Transcription
The world today is changing rapidly, with technology development driven by basic science. China is the second largest economy and puts a lot of effort into basic science research. In 2025, China's total R&D investment exceeded 3.92 trillion yuan, about 569 billion US dollars, reaching 2.8% of GDP. Basic research funding last year hit nearly 280 billion yuan, accounting for 7.08% of the total R&D spending. Moreover, young talents from China and abroad are devoting themselves to basic science, and their cause eventually will contribute to the development of humanity.
I talked to Shing-Tung Yau, who along with his colleagues is working hard to bid for the International Congress of Mathematicians, or ICM, in Hong Kong, China.
"Professor, so good to see you again."
"Yeah, me too."
"You see there's fierce competition in AI."
"Yes."
"For sure."
"Right."
"And related to it, basic science."
"Yes."
"Um, so, how does that work in today's world?"
"Well, AI is very powerful. They help us to learn many things. AI has a big memory because they were able to think of almost anything together, even think about it in some way. So, it helps us a great deal. But, you cannot depend on AI only because what AI could do is to get what we know before and digest it better. They cannot create. And mathematics and many forefront science, the development needs pioneer thinking, something that we do not expect before."
"So, you don't think AI is going to, you know, become a something of its own in a way, as advocated by some, you know, AI?"
"I don't believe that because, uh, what makes science to be advanced is something totally unexpected. Each time when we make a big jump forward, it's because something suddenly happened which you have no absolute no idea that would happen. Uh, and they are certainly would not think of this kind of things."
"But recently, some news suggests that artificial intelligence has helped a human being to solve some of the earlier very complicated mathematics problems."
"Yeah."
"And that human beings did not necessarily manage to achieve, but with the help of AI, things are done. What do you think about the role of AI likely to play in human beings eventually using it as a tool?"
"Okay. Uh, first of all, mathematics is somewhat different from many other subjects. Uh, over many years, 100 years, 200 years, 300 years, mathematicians have created many interesting questions. I would say billions of questions that have been there. Not every problem is interesting. Uh, at least to the, uh, to some group of people, it could be exciting, but not necessarily interesting for other people. What we consider to be important in mathematics in general should have really vast influence on other fields besides its own. And what AI..."
"Some examples."
"Well, I mean, the famous Riemann hypothesis has not been solved, but it's supposed to understand number theory in a very complete manner, and the math method of Riemann zeta function is useful for statistical mechanics, for many different subjects. It's very fundamental. And there are many subjects like this, uh, we we can create. And they change the way that mathematics was developed. But what AI can solve so far is far away from this level."
"Well, what is the level now?"
"Well, what they can solve is some problems. Uh, frankly, I don't care. And some people do care, but some people, I don't know."
"What do you mean by you don't care?"
"Well, it's interesting, nice, cute problem. But it's not, it doesn't affect the full, the flowing chart of the whole mathematics development. It does have some interest or some special development, but not for the whole world."
"Well, what if you use Chat GDP, how much problem of how much mathematic problem it would help to solve?"
"Well, we don't know. It depends on people working on it, but there are problems that we think Chat GDP could help. But how much help we can get, we are not 100% sure. We are working. We have a group here working on some very interesting problem, I think. A problem that many people care about. And, and if a problem takes a year to to finish, and we we we want to help from Chat GDP, for example."
"Mhm."
"But if not, we..."
"Like what kind of problems?"
