The unparalleled talent of the country started from Harbin Institute of Technology

Chapter 230, The th International Congress of Mathematicians (Thank you everyone)

On July 5, 1983, Wang Duoyu left Harbin Institute of Technology and came to Beijing.

By this time in July, John Milnor and others who were staying at the Ice City Institute for Advanced Study had already chartered a plane and left. They went to Warsaw first, and Wang Duoyu did not go with them.

In a large courtyard on Wenjin Street in Beijing, Wang Duoyu was chatting with Lu Yangui, Fang Lihe, Wu Guozhong and others.

It's not just small talk, but serious business.

Lu Yangui and his colleagues are still very concerned about the Mach 5 fighter project.

After all, Harbin Institute of Technology is located in the Ice City, more than a thousand kilometers away from Beijing, so it is difficult to know what is happening in time.

So before Wang Duoyu left for Warsaw, everyone sat down and chatted.

Harbin Institute of Technology is responsible for three major parts: power unit, avionics system and fuel system. Among them, Wang Duoyu is mainly concerned about the first two, while the fuel system is the responsibility of several departments of Harbin Institute of Technology, such as the Department of Materials.

In the history of the original time and space, Harbin Institute of Technology actually focused more on the overall design of payloads, so there were no aviation fuel-related majors.

But at this time and space, under the suggestion of Wang Duoyu, and since Harbin Institute of Technology is not short of money, the professional settings are very complete.

Besides, aviation fuel is actually an engineering major. Harbin Institute of Technology has already added majors in engineering, science, etc., and there are relevant departmental teachers and students.

No matter how unconventional it is, such a major is necessary.

In terms of science and engineering, Harbin Institute of Technology has never been biased!

The power unit and avionics system are the most critical parts of the Mach 5 fighter project, especially the power unit, which is the core of the core.

"Our Harbin Institute of Technology has now advanced the design drawings of the sub-combustion ramjet engine to about 15%. Once high-temperature alloys and other related materials are developed, we will proceed to the next step of testing."

"Once the testing is complete, our overall design drawings will be around 27 percent complete, which is barely three-tenths of the way there."

Hearing Wang Duoyu's words, leaders including Lu Yangui, Fang Lihe, and Wu Guozhong couldn't help but nodded happily.

At the end of the previous year, Wang Duoyu had already taken out all the design drawings of the Mach 5 fighter.

The capital gathered many experts, and in less than six months, they worked overtime day and night to finally verify all the design drawings.

Then the project was launched in May last year, and only one year and two months have passed. I didn’t expect that the power device has advanced so much. Harbin Institute of Technology is really amazing.

Don't think that 15% progress is slow, it is actually very fast.

The design drawings of the power unit are definitely the most core and key part of this project, and also the most complex. Many of the materials used in it are extremely difficult to develop.

At present, the easiest bones have been chewed, and the hardest bones will be chewed in the next few years.

After the conversation was almost over, Wu Guozhong asked:
"Professor Wang, is your project department facing any difficulties right now? Do you need our help?"

Wang Duoyu shook his head:
"If there is a need, we will definitely not remain silent, but for now, these are all technical matters, and there are no other personnel issues."

He did not mention Lin Dehong's matter. After all, Lu Yangui had already handled it, and there was nothing to mention.

After skipping this topic, Fang Lihe continued:

"Duoyu, you will be leaving for Warsaw soon. We have already prepared the relevant security plan. You will just need to actively cooperate with Comrade Yan Daowen's work when the time comes."

"Okay, leader, I have no problem."

The security work is handled by professionals, so Wang Duoyu naturally doesn't need to worry about it.

After coming out of the Wenjin Street compound, it was already dusk.

Back at No. 87, Zhongguancun West Street, the little guy Wang Junhong was running around in the yard, followed by two puppies.

Liu Xiaoli, Liang Xiufen and others were watching him from the side.

This time, Wang Duoyu will go to Warsaw alone, while Liu Xiaoli and the others will stay in Beijing for a few days and return to Ice City together after Wang Duoyu returns.

The next morning, Wang Duoyu said goodbye to Liu Xiaoli and the others, and then took a car to Nanyuan Airport.

Those who flew to Warsaw on the same plane with Wang Duoyu included Shiing-Shen Chern, Luogeng Hua, Chen Jingrun and others, who can almost be said to be the most cutting-edge group of people in the domestic mathematics community.

