Text |Wang Zhaoyu
Those who won the Mathematics Olympiad in their early years may not be able to do a good job in mathematics. Ivan Fesenko, a professor at the Institute of Theoretical Sciences at Westlake University, told China Science News.
Ivan Fesenko thinks the current state of mathematics in China is very strange – in the Mathematical Olympiad, most of the winners are Chinese; But the breakthrough contributions of Chinese mathematicians seem to be inferior to those of France, the United States, Russia and other countries.
In November 2023, Ivan Fesenko, who joined Westlake University full-time, decided to do something about it. He found that many countries that have produced excellent mathematicians pay attention to the connection between universities and high schools, and hold activities such as winter and summer schools and "math clubs" for high school students, so that they can get in touch with mathematics researchers in advance and feel the charm of advanced mathematics. However, China lacks similar activities.
Ivan Fesenko proposed a similar event at Westlake University for outstanding high school students aged 16 to 18. Westlake University can support these high school students with the associated costs.
ivan fesenko**。
Whether the Olympiad champion has the potential to do a good job in mathematical research
Judging by his resume, Ivan Fesenko has a lot to say on this issue. Because he is both "a person who won the Olympiad in the early years" and "a person who can do a good job in mathematical research".
45 years ago, teenager Fesenko won the All-Russian High School Mathematics Olympiad. Later, he became a mathematician, received the Petersburg Mathematical Society Prize, and was a professor of mathematics at the University of Nottingham in the United Kingdom for 27 years.
His student Caucher Birkar, who was once a "farmer's son" who could not even speak English, won the Nobel Prize in mathematics, the Fields Medal, which changed his fate.
China Science News: Achieving excellent results in the Mathematics Olympiad is not necessarily related to the ability to study mathematics. Can you elaborate on this point?
ivan fesenko：
The Olympiad is like a competition between a group of people to see who can draw a proposition the fastest and best in a limited time; The study of mathematics is like an artist spending days, months, or even years on a painting to finally achieve an artistic breakthrough.
Olympiad math problems belong to elementary mathematics or lower level college mathematics, and the skills required for advanced mathematics are completely different from those required for Olympiad mathematics.
China Science News: Many Chinese parents train their children to learn Olympiad mathematics, what impact do you think this will have on the training of future mathematicians in China?
ivan fesenko：
It depends on the age. Middle school is a suitable stage for Olympiad math because at this age, students are not yet able to learn advanced mathematics, which is too early for them.
But for gifted high school students, the Olympiad is no longer so suitable. I talked to a couple of mathematically gifted Chinese high school students and found out that they didn't know advanced math when they were 17 years old, whereas I did, when I was 15. Because of the preparation for the college entrance examination, they have been studying advanced mathematics two or three years later than me.
I believe that China's outstanding high school students should be provided with opportunities to be exposed to advanced mathematics and university researchers, including doctoral students and postdoctoral fellows, at the age of 16 and 18.
China Science News: In your opinion, what are the main problems of mathematics education in China?
ivan fesenko：
China has a population of 1.4 billion, but I regret that there are no Fields Medal winners in Chinese mainland's education system. I think this is due to the lack of a "motivational connection" between college and high school.
High school, especially the last two years, is the best period for teenagers to deepen their studies and develop their talents. In Russia, children with a talent for mathematics pass entrance exams and enter specialized mathematics high schools, rather than ordinary high schools. They receive a more intensive education in mathematics at the age of sixteen or seventeen, including college mathematics and advanced mathematics, and are motivated. At the end of high school, they take a special test, and the mathematics part is much more difficult than the mathematics of the national examination, but some of the national examinations may be exempted.
In China, almost all high school students are required to dedicate the last two years of high school to the gaokao in preparation for the gaokao, and they do not have time to study advanced mathematics or do additional research.
In China, there are only two ways to avoid the college entrance examination: parents have money and send their children to university in developed countries; Or the student is part of an international mathematics competition team. But the proportion of the latter is too low.