"Uh, suppose we want to understand symmetries. You know, how things symmetry. This is called group theory nowadays. There's a many, 20 years ago, math didn't create term called group theory, which means symmetry. How objects symmetric to each other and all that. Now, infinite symmetry like rotation, but they are finite symmetry. For example, you look at a mirror, you reflect from each other, there's a symmetry, finite symmetry. And you look at some poly- there's some reflection. It's called finite symmetry. The group, finite symmetry, the group of finite symmetry, that's a group theory, has been passed over for mathematicians for many, many years. And about 30 or 40 years ago, mathematicians declared now we can classify them all. We understand how they were built completely. Well, this subject has been exciting and even important because the symmetry appears in many important subjects. In number theory, in geometry, in physics, and all that. To understand the fundamental symmetry is always an important tool in many different subjects. I'm probably in all science. Okay? So, the consequences therefore would be tremendous important. But the classification, when it was announced to be complete, it takes 3,000 pages to prove and to accomplish, and it depends probably over 100 papers. And each paper does some part of it. So, you have a huge group of people working on a difficult problem. But, you know, mathematics cannot make mistake in any step. Any people know that you will write a 3,000 pages paper, you're bound to make some mistakes here and there. And now the question is, are we finished in classifying this things? Because it's composed of 100 different papers from different authors. If one single paper has a mistake, the other step could be completely wrong. And yes, our task is to make sure it is correct. So, we are doing, we're developing based on AI to understand this procedure, that it is actually reliable. So that it would be actually important contribution to mankind. That this symmetry that we classify is reliable. So you can use it for life and death problems. You can say that, okay, we are no problem."
"As Plato said, mathematics is always the most important as part of the basic science. What role does mathematics play these days at the age of AI?"
"Well, mathematics is the basis of all basic science. Without mathematics, there's nothing we can use to understand nature, including AI. Because mathematics is a subject not only to understand the objects that we saw, but also to understand the relations, the rules behind them. Especially universal rules behind many different phenomena. And mathematics has a beautiful way to express these rules in simple symbolic language that we can put it into computer, for example, or under, in the old days, using pencils and papers. We can write it down."
"Since you came back to China,"
"Right."
"you have been very keen to make sure in China's basic science, should I say, rainbow, "
"Yeah."
"the part of mathematics is crucial. Now you established Children's Academy, and it's been here for years already, and you've been the talents you cultivated in this academy not only contributing to artificial intelligence, bioinformatics, and also economics, and the list goes on. So, from your track record, how do you see mathematics could be a leading basic science that bring all the vitalities of other basic science forward?"
"And mathematics, as I just mentioned, is the link between all subjects because they develop some universal law. Some of the phenomena that we thought they are very distinct from each other turns out they are all similar to each other. You know, planet movement is using one over R squared law, inverse squared law. But electrons and atoms are similar to that. So, there are many similarities between different structures from large to small, from biology to medicine to economics, they have some very simple rules which are very similar to each other. When we understand the structure here, we can use the same understanding to other structures. One of the important reasons that coordinate is so important, then we can use algebra, very powerful algebra, and numerical analysis to understand geometry now. Uh, some, some of the things which cannot be done by just looking at that one subject only. But by looking at the other subject linked to it, we solve many important and difficult problems in one shot by crossing disciplines. So, crossing disciplines is a very important behavior in modern science. Most people, when they solve an important problem, it's because they understand different subjects and then apply the tools from one subject to this subject."
"To provide more platforms for international cooperation. That's what you've been very keen these days. For example, trying to promote Hong Kong as the destination for ICM, International Congress of Mathematics. Why are these platforms important, do you think, Professor?"
"ICM is the tradition of mathematicians in the last 100 years, yes, that we develop such a tradition. Each 4 years, there will be a meeting by all, by by the most important leaders in the world. They come together, they present the best work they have done in the last 4 years, and many of the work are actually just starting, and they lay out the future of what mathematics should be, and many young people learn from this congress, and they know what the future should be. So, this is extremely important for young guys to learn from them. So, it's mathematics and the future of science. I think that there's a reason why I want to bring ICM to Hong Kong. Hong Kong is the really the most free region in the world where you have no visa need, and you can have complete freedom in academic research and study. In Hong Kong, even students were able to participate in election of presidents of the universities, discussion in a very free manner, and I really feel that is a very good place to do it. And now nowadays, there's getting to be a lot of geopolitical problems which I think is very annoying to many people. So, for me, I, we, we open up for everybody. From a former center here, we have about 80, 40% of our faculties are non-Chinese, actually. And we have people from Iran, people from Israel, people from Russia, people from Portugal, and people from Latin America, from Africa. We have all. And I think this is great because then we just exchange ideas freely between us. And we are doing it in Hong Kong."