Many leaders came to see him off, including Lu Yangui and others.

Liu Deben and his team did not come to Beijing, but stayed in the rear base of Harbin Institute of Technology.

At eight o'clock in the morning, Wang Duoyu and his friends took a flight from Nanyuan Airport and headed to Warsaw in Europe.

The straight-line distance between the two places is 7,000 kilometers, and it requires passing through several countries along the way.

The current flight cannot fly directly. It is necessary to stop in XJWLMQ in the middle and then fly directly to Warsaw.

The straight-line distance from Beijing to WLMQ is 2,700 kilometers, so it is almost half the distance.

Stop at WLMQ, refuel, take a break, and then take off again, and you will arrive in Warsaw very quickly.

There's not much to say about what happened in between. Anyway, the flight time at that time was not very fast, and my butt was definitely sore from sitting.

After arriving safely in Warsaw, Wang Duoyu and his friends wanted to sleep before they even got off the plane because they were very tired.

This International Congress of Mathematicians was quite lively. According to media reports, at least three thousand people came.

In fact, in the history of the original time and space, the total number of people who attended the conference was only 2,300, which was in sharp contrast to the more than 3,000 people in the 1978 session.

"Professor Wang, welcome."

At the airport, Oduiqi, chairman of the executive committee of this International Congress of Mathematicians, personally led Olitz and others to the airport to welcome Wang Duoyu and others.

Obviously, Shiing-Shen Chern, Luogeng Hua and others were also on this flight, but they were still treated differently.

why?
In terms of his current status in the global mathematics community, Wang Duoyu is absolutely the undisputed number one.

Even if Alexander Grothendieck came, he could only rank behind Wang Duoyu.

What's more, Grothendieck has been excluded from the French mathematical community, and the global mathematical community does not seem to be very interested in him either.

The reason is that this guy was too radical back then.

“I’m so flattered.”

Wang Duoyu said quickly that he was indeed quite surprised.

In fact, mathematicians are straightforward and not very good at managing these social relationships.

It’s not that they can’t, it’s that they just don’t want to and don’t want to.

In terms of IQ, mathematicians around the world are definitely the smartest group of people, and their IQ is definitely the highest.

The same goes for Ao Duiqi, a very smart person, but he is already old. As the saying goes, age makes wisdom, this guy is really powerful and knows how to handle things.

Odichi definitely made a great contribution to the fact that this International Congress of Mathematicians could be held in Warsaw, and the same goes for Dang Olitz.

They are all Polish mathematicians, so of course they are inclined towards Warsaw.

After the pleasantries, everyone got on a car and left the airport.

After arriving at the hotel, Wang Duoyu and the others adjusted to the jet lag and didn't think about so many things anymore.

In a blink of an eye, it was the next day. After adjusting to the time difference, Wang Duoyu did not wander around the famous attractions in Warsaw, but was surrounded by a group of mathematicians.

Due to the current relationship problems in Warsaw, most of the participants from all over the world, including Wang Duoyu, were concentrated in several hotels.

Wang Duoyu and his group were gathered in the best hotel in Warsaw.

Since it is the best hotel, the mathematics professors and doctors living here must be the top group of people.

But these people really want to talk to Wang Duoyu about the proof papers of the geometric Langlands conjecture, the proof papers of the restricted Burnside conjecture, the proof papers of the honeycomb conjecture, etc.

No matter which guess it was, they all wanted to talk to Wang Duoyu.

In particular, John Thompson, a mathematics professor from the United States, won the 16th Fields Medal in 1970 for his two major achievements: the Burnside conjecture and the Frobenius conjecture on finite simple groups.

However, due to Wang Duoyu, the generalized Burnside conjecture he proved that year was falsified.

So he actually wants to talk to Wang Duoyu about this issue now.

However, John Thompson cannot get a number now because there are so many people here, and he is certainly not that great.

Joseph Cohen, Michael Attia, Smale, Lars Hermann, John Milnor, Hironaka Heisuke, etc., every one of these people is a Fields Medal winner.

But there were so many of them, and Wang Duoyu couldn't chat with them one by one. He could only communicate with a few familiar people.

