Do you want to start with Olympiad or not? We asked the Olympic champion.

Cover News Reporter Bian Xue

"Olympiad is just an exam, which is the most difficult exam in middle school, but if compared with mathematics research, the magnitude is far from enough." In an interview, Yuan Xinyi defined what he used to be best. This sentence came from the mouth of an international mathematical Olympiad gold medalist, somewhat paradoxical. He got the ticket in his best competitive way, and then found that this ticket led to a completely different arena.

In 1981, Yuan Xinyi was born in an ordinary rural family in Macheng, Hubei. In the summer before the second day of junior high school, he bought a book "synchronous tutoring of junior high school mathematics competition" in the bookstore in the town, "just like those people in martial arts novels got a secret book at once." Since then, he sent Huanggang Middle School to the first place, entered the national team, and won the gold medal in the 41st International Mathematical Olympiad. In 2000, he entered the School of Mathematical Sciences at Peking University.

However, after entering mathematical research, Yuan Xinyi found that the advantages accumulated in competitions would not automatically be transformed into scientific research advantages. "The competition questions are given by the person who wrote the questions. The answers are known and must be made. There is a clear time limit and the knowledge used is predictable." Yuan Xinyi told reporters: "Research is completely the opposite. Find the problem yourself, and the result is uncontrollable. Even what you want to prove may be wrong, and the knowledge involved may be unknown." "A competition problem may be solved in a few hours. A research problem may take weeks, months or even years." Yuan Xinyi compared the difference between marathon and sprint, "100 meters sprint, you can feel the intensity of competition from the beginning to the end. But the competition of marathon has been watered down, and it is more about overcoming its own shortcomings."

When he entered the School of Mathematics of Peking University in 2000, Yuan Xinyi's class had more than 30 people, more than half of whom were from competitions. They are the group of people who were later called "the golden generation of mathematics in Peking University" by the media. But in it, what Yuan Xinyi felt was not the superiority of genius, but a huge confusion.

"Math is so difficult, can I pass it?" "Math, can I support my family?" This kind of confusion will not appear in the Orsay system. Olympiad has standard answers, rankings and gold medals. But mathematical research has no standard answer. Facing an open world, no one will tell you whether this road will work or not.

The transition is gradual and conscious. "I am a problem-solving mathematician. Because I was born in Olympiad Mathematics, I will naturally be used to solving problems and be better at solving problems." Yuan Xinyi said, "But later, I hope I can establish important theories."

This shift sounds abstract, and Yuan Xinyi illustrates it with a concrete example.

He told the cover news that when he paid more attention to solving problems in the past, if he found a new concept, he would ask himself: what is the use of defining this thing? If it is useless, it is a waste of time. But then Yuan Xinyi's idea changed. "If this thing is beautiful and naturally appears here, write it down first and develop it first, whether it is useful or not." Yuan Xinyi said.

Yuan Xinyi and his mentor Zhang Shouwu jointly establishedAdele's line cluster theoryThis is how it is done step by step. "At first, it was only a prototype. It was not even taken seriously by everyone, and the articles were not well published." Yuan Xinyi said, but around 2020, they re-examined this theory and discovered a new way of building it. "This new vision is much higher than the original and has become a very useful theory."

From solving problems to establishing theories, Yuan Xinyi believes that it is necessary to "activate his curiosity". "When the person doing the problem sees a problem, what he thinks about is how to solve it. But the person doing the theory will ask several more questions: Why does he do it like this? Why doesn't he do it like that? Why should he choose the parameters like this?"

In 2020, Yuan Xinyi resigned his tenure at the University of California, Berkeley, and returned to Peking University full-time. He is one of the first scholars to return to China full-time after being tenured in American universities.

After returning to China, based on Adele's line cluster theory, he constructed the arithmetic model line cluster on the curve module space, transformed the consistent Bogomolov conjecture into the large nature of the arithmetic model line cluster and successfully proved it. The 105-page paper was published in the top international mathematical journal, the Annual Journal of Mathematics.

"(After returning to China) the quality of learning has improved in the United States, but the reason is not all personal efforts." Yuan Xinyi told reporters, "It's a coincidence and an opportunity that I collaborated with Professor Xie Junyi (to write) a good article. In addition, there were many breakthroughs in the mathematical community on related issues in 2018 and 2019, and the work of three mathematicians, including Gao Ziyang, inspired me to notice something I hadn't discovered before."

As a former Olympic gold medalist, Yuan Xinyi is often asked the same question by parents: Does the child want to learn Olympiad? His answer is more cautious than many people think.

"Mathematical Olympiad is helpful to mathematical research, which is certain." Yuan Xinyi added: "If you do too much Olympic math training, you may go too far."

"Excessive Olympiad training has two negative consequences. The first is the wear and tear of interest. If you keep letting your child do it, he will lose his freshness in the end and may erase his interest." Yuan Xinyi told reporters that the second is the suppression of creativity. "If you have been working hard to solve the problem, people will habitually think about what routine to use to solve the problem. If you are too accustomed to the routine, you may only adapt to this way of thinking in the end, which is not conducive to doing mathematical research in the future."

In Yuan Xinyi's view, from the perspective of selecting scientific research talents, the biggest problem of Olympic Mathematics is that it turns mathematics into a kind of competition. Competition has a standard answer and a fixed path. True mathematical research is just the opposite: there is no outline, no known answers, and even no clear questions.

"For young people, we must first learn the traditional way of research." When talking about the mathematical research in the AI era, Yuan Xinyi suggested, "When students write their first paper, they hope to do it independently. They can use their AI to look up a little bit, but they can't rely too much on it. They should train their abilities first. Wait until they know how to do the research, then take the initiative to use the AI."

In Yuan Xinyi's opinion, don't rely too much on crutches before learning to walk on your own. "(Students) should choose the subject of scientific research with moderate difficulty. Too simple without challenge, too difficult and always fail. They should choose a height that they can reach after their own efforts." Yuan Xinyi said.

From Macheng Township to Huanggang Middle School, from the "Golden Generation" of Peking University to a tenured professor at Berkeley, and then back to the podium of Peking University, Yuan Xinyi has walked this road for more than 20 years. He has won the Olympic gold medal, the ICCM Prize in Mathematics, and now the Future Science Award. He said he was "not a genius". "Since I was a child, I have always had a strong interest in mathematics, and I have been focusing on mathematics persistently. Today's results are the result of continuous persistence and years of accumulation." Yuan Xinyi said.