Mathematical talent should be regarded as a national treasure, especially among young people. The current education system should be improved so that it helps talented young people, rich and poor, to develop their talents as much as possible.
China Science News: There are also "competition students" in China, who invest a lot of time in high school to study a certain subject, get in touch with the difficult knowledge of university, and can also get a corresponding advantage in the college entrance examination. How would you rate it?
ivan fesenko：
The number of such students is too small. There are about 10 million to 12 million high school graduates in China every year, but only 200 to 300 can be "competition students" and enter top universities without being trapped in the college entrance examination.
Establish "math circles" for high school students
Ivan Fesenko told China Science Daily that in Russia's big cities, there is an activity that is popular among high school students called "Math Circles". In the evenings, high school students gather with professors and mathematicians from local universities to discuss math problems freely and casually.
In order to help gifted teenagers discover their interests and develop their research aspirations at an early stage, Ivan Fesenko wants to establish a "math circle" in China for high school and first-year students to interact with older math researchers.
China Science News: Westlake University is not one of the strongest universities in mathematics in China, why did you choose it?
ivan fesenko：
I love working at the "New Mathematics Center" where there is a lot of potential. When I first started working at the University of Nottingham in the UK, the school was not very strong in pure mathematics, but our efforts have increased it a lot.
With the exception of the University of Hong Kong, Westlake University is more international than any Chinese university. It has one of the highest percentages of foreign specialists, especially mathematicians, and all classes are taught in English, so foreign professors can start teaching or doing research as soon as they arrive.
Another reason is that I prefer Hangzhou to many Chinese cities such as Beijing. As the capital of China during the Southern Song Dynasty, many of China's famous poets and artists lived in Hangzhou.
China Science News: What are your plans at Westlake University?
ivan fesenko：
My responsibility is to inspire more young mathematicians in China to grow up. I have the experience of working with 60 young researchers, some of whom are now full professors at universities in Japan, China, France, the United Kingdom, the United States, etc.
China Science News: What is the current progress of holding a mathematics summer school for high school students and freshmen?
ivan fesenko：
Westlake University generously provided start-up funding. The problem is that Chinese universities can't pay all of their summer and winter school expenses for high school students and freshmen due to regulations.
Perhaps in some agricultural region in western China, there are math-gifted teenagers whose families can't afford to pay for it and need a university to cover the costs. In Japan, Russia, and Germany, there are summer and winter schools for high school students, and the cost is borne by the university.
Given China's population, there may be 10 future mathematicians among the students who take the college entrance examination each year. We deserve to find them and help them grow.
Now there's a way to find a sponsor. We're meeting with some businesses in Hangzhou, and maybe they can help. It's a really small expense, not a big amount. Last month, someone at a large company told me that they might be able to help.
China Science News: You have a student who won the Fields Medal and he comes from a peasant family, can you tell us his story?
ivan fesenko：
When we first met, he was in his early 20s and didn't speak English yet, but it was clear that he was a very talented guy. As a professor at the University of Nottingham in the UK, I started doing research with him, helping him solve mathematical problems and supporting him psychologically.
Genius mathematicians need a lot of psychological support.
When unable to solve a problem, young mathematicians are likely to become depressed, doubt themselves, and think that their mathematical skills are simply not good. The teacher needs to provide psychological help and tell him that he can try again next month, or try a different approach. I would be happy to provide this assistance to students.
I would like to recommend a Korean drama "Melancholia" to everyone, which is recommended for all high school and undergraduate students who are interested in mathematics**. It's the best TV series I've ever seen, it shows how to work with high school students who are gifted with math, and it does a great job of showing the role of teachers.
China Science Daily: What other activities do you have at Westlake University in 2024?
ivan fesenko：
I will welcome my first Chinese PhD student in September and work with her. She is currently studying for a master's degree at Tsinghua University. I have another PhD applicant. In addition, a postdoctoral researcher from Australia will join my group.