Of course, let’s forget about people like John Milnor. We are too familiar with each other and see each other often, so we won’t talk about them.

In fact, Wang Duoyu prefers to chat with Grothendieck, but this guy has been kicked out of the mathematics community and is now a professor at the University of Montpellier.

But instead of meeting Grothendieck, Wang Duoyu met Pierre Deligne.

"Deligne, nice to meet you."

Wang Duoyu shook hands with Pierre Deligne, exchanged a few pleasantries, and then started chatting.

This guy's research scope is also very broad. In addition to some of the most famous Weil conjectures in algebraic geometry, this guy also studies Hilbert's 21st problem, Hodge theory, the relationship between modular forms, Galois representation and L series, modular theory, etc.

So Wang Duoyu had a lot of topics to talk about with the other party, whether it was model form, model theory, or Hodge theory, he really wanted to communicate a little.

Nowadays, Wang Duoyu only has the paper proving the Collatz conjecture and the third paper proving the geometric Langlands conjecture. He no longer has the others.

After completing the proof of the geometric Langlands conjecture, Wang Duoyu will certainly continue to tackle other mathematical conjectures.

For example, infinite-dimensional partial differential equations, the hyperplane conjecture in Banach space, the main conjecture of complex dynamical systems in chaos, the basic lemma of the theory of automorphic forms in the Langlands program, etc.

The day passed quickly.

Wang Duoyu also gained a lot from communicating with Pierre Deligne and others.

The second day was the opening ceremony of this International Congress of Mathematicians. The entire conference process actually consisted of an opening ceremony, academic reports, group discussions and a closing ceremony.

On the day of the opening ceremony, everyone came to the largest indoor conference hall in Warsaw, and the Chairman of the Executive Committee, Oduiqi, delivered a speech at the opening ceremony.

Currently, the International Congress of Mathematicians only awards the Fields Medal, and the Nevanlinna Prize was only established this year.

So the award ceremony is actually at the closing ceremony, otherwise many people would not attend the closing ceremony.

However, on the day of the opening ceremony, when Ao Duiqi announced the list of relevant speakers, the opening ceremony had actually ended, and the follow-up was the report meeting.

The first person to hold a one-hour report meeting was Wang Duoyu.

His situation is more complicated because many people hope that he can make a longer report, so yesterday, Ao Duiqi and others discussed it with Wang Duoyu.

On the first day of the conference, that is, after the opening ceremony, the whole day was devoted to Wang Duoyu's lectures.

Others report for 45 minutes or one hour, but Wang Duoyu reports for one day.

This is the first time such an exception has occurred in all the conferences held so far.

Being able to give a 45-minute report at the International Congress of Mathematicians is already very impressive, and a one-hour report means that you are the world's top mathematician.

As for Wang Duoyu's one-day report meeting, it is unprecedented.

However, if you think about it carefully, Wang Duoyu gave a lecture every year in 1979, 1980 and 1981, and each lecture attracted more than a thousand people to attend.

Although the circumstances this time were special, Wang Duoyu still produced two proof papers: the proof of the honeycomb conjecture, the proof of the restricted Burnside conjecture, and the proof of the geometric Langlands conjecture.

Although in terms of fame, the above three cannot be compared with the previous Poincare conjecture, Fermat conjecture and ABC conjecture, but in terms of importance and promotion of the development of mathematics, proof papers such as the geometric Langlands conjecture are definitely more important than them.

It is even more important than Fermat's conjecture.

After all, Fermat's conjecture is just famous, and its application is only relatively good in cryptography, computer science and mathematical research. Compared with the geometric Langlands conjecture, it is still slightly inferior.

Of course, these are all very important mathematical problems and are one of the important topics that promote the development of mathematics. Although there are differences in difficulty, there is actually not much difference in importance.

"The opening ceremony is over. Professor Wang Duoyu's lecture will begin soon. Everyone please go to the bathroom before the lecture begins."

Olitz said this at the podium.

Most people thought this was reasonable, but some people, such as John Thompson and Hironaka Heisuke, found it outrageous.

Why?

John Thompson and the others actually understood why Wang Duoyu did that, but they were just very unhappy.

Why must Wang Duoyu be treated specially?
too disgusting! !
And the most important thing is that when other people gave reports, it was not in a conference hall where everyone listened together, but in a relatively smaller lecture hall, and there must have been other mathematicians giving reports in other halls at the same time.