"Well, when you are thinking of ICM significance, many others are also impressed by that. For example, Japan, for example, the UK. How do you think with the energy that you certainly presented, and also of the, of Hong Kong, how do you think it can win in this friendly competition?"
"Well, first of all, I think a very important background is that we are producing more and more mathematicians in China and in Hong Kong. It is almost like exponentially increasing. Right now, in Beijing City alone, we, the BIMSAR, who I am in charge of a research institute, they have about 200 researchers. In Tsinghua, we are in charge of 150 researchers. And in Morningside, I'm a director also in the academy. We have about 50 people there. And among the students, we have about 1,200 students working in mathematics. This is just in Beijing City. The mathematicians related to me, we are talking about more than 400. No country, no no city in the world has that many mathematicians grouped together. So, in Beijing City alone, we are close to 1,000 mathematicians. And we are still growing, and these people are moving around. I mean, they will go to Hong Kong, they will go to Shanghai, and we are working together. So, in Shanghai, we are also growing, and also in Hong Kong. And in Hong Kong, we are developing several universities together. There are about seven universities who are interested in mathematical science. And I think we have a very good relations among ourselves. So, the number of young guys are growing, but on the contrary, in many countries, the number of mathematicians actually, uh, decaying the number. Uh, I think it happens in Japan, it happens in, uh, England, and all these countries. Uh, not only because of, uh, the government investment is, uh, getting, uh, less and less, but also the people's, young people who are interested in mathematics has been, uh, decaying. They, they are not as many as before. Uh, so, it's very different from us. We are young in terms of, uh, development in the future, we are very young, and we are looking forward for exciting development in the future. And yet, they are kind of looking down, uh, in the sense of the number decaying, and the young people are not excited about the future."
"What about talent? Uh, we have seen a new wave of talent, uh, coming to China, whether they're Chinese by origin or not. Um, how much do you see China is attractive in that sense to many of those scientists in the basic science area?"
"Well, now we are getting better and better, and we are trying to build an environment that is accommodating, uh, this non-Chinese foreigners. And, um, for example, when the non-Chinese came, the one of the important questions they have to deal with is children's education. Children's education is tough because they don't, they don't speak Chinese."
"So, but now we have many more international schools, and even, uh, even the government is supporting these schools. And I personally actually helped to, uh, Tsinghua University to build some classes whose major task is to train the students coming from foreign countries. So, they are pretty happy. So, this part is improving, but it's still, uh, somewhere to go. Uh, the second thing is about, uh, housing. Housing is much better nowadays compared to old days. And you also, it's also much cheaper. And then also entertaining, for example, you go to opera, you go to..."
"Cultural life."
"Music and all that. It's getting better. You can listen to, uh, ballet dancing from Moscow. Uh, you, you can watch that. You can listen to major opera singers and all that in Beijing City nowadays. So, getting better and better. And most important of all, I think, is medical care. American, because of HMO, and they want to save money, they don't allow you to go for checkups too often. In China, you can go to checkups much more often than other countries. And, uh, for example, a very major musician came, uh, half a year ago. He said, 'Oh, I have some problems hearing a series of on, uh, in the head.' So, I said, 'Okay.' We brought him to the major hospital in Shanghai, Union Hospital. So, he went in at 9:00 a.m., and then they immediately put him in CAT scan, in several major tests immediately. And 2 hours later, they tell him the diagnosis says that you have no problem. So, he was released and very happy and comfortable. No problem. So, this is something that I think the Chinese medical care is far better than America."
"Well, there are a lot of things that's contributing to the attractiveness, so to speak, for whether it's scientists or others who can contribute. My final question for you is about the younger, very young generation because the Children Institute that you have here mainly is having high school students that are really spearheading in the field of mathematics. They don't need to go through the so-called the only small bridge..."
