2022/11/08
Source of information: Science and Technology Daily
Text: Zhang Galen|
Editor: Yan Yuan | Editor in charge: Zhiyuan
Zhang Yitang had almost no opening remarks, and he went straight to the theme as soon as he opened his mouth. “Let’s introduce what Landau-Siegel Zero is.”
This is an open academic report for teachers, students and the public of Peking University. On the morning of November 8, Zhang Yitang, a Chinese-American mathematician and a professor at the University of California, Santa Barbara, described his research process online to prove the Landau-Siegel Zeros Conjecture.
There was a whiteboard standing beside Zhang Yitang, and there was another one at hand. He didn’t use PPT, whiteboards, markers and erasers were all his presentation tools. He wrote as he spoke, erasing when he was full.
On November 7, 2022, Yitang Zhang re-published his paper on the Landau-Siegel Zero Conjecture – “Discrete mean estimates and the Landau-Siegel Zero”, the paper Published on the preprint site arXiv.
In mid-October, Zhang Yitang revealed at the Peking University Greater New York alumni meeting that he essentially solved the Landau-Siegel zero-point (conjecture) problem. Since then, the result has attracted widespread attention.
In 2013, Zhang Yitang made a breakthrough for the solution of the century problem “twin prime conjecture”. Some people say that if he can make Landau Siegel zero, it is equivalent to a person being struck by lightning twice.
Zhang Yitang said at the beginning of the report that many people do not do number theory and do not understand what this problem is solving. Some people think that the Riemann hypothesis is proved wrong. “I don’t have this ability, I just partially solve the Riemann hypothesis within a certain range. It should be correct.”
If the generalized Riemann conjecture is believed, the Landau-Siegel zero should not exist. The Landau-Siegel null conjecture asserts that the Landau-Siegel null does not exist. Zhang Yitang said that his work has essentially proved the Landau-Siegel zero-point conjecture, but the work can continue to improve. Once the Landau-Siegel zero-point conjecture is proved, many new breakthroughs can be made, simplifying and strengthening many classical number theory results.
For most ordinary people, Zhang Yitang’s speech is not easy to understand. Although he used two whiteboards to introduce his ideas. “My paper still needs some revisions and additions, and some simplifications,” he said in response to questions.
I listened to his entire lecture. I almost forgot any advanced mathematics knowledge, and after listening to it, I was like a cloud. But a metaphor of Zhang Yitang is interesting. He said that in order to prove the zero-point conjecture, for so many years, he searched like a needle in a haystack, but the needle was not found. But in the process, he figured out the topography of the seabed, and finally found that he could achieve his goal without the needle.
Previously, Zhang Yitang made an online report to the teachers and students of Shandong University. After the report, the school held an academic salon with the theme of “Tradition and Innovation” focusing on Professor Zhang Yitang’s research process.
Zhang Yitang said at the salon that Peking University’s rigorous style of study had a deep influence on him, and all he could do was to inherit this tradition. “Sometimes it’s more important to ask yourself, what is the meaning of the knowledge you have learned? I mean the meaning is in mathematics, where can it be used or what role does it have. Sometimes ask this question more, Learning can only be done solidly.” He said that mathematics needs to be drilled deeper, but sometimes, when you don’t know how to move forward, it is best to stop for a while, go back to your starting point, and ask yourself what you want to do. It is the “not forgetting the original intention” that is often said now, which is very helpful to your entire research.
Zhang Yitang is regarded as a “legendary mathematician”. There are many introductions to him online. The first half of his life was difficult and unknown, and it was not until he was nearly 60 years old that he became famous. In fact, for Zhang Yitang, the Landau-Siegel zero-point conjecture is the “big problem” he has determined to study since his youth. On the contrary, the research on twin primes that gave him great fame was a “side escape” in a long insistence.
Now, his long-term focus on advancing the Landau-Siegel zero-point conjecture has finally made significant progress.
In the academic part, we can’t understand much, but there are some things in common.
As Tian Gang, an academician of the Chinese Academy of Sciences and director of the Beijing International Mathematical Research Center of Peking University, said at the beginning of the report, “the mathematical spirit of our Peking University lies in the pure love for mathematical truth, self-confidence and self-improvement, and the courage to challenge big problems. What’s more is that even in the face of adversity, he never gives up and perseveres in his efforts. Professor Zhang Yitang interprets the spirit of Peking University mathematicians by example, which is admirable. I hope that the younger generation here can be like Professor Zhang Yitang, on the road of academics and life. Stay pure and loving, always confident and brave.”
Original link: This is a live broadcast that I don’t understand and want to listen to