On the contrary, Wang Duoyu was able to have a conference hall to himself, and everyone listened to his report together. It was simply outrageous, it was outrageous to the extreme.

Regardless of what Thompson and others thought, many people still welcomed and looked forward to Wang Duoyu's next report, so many people actively cooperated and even applauded.

Ten minutes later, the entire conference hall fell silent, and Wang Duoyu was invited to the stage to begin his report.

"I am very grateful to President Ao Duiqi for his kind invitation, and I am also very grateful to everyone for coming to this International Congress of Mathematicians. This is my first time attending, and I am very surprised."

On the stage, Wang Duoyu smiled and spoke confidently.

He was already accustomed to such scenes, and he did not feel nervous or excited at all. Deep down, he was very calm, without a single ripple.

Seeing him standing on the stage and giving a speech leisurely, Hua Luogeng, Chen Jingrun, Su Buqing and others in the audience were deeply moved.

In particular, a group of older generation mathematicians who studied abroad, such as Duan Xuefu, felt this most deeply.

Decades ago, our country was weak, and most people like Duan Xuefu received money from the Boxer Indemnity Fund and went to Europe and the United States to study abroad at public expense.

At that time, when had I ever been respected so much abroad?
At this time, Wang Duoyu was not only respected by foreigners, but also madly worshipped by these foreigners.

Not to mention the more than 3,000 people who came to the scene, just the top mathematicians who went to Harbin Institute of Technology and the foreign students who came to Harbin Institute of Technology, there are now almost more than 500 people.

It can be said that Wang Duoyu has more than 500 followers abroad.

“Chairman O’Duiqi told me that many people want to hear me talk about my papers proving the honeycomb conjecture, the restricted Burnside conjecture, and the geometric Langlands conjecture.”

"Well, I'll just give you a brief talk today, but time is limited, so I'll spend three hours this morning talking about two papers proving the geometric Langlands conjecture, and one hour each this afternoon talking about the restricted Burnside conjecture and the honeycomb conjecture."

"Well, by the way, I'll be teaching at Harbin Institute of Technology after the start of the school year in September. My main topics will be the three questions I just mentioned."

"When the class starts, I will explain in detail the mathematical tools and theories used in these three math problems. If there are students or professors who don't understand, you can come to Harbin Institute of Technology and we can discuss it further."

Wow!
The entire conference hall erupted in an uproar; no one had expected Wang Duoyu to actually teach again. Most of the masters and doctoral students, who had been pessimistic and thought they wouldn't understand, were so delighted when they learned that Wang Duoyu was teaching.

Now that I have the opportunity, I must go and attend the course.

If you miss such a rare opportunity, you will regret it for the rest of your life.

Wang Duoyu saw this, his expression did not change at all, and he said:

“Okay, let’s get started.”

The conference hall soon became quiet. Everyone listened to the class attentively and no one talked about what had just happened.

Such a scene made Hua Luogeng, Duan Xuefu, Su Buqing and others even more surprised and very pleased.

What was surprising was that Wang Duoyu's every move attracted the constant attention of more than 3,000 people in the conference hall, and everyone was very willing to obey his words, just like the orders in the army. It was so exciting.

What makes me happy is that Wang Duoyu in front of me is a real Chinese. Like Duan Xuefu and others, he has black hair, black eyes and yellow skin. He is a descendant of the dragon.

China's mathematics community has successors!
In other words, China's mathematics community has finally produced a person who can have a significant influence on the global mathematics community.

The following time was Wang Duoyu's performance time.

After the three-hour report, John Milnor, Charles Fefman and others gained a deeper understanding of the geometric Langlands conjecture and gave it a lot of thought.

The next stage is to build a bridge to extend the known equivalence results to more general cases, but this does not seem so easy.

Shing-Tung Yau, David Bryant Mumford, Robert Langlands and others were all frowning and thinking deeply, perhaps there was still a way to solve all this.

They all wanted to build the bridge as soon as possible, but they didn't know that Wang Duoyu had already built the bridge, but he just didn't show it to them.

The proof of the geometric Langlands conjecture is never achieved overnight.

As one of the hottest topics in mathematics today, it has attracted the participation of many top mathematicians.

