Then, the mathematician shared his own research experience, life and current state of mind and feelings. The following is an excerpt from the article.
Many people are very interested in my experience. They think that I have spent so many years studying very difficult math problems. Have I ever thought about giving up and how have I persisted? I also want to take this opportunity to talk with you.
As for the Landau-Siegel zeros conjecture, I didn’t think about giving up, because my entire thinking has been intermittent over the years. In 2007, I published a paper on the Landau-Siegel zeros conjecture. In fact, there was possibility of continuing the research at that time, but then I encountered a situation, that is, the problem of twin prime numbers became popular, so I was on it from 2010 to 2013. As a result, I proved that there are infinite pairs of prime numbers with gaps of less than 70 million. Later on, I thought I still had to continue research on the Landau-Siegel zeros conjecture, so I went back to this problem. I usually think about several problems at the same time, paying attention to this for a while and that for a while. Actually I started thinking about the Landau-Siegel zeros conjecture at the end of last century. I like to think about several problems together. If one problem is initially solved, and the thinking on other problems will go on, all of which are relatively big problems.
A few days ago, after my paper was published, I gave an online lecture at Peking University. Chengbiao Pan, a professor at Peking University and also my advisor when I studied for a master’s degree, commented: “After listening to Yitang’s idea today, [I think] it is very clear that this is an important new idea of screening method, which has great development potential and is difficult to realize.” I immediately replied: “Professor Pan’s affirmation is more valuable than the praise from 10,000 people.”
Today, I talked with a young man who paid attention to my thesis on Zhihu, and learned that he was a freshman at a university in London and studied mathematics. I think it is not easy for him, because he has been able to learn the courses I studied in graduate school in his freshman year, which shows that he has made rapid progress and paid a lot. He is indeed a very smart young man. I hope young people like him can use their imagination and don’t regard the things of their predecessors as supreme. Can I do this thing differently, or can I break through it? You young people have a great future by constantly asking questions and trying to find new ways.
As for my planning of the future, I won’t give away these math problems. I think I probably have to do mathematics all my life. I don’t know what to do without doing mathematics. People have asked questions about my retirement. I’ve said that if I leave math, I really won’t know how to live.
Usually, while at home, my wife thinks that I don’t talk much. After dinner, I always stay in my room, listen to music and enjoy myself by wearing headphones. She is afraid that my mental state will gradually deteriorate, and jokes that if I become like that when I’m old, she will suffer and have to push me in a wheelchair. So she prepares the materials of dishes every day and let me learn to make meals when I go back home, no matter how bad the dishes I make are. On weekends, sometimes I invite a few math research colleagues to my house to drink and chat, but they say I sometimes become distracted when chatting. My wife thus often condemns me for being impolite, saying that I will have no friends in the future.
My wife also thinks that I’m not very romantic. Once when we went to Vienna to listen to concerts, we went to the University of Vienna because I wanted to see the statue of Kurt Friedrich Gödel (Austrian-American logician and mathematician). After searching for a long time, I still couldn’t find it, until I met a professor who had just got off work and told us that there is no statue of Gödel there. But I am very grateful to her for bringing me to the concerts, because I like listening to symphonies. I like all the famous classical music masters, first of all Beethoven, especially his Sixth Symphony.
I also like Brahms, other piano music composed by musicians like Tchaikovsky and Chopin, especially the latter’s work, Polonaise in A Flat Major, Op. 53.
In fact, when I was young, I also liked campus songs of that time, and Su Xiaoming was my “idol” at that time. My roommate at Peking University said that I turned against others when people mentioned anyting bad about Su Xiaoming. When my wife and I went to Princeton University a while ago, we lived in the home of Wu Gang, an alumnus of Peking University. His home had karaoke, and we played Su Xiaoming’s songs there. I might have been out of tune because they all laughed when I was singing her songs.
I also like Chinese classical poetry very much, among which Chinese poet Du Fu’s poems are the most appreciated, such as the lines of “Hearing of the Recovery of the Regions North and South of the River by the Imperial Forces”, which reads:
Through the Sword Pass comes sudden news of recovered lands in the north, And, hearing it, I drench my clothes with tears. I gaze at my wife and children, all grief forgotten, And roll up my papers at random, wild with joy. The sun has not yet set, yet I feel I must drink and sing; Lovely spring shall be our companion as home we go; We shall sail through the Yangtze Gorges, Down to Xiangyang and the road to old Luoyang!
The last line shows Du Fu’s unrestrained mind. I’m never tired of reading, and the feelings contained in this poem are countless. Du Fu has so many poems, and there’s another one titled “Climbing a Terrace,” in which the first three lines are:
Wind blusters high in the sky and monkeys wail; Clear the islet with white sand where birds are wheeling; Everywhere the leaves fall rustling from the trees, While on for ever rolls the turbulent Yangtze. All around is autumnal gloom and I, long from home, A prey all my life to ill heath, climb the terrace alone;
I also love the last line here. The antithesis is so good and it is very natural. These lines have been passed down for more than a thousand years, so that future generations can taste it word by word.
A few years ago, a director came to me and said he wanted to make my story into a movie, just like “A Beautiful Mind,” a movie about John Nash, a brilliant but antisocial mathematician. I don’t want that. After all, the internet has said enough about me. I hope it’s best not to interfere with me. Nash was a great mathematician, and he made unique contributions in several fields such as mathematics. This film was made very well. Many young Chinese students I’ve met said they have seen it.”
Now, I also help my little granddaughter with her mathematics lessons. When she was in second grade at primary school, she especially liked math and signed up for a computer programming class. The class was full of high school students. She was the youngest. At that time, she couldn’t even multiply. Later, I helped her make up for it. Now she is nine years old, and she has been in the fourth grade. The school has chosen her to be in a “math genius” class. She is very talented and once said to me, “Grandpa, I want to fulfill your wish and win the Fields Medal for you.” Actually, I have no regrets about this award. I didn’t take these things too seriously.
Nine years ago, when I visited Princeton University for the first time, someone asked me which poem could summarize my mood at that time. I quoted lines from Du Fu’s series poem “Chant on Reminiscing Historical Relics,” which reads:
Poet Yu Xin lived a miserable and unspectacular life, The poetry of his sunset years had a great influence on the capital Jiangguan.
The same goes for today.