I will also be hosting a range of international visitors. I think it's important to increase the number of visits from foreign mathematicians to China. Many mathematicians, such as those in Europe, have a wrong impression of China, they know nothing about modern China.
The society of the future is a mathematical society
Ivan Fesenko predicts that in the future, higher mathematics will become the most "popular" profession, because the society of the future must be a mathematical society.
In the mathematical society, all members of the society need to have stronger mathematical knowledge and thinking, think about problems like mathematicians in daily life, and apply mathematical knowledge. He said.
He talked about the strong attack of artificial intelligence, especially ChatGPT, and if China wants to lead the world in industry, it must need the strength of more mathematicians.
China Science News: You emphasize that mathematics is becoming more and more important in this era, can you talk about it in detail?
ivan fesenko：
CEOs of the world's leading companies and countries** know the importance of mathematics. We are experiencing a digital and artificial intelligence revolution that will fundamentally change many sectors of the economy and many professions will be replaced.
Many Chinese parents want their children to pursue a career as a financial analyst, doing some analysis for ** exchanges or investment banks. But these occupations are likely to be replaced by AI, and children will be out of work in 10 years. The question is, which professions are still very valuable and will not be replaced by AI?
Higher mathematics is one of the preferred careers because it is the foundation of all developments in computer science and artificial intelligence.
Mathematics has played an important role during the pandemic in recent years. Use mathematical models to determine when restrictions will be eased. But previous epidemiological models were of low quality.
In the UK, for example, modellers are completely wrong that 5 million people will die in the UK at the start of the pandemic. Later, together with statisticians and epidemiologists, we formed small groups to make better models for ** to use.
In the UK, easing restrictions a day earlier could save the national economy $2 billion. This is precisely the opportunity for mathematicians to make a huge contribution to the national economy.
China Science News: When discussing the relationship between mathematics and artificial intelligence, please talk about how mathematics can contribute to artificial intelligence?
ivan fesenko：
ChatGPT was discovered by engineers and computer scientists through trial and error without understanding how it really works. It's like a group of people assembling a nuclear bomb with different uranium and plutonium, but they don't understand the basic physical laws of the nuclear process, and then they are likely to make mistakes and happen.
At the moment ChatGPT works, but we don't know why it works and what its fuzzy development will bring. The only way to do this is to get mathematicians involved to discover the mathematical laws by which ChatGPT operates.
Without good semantics, ChatGPT can become very dangerous. Elon Musk and others have been interviewed on this topic. ChatGPT can only become manageable if mathematicians are truly involved, and it is possible for humans to truly dominate its development.
At present, there is still a long way to go in the development of artificial intelligence. The human brain has two hemispheres, the left hemisphere is responsible for logical thinking, and the right hemisphere is responsible for images and overall vision, as well as intuition. AI can't do what the right hemisphere of the brain does.
In the field of mathematics, artificial intelligence can only help with logical operations, but cannot solve esoteric mathematical problems. At the moment, mathematicians do not expect it to solve these problems. Breakthrough discoveries require a fresh perspective and a new understanding of the problem, which cannot be achieved by AI. So humanity is still stronger.
China Science News: You wrote an article about the danger of mathematicians becoming utilitarian. Can you tell us more about that?
ivan fesenko：
In the history of computer development, there is a very famous American company called Bell Corporation. There's a poster on the wall of their lab that says, "Do something beautiful or do something useful."
Those best mathematicians don't study math to make money or get a position at a certain university, but because they genuinely love math. Mathematics may be more important than their families and loved ones, and it is necessary for their survival.
But for various reasons, in the last 20 years, many people have entered the field of mathematics, and their attitude towards mathematics is that of salarymen, just to do something to earn a salary, and there is not much enthusiasm and inspiration for advanced mathematics. This affects the quality of mathematics. Although there are many ** published so far, most of them are of low quality.
We need more great mathematicians. Remember, it's either beautiful or useful, but not mediocre.