For example, mathematicians who won the Fields Medal in recent years, as well as mathematicians who won the Fields Medal in previous years, are unwilling to fall behind.

In fact, along with Smale, even Grothendieck was secretly deriving geometric Langlands.

Just because the Langlands Program is the grand unified theory of mathematics, anyone with a little ambition would want to contribute a little and leave their name in history.

At present, Wang Duoyu has become the best evidence for the Langlands Program by proving the Fermat conjecture.

He has now published two papers proving the geometric Langlands conjecture, which has comprehensively promoted the development of the Langlands Program and allowed everyone to see the bright future of the Langlands Program.

It seems that the grand unified theory is about to be realized.

But in fact, top mathematicians are very clear that although the future is bright, the process will inevitably be complex, changeable and dark.

Whether we can successfully overcome the current difficulties and successfully realize the grand unified theory, there is still a long way to go.

The three-hour report time passed in the blink of an eye. Wang Duoyu had finished his report. The question time was moved to fifteen minutes later because everyone needed to go to the bathroom and Wang Duoyu also needed to go to the toilet.

After standing on the podium for three hours, a man in his sixties or seventies would have collapsed long ago, but Wang Duoyu remained calm and was not affected much.

Fifteen minutes later, applause broke out, which was everyone's gratitude to Wang Duoyu.

After the applause, the question-and-answer session officially began. Thompson was the first to raise his hand to ask a question, but Wang Duoyu did not call his name.

There were more than 3,000 people at the scene, and more than half of them raised their hands. Wang Duoyu didn't even notice Thompson.

Wang Duoyu randomly selected a few people to ask questions, and he was not afraid of these questions at all.

Shing-Tung Yau, David Bryant Mumford, John Milnor, Charles Fefferman and others had asked the question long ago, and Wang Duoyu was able to answer it smoothly, let alone others.

Besides, before submitting the paper for review, Wang Duoyu checked it over and over again, so there was no way there could be any mistakes.

The question and answer session is over, and this morning's report is also over.

During lunch time, everyone was still discussing the wonderful report that had been given that morning. Although most people did not understand much, this did not prevent them from discussing the matter.

Wang Duoyu alone took up an unprecedented amount of lecture time at this International Congress of Mathematicians. He truly deserves to be recognized as the emperor of mathematics. Awesome!
The afternoon report will continue, with Wang Duoyu placing the honeycomb conjecture in the first half and the restricted Burnside conjecture in the second half.

The report of the paper proving the honeycomb conjecture did not cause any waves.

Because this paper has been published for more than a year. It was Andrew Wiles who was responsible for reviewing and publishing this paper after he took over as the editor-in-chief of the "HIT Mathematical Journal" in March 1982.

It's already July 1983, which is just over a year.

After such a long time, many top mathematicians have already studied it thoroughly.

If it was any falsification, it would have been exposed long ago. How could they wait until now?
There is no way. The honeycomb conjecture has troubled mathematicians for thousands of years, and the author of the proof paper is Wang Duoyu. Who doesn't want to study it thoroughly and then disprove it?

Unfortunately, Wang Duoyu's paper is very rigorous and naturally cannot be falsified.

After Wang Duoyu finished his report on the honeycomb hypothesis, the entire conference hall burst into applause. Everyone was very happy and excited.

The question-and-answer session was much quieter, far less so than the one in the morning, where everyone raised their hands.

After a short fifteen-minute question period, the report came to an end.

Then we took a fifteen-minute break, and then the last report of the day began, which was also a report that many people were looking forward to.

It can even be said that the reason some people came to attend this mathematician's conference was actually to see Wang Duoyu report his paper on the proof of the restricted Burnside conjecture.

why?
Because before this paper, Wang Duoyu also wrote a paper about falsifying the generalized Burnside conjecture. In this paper, he also proposed the restricted Burnside conjecture.

John Thompson, the original author who was disproven, was also present at the scene. As a former Fields Medal winner, he is 52 years old this year. So can he defeat the arrogant Wang Duoyu?

Although mathematicians are more devoted to the pursuit of truth than the gossipy aunties in the village intelligence organization, mathematicians are also human beings. Who doesn’t like to watch the fun and eat melons?

Especially the big news in the mathematics world, they like it the most!
"In today's last report, let's talk about the restricted Burnside conjecture. Speaking of this conjecture, we have to mention the Burnside problem."