"[laughter]"
"...the graduates of our high school in China have to go through, which is the college entrance exam, the Gaokao. They can immediately get into the Children Institute, an important part of Tsinghua University, the most coveted university in this country. So, how is that going? Do you see that is the road for China and for other universities?"
"It's not just for China. As I explained to you, I gave lectures on the history of mathematics. I've gone through more than 300 biographies of famous mathematicians. Almost all of them start their interest, excitement in mathematics by the age of 12 to 13."
"The age of 12 to 13."
"They got excited about it, and then one way or the other, they will talk with the masters in the field and then get developed. And I think we should give the same chance to some of our students in China. And I actually went to many of these, uh, high schools or middle schools. I talked with these kids. I was totally amazed how much, uh, they know and how well motivated they are."
"What do you mean? Tell us more about it."
"Okay, we have, uh, about 2 years ago, we grouped a bunch of, uh, well, you know, all the, uh, 30 students from, uh, elementary school who's just turning into middle school. So, uh, two years, so, grade seven, huh? And, uh, so, I asked some of my friends who are academicians to come to teach the young kids."
"Okay."
"So, I watched the, the first lecture. So, my friend was a number theorist. He asked these kids, uh, well, let's talk about, uh, numbers. And I want to tell you what prime number is. There is a one, three, one, two, three, and all that. They all got no. Yet, they, they are excited about asking questions. And then they said, 'Now, we go a little bit further. I want to look at those prime numbers which can be written as a square plus b square.' Uh, integer square."
"That's beyond my intellectual."
"And the kids watched it and they start to do one by one by one. And then they come up with a conclusion. Oh, they have to look, look like 4m + 1. And four times the integer plus one. And they found it just by them. And I was totally amazed."
"That was really impressive."
"In a, in a matter of half an hour, they did all this in one lecture."
"It out."
"It out by themselves. And not only one person, the whole group was asking questions and were got very excited. And I was very pleased. They ask questions, they try to answer it. But when they finished, they are playing fighting each other."
"[laughter]"
"Small kids. Yes, they like it. Yeah, so I'm very excited by..."
"But, but, but you know, Professor, there were earlier debates in China, you know, whether these children with special, you know, kinds of curiosity and talents should be put together in an institution or in a class like what you're running right now here in Tsinghua, because some of the earlier Shaonian Ban with the Chinese, the Keda Chinese University of Science and Technology did not necessarily work that well."
"It depends on people and, and I think it's very important you work as a group. If you get a very special talent training one by one, they are under a lot of tremendous tension because she was considered, or she was considered to be the best, far better than other people. She has too much psychological burden. If you put 10 of them together, they are competing among themselves. They do not see himself to be far better than the other people. And so they are working together as a group, and I think they are much more balanced view of our life and balanced view about how to study. And they are not lonely also. To train very, very special talent, a very, very important problem is friends, no friends. And here we build a group of them together. They are friends, they work together, and they know each other, and they respect each other. I think this is the best environment for them."
"So they can feel they're part of the community."
"Right, right."
"And that sense really helps them, right? Exactly. To not only excel in their academic studies, but also be a quote unquote, a normal person, right?"
"Exactly, exactly."
"Yeah."
"This, this is not only in China, I mean, in, um, France, for example, or in Germany, or in, in Russia, they have special talent schools. You got, for example, in France, you have the famous École Normale Supérieure. They, they, they train the real talent students. And they pick them up. They train you in a special way. They did well. There are many things we have to improve, but, but globally, I think we, we are fine. Just imagine, uh, each year there are about 14 million high school students graduate. Out of the 14 million, we pick about 100 students and train them. It's a small percentage. It's really very tiny percentage. And once we have this small group going well, they will become the leaders of this large group of people. And we need some leaders, uh, to help."
"Professor, it has always been a great pleasure to talk to you and learn a lot along the conversation. Thank you so much."
"Thank you."
"Thank you. Thank you."