On the podium, Wang Duoyu's expression was no different from before, and his tone was the same.

But the people in the audience listened more attentively, and some of them looked at John Thompson from time to time, wanting to see the changes in his expression.

In that year, John Thompson collaborated with Walter Fitt to publish a paper titled "Solvability of Odd-Order Groups", proving the theorem that every non-cyclic finite simple group has an even number of elements.

The discovery of this theorem is of great significance for understanding the structure of finite groups and was a huge sensation in the 1960s.

Because every finite group is made up of constituents, and these constituents are finite simple groups.

Subsequent research by John Thompson included the identification of all minimal simple finite groups, that is, those groups whose all proper subgroups consist solely of cyclic constituents.

“I have already presented a counterexample in a previous paper.”

On the podium, Wang Duoyu was still presenting his thesis, but he just briefly touched upon it and did not elaborate on it in depth.

In 1902, Burnside raised a question in combinatorial group theory: a finite generating group Gi＞, where each element is of finite order, is Gi＞ a finite group?
The answer is no. Wang Duoyu has proved this in his paper. He not only provided a counterexample, which is the theory known as Wang's Theorem, but he also proposed the restricted Burnside conjecture.

Everyone listened with great interest, but some people were disappointed to see that Thompson just listened to the report with a blank expression but did not react at all.

Soon, with Wang Duoyu's presentation of Wang's theorem, counterexamples and proof of the restricted Burnside conjecture, the report meeting came to an end and was about to enter the question-and-answer session.

The applause at the scene was long and lasting.

A few minutes later, the applause died down and Wang Duoyu announced the start of the question-and-answer session. Everyone subconsciously wanted to raise their hands but put them down instead.

John Thompson was the only one who raised his hand.

He noticed that he was the only one who raised his hand, and no one else raised their hands, but he remained calm and continued to raise his hand.

Wang Duoyu was stunned for a moment, but quickly recovered and said with a smile:

"It seems no one has any questions. In that case, I will finish answering Professor Thompson's questions and then conclude today's report."

As soon as these words were spoken, everyone started raising their hands to ask questions.

It's fun to watch a show and enjoy it, but it won't work if it involves your own interests.

Many people also have questions about this paper proving the restricted Burnside conjecture.

Moreover, many people are confused just by understanding Wang's theorem.

In Wang Duoyu's paper, the theorem is described as follows:

Let A=K
The detailed process of the entire theorem is very long, occupying thirty-two pages of the paper.

This theorem is actually an important theorem about class domain towers, which solves the problem of whether class domain towers can be solved within a finite number of steps.

As early as 1930, Hilbert proved that any number field K can be embedded in a finite extension, becoming a Hilbert class field.

In this class field, every ideal of the primitive number field becomes a principal ideal.

However, the Hilbert class field itself does not necessarily have class number 1. The class field tower problem asks whether iterating over the Hilbert class field will be stable after a finite number of steps.

In this Wang's theorem, Wang Duoyu proved that the class domain tower can expand infinitely by constructing infinite examples, thus negating the assumption that the class domain tower will be stable within a finite number of steps. As a result, for every prime number P, there is an infinite group G generated by 3 elements, and the order of each of its elements is a power of P.

This provides a counterexample to the generalized Burnside conjecture.

Just regarding understanding Wang's Theorem, many people have a lot of questions, and everyone wants to get clarification, so naturally it is impossible to give the opportunity to ask questions to John Thompson.

It can be said that Wang Duoyu's words just now easily resolved the embarrassment.

After everyone raised their hands, Wang Duoyu still asked John Thompson to stand up first and ask questions.

Because Wang Duoyu knew very well that if he did not allow the other party to ask questions, who knows how the media would portray him later, and John Thompson would definitely not let him go.

Therefore, instead of being stared at all the time, it is better to take the initiative to take this opportunity and let the other party ask questions.

In the conference hall, everyone watched John Thompson stand up and heard him ask several questions.

"Hello, Wang, nice to meet you, and thank you for giving me the opportunity to ask questions. My question is..."

In total, John Thompson had five questions, two of which were about Wang's theorem and three about the proof of the restricted Burnside conjecture.

Moreover, these five questions were very to the point and very crucial, which made many top mathematicians present feel refreshed.

No one is a fool or an idiot, and most of the people sitting in the conference hall, especially those sitting in the front, are top mathematicians.

It's even more impossible to be a fool.

After hearing the other party's question, Wang Duoyu smiled and said:

"Thank you very much, Professor Thompson, for your questions. The five questions you raised are all very crucial and well-asked. Now let's discuss them one by one, starting with the example questions regarding the theorem."

"I've already given a very detailed account of the content on pages 17 to 39 of the paper, but it seems that some people don't quite understand it. So let me break down this difficult part for you."

There is a gap between geniuses, and this gap may even far exceed the gap between ordinary people and geniuses.

So some people cannot understand some examples in this theorem, and Wang Duoyu can only continue to break down the steps.

Everyone in the conference hall listened very attentively.

Although Duan Xuefu and others are old, they still stare with their eyes wide open, prick up their ears, and listen very attentively.

When it comes to communication between mathematicians, language has never been an obstacle, because they are all leaders in mathematics research, and mathematics is the language of God.

A large number of mathematical symbols appeared on the blackboard again. To ordinary people, these symbols were just scribbles and were completely incomprehensible.

But for mathematicians, this is a basic operation. However, when they see some of the mathematical symbols and tools created by Wang Duoyu, they are also a little confused. They are also trying hard to understand these symbols seriously.

"OK, I've answered the two questions about theorems above. Now let's talk about three questions about this restricted Burnside conjecture."

On the podium, Wang Duoyu remained calm and composed as he continued his statement:
"If you have thought carefully about my paper, you should remember the restricted Burnside conjecture I proposed, right?"

This is a very basic question. With so many mathematicians present, it is impossible that they cannot understand the conjecture proposed by Wang Duoyu.

But Wang Duoyu couldn't possibly go to such lengths to say such nonsense, right?

The restricted Burnside conjecture asks: Given a group G with m generators and index n, is the order of G necessarily no greater than some constant that depends on m and n? Equivalently, is there a finite number of finite groups with m generators and index n that are isomorphic?
It is actually very difficult for researchers without a doctoral degree or above to understand this problem.

As we all know, groups with finite elements are one of the important contents of group theory.

The number of elements it contains is called the order of the finite group.

In the history of mathematics, many concepts of abstract group theory originated from finite group theory, which can be divided into two categories: solvable groups and non-solvable groups.

Rather than a solvable group, that is, a simple group.

The study of finite groups originated very early. Its formative period is associated with the names of Cauchy, Lagrange, Gauss, Abel, and later Galois, Jordan and others. How to determine solvable groups and simple groups is an important development direction after the establishment of abstract group theory.

The German mathematician Herder once studied simple groups and solvable groups in detail, and proved that: a cyclic group of prime order is a simple group, and the commutative group composed of all even permutations of n (n≥5) letters is a simple group.

More than ten years ago, John Thompson and Fite proved the Burnside conjecture in finite groups: groups of odd order must be solvable groups.

This proof promoted the development of finite group theory.

The complete classification of finite simple groups, that is, finding all isomorphisms of finite simple groups, was finally solved two years ago after about forty years of efforts by hundreds of mathematicians.

As long as you can understand the above content, you can have a general understanding of the restricted Burnside conjecture.

Of course, this is just an understanding. If we want to fully understand this issue, we still need more in-depth research.

"Please look at page 87 of the paper. I mentioned a very important point there, and I believe many people have overlooked it."

On the podium, Wang Duoyu was still answering John Thompson's last question.

Five minutes later, when Wang Duoyu finished his presentation, the conference hall fell into a brief silence, followed by thunderous applause.

At this point, even John Thompson had to admit defeat.

The five questions he raised were the ones he discovered after carefully studying and thinking about the paper proving the restricted Burnside conjecture over the past six months.

Even he himself could not answer these questions.

I didn’t expect that Wang Duoyu could solve it in such a short time.

This made John Thompson admire him very much, as if he, an ordinary academic, had been thinking about the problem for a long time, racking his brains, but still couldn't figure it out.

As a result, I asked Wang Duoyu, the academic genius, and he actually answered the question in less than twenty minutes.

clothes!
PS: When I woke up, I got a surprise, 320 monthly votes, thank you!

(End of this chapter)