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Chapter 141, Let Chen Jingrun wipe the blackboard? (Subscribe)

"In the world of the Möbius strip, the two sides of a plane are connected to form a single surface. If you cut a Möbius strip in half, you don't get two narrow strips. Instead, you get a loop that's the end of the strip twisted twice and then joined together. If you then cut this loop in half, it becomes two loops."

“From the Seven Bridges of Königsberg to the Möbius strip, the trefoil knot, the Klein bottle, and so on, what is actually happening is that the positive and negative distortions of three-dimensional space are connected together in four-dimensional space.”

"The Poincaré conjecture is inseparable from the structure of circles. Circles are quite magical topological structures, and they have some seemingly ordinary but profound properties."

At the podium, Wang Duoyu spoke eloquently. He was not reiterating the paper, because the paper had already been published and had been studied by many people for half a year.

If you have any questions, you can ask them later. What's more, before the paper was published, Smale, Yau and others had already studied it in detail, so there is no possibility of any problems.

The reason why he explains things in a simple and easy-to-understand way is that some parts really need to be explained in a simple and easy-to-understand way.

He also discovered that if he spoke too deeply, many people in the back row really wouldn't understand.

"Being the most interesting dimension, four-dimensional manifolds cannot be roughly visualized like three-dimensional shapes, so in my paper I proposed an infinite process for constructing the handle structure internally."

On the blackboard, as Wang Duoyu spoke, a set of equations emerged, and he also simply drew the geometric structure figures, followed by the relevant mathematical symbols.

When Qiu Chengtong, Smale and others heard this, their eyes widened and their brows furrowed.

A few days ago, when Wang Duoyu was communicating with everyone at the Jingxi Hotel, he had already said that in three dimensions and the dimensions of the construction site, the topology of a certain shape is mainly determined by geometric considerations.

These geometric properties include attributes that change when the shape is distorted, such as length and angle. In contrast, in five dimensions and higher, the geometric representation of a shape no longer severely constrains its topological possibilities.

In other words, the fourth dimension happens to be the dimension where geometry and topology begin to tear each other apart, which leads to the emergence of very beautiful and complex research topics in both fields, namely the many mathematical tools proposed by Wang Duoyu, such as the theory of four-dimensional manifolds successfully derived using the Casson structure.

"From the above, we can see that the standard spherical measurement induced from space, when measured again, is a standard constant cross-sectional curvature space, and the cross-sectional curvature is a positive number."

Wang Duoyu was still giving his report. More than half of the two-hour report had passed, with only about half an hour left.

As time passed, Wang Duoyu was finally about to finish.

"So, to summarize, by classifying compact four-dimensional manifolds with positive curvature operators and then using the four-dimensional framework structure, it is entirely possible to deduce that any compact four-dimensional manifold that can gradually bend, shrink, and expand into a four-dimensional sphere is actually topologically equivalent to this four-dimensional sphere."

"The above is the entire content of my paper. Thank you everyone!"

Following Wang Duoyu's words, the entire conference fell silent for a few seconds. Then, led by Smale, Shing-Tung Yau, Shiing-Shen Chern and others, the entire venue suddenly erupted in thunderous applause, which was very loud.

Almost everyone was very excited. Zhu Ling, Yang Nianzhen, Xue Xiaoling and others were the most excited. Their palms were red from clapping, but they seemed to feel nothing and continued to applaud vigorously.

If women take the initiative, men really have nothing to do.

Judging from the expressions of Smale, Shing-Tung Yau and others, it is not difficult to find that there is absolutely no problem with Wang Duoyu's paper.

Robert Langlands was a mathematician in his prime, and he also understood Wang Duoyu's paper, so the four-dimensional Poincaré conjecture had been solved.

Then all that is left for others is the three-dimensional Poincaré conjecture and the final capping process, which can completely prove the entire Poincaré conjecture.

However, when Smale proved the Poincare conjecture in five-dimensional and higher spaces, he had already written a paper of dozens of pages, and now Wang Duoyu's paper is also hundreds of pages long.

It is no wonder that Chen Jingrun's paper proving '1+2' was over pages long, even without the detailed process. If the detailed process was included, the number of pages would be even more exaggerated.

That is to say, if we add the Poincare conjecture in three-dimensional space and the final capstone paper, I am afraid that the proof of the entire Poincare conjecture will take up several hundred pages, or even thousands of pages.

Very exaggerated!

But that's mathematics!

Rigorousness is an attitude that mathematical researchers must have, otherwise problems are likely to arise.

The applause was thunderous and lasted for more than five minutes.

Kunale was so envious that he wanted to replace him immediately.

At this moment, Wang Duoyu spoke.

"Thank you, everyone. Thank you. The next twenty minutes will be for questions. If you have any questions, please feel free to ask."

Asking questions is an inevitable process of a report meeting.

So, when Kunale heard this, he immediately raised his hand to ask a question.

However, his raised hand received no response, and Wang Duoyu chose Sergei Novikov, a mathematician from the Polar Bear Empire.

Sergei Novikov won the Fields Medal in 1970. He is 41 years old this year and is extremely good at algebraic topology and solitary wave theory.

"Thank you. Mr. Wang, I'd like to ask you about the framework theory you mentioned on page 39 of your paper. Could you elaborate on the relationship between this argument and the expansion of four-dimensional space?"

hum!
Upon hearing this, Shing-Tung Yau, Smale, Robert Langlands and others exclaimed in surprise.

Because they could understand what Sergei Novikov said, and they were also very clear about Wang Duoyu's paper. Throughout the paper, Wang Duoyu created many mathematical tools, such as this framework theory.

The so-called frame theory is just a tool for studying the properties of compact four-dimensional manifolds, but it plays a very important role in it. Therefore, Wang Duoyu has actually elaborated on this theory in detail and constructed it using nonlinear differential equations.

Logically, Sergei Novikov shouldn't ask any more questions.

But he still raised the question, which only proved that he was really looking for trouble.

Not only is he looking for trouble, but he also wants to embarrass Wang Duoyu. If Wang Duoyu is really not prepared, then he may not be able to prove this relationship.

Although Qiu Chengtong and others had confidence in Wang Duoyu, they were still worried that Wang Duoyu would answer incorrectly.

What a pity, how could Wang Duoyu not be prepared?
"That's a good question, a very tricky one, but you asked the wrong person. This question isn't difficult at all."

When Zhu Ling heard Wang Duoyu say this, her heart suddenly tightened, and then she relaxed.

She knew her man could do it.

Before the report meeting started, she also asked Wang Duoyu what the general process was.

The question-and-answer session is one of them, and it is also the most exciting moment of the entire report meeting.

Almost all the people who asked questions had only one purpose: to point out the detailed errors in Wang Duoyu's argument!

Wang Duoyu's paper has been studied by others for half a year. In such a long time, those who can understand it have already read it thoroughly, and those who can't understand it will never be able to do so, and there is no way to force yourself to do it.

This is math!
Sergei Novikov is a Fields Medal winner and is also very good at algebraic topology, which is exactly his research field.

So the questions he raised were definitely not that simple.

Wang Duoyu wrote down the entire derivation process in detail on the blackboard.

Of course, it is not very detailed, because most of the details are definitely hidden. After all, Sergei Novikov is a top mathematician, and Wang Duoyu certainly does not need to tell him some of the too detailed processes.

If this is the case, then it would be too long-winded. It is equivalent to him writing out in detail the process of 1+1=2 to the other party, which is totally unnecessary.

After a while, about five minutes or so, Wang Duoyu stopped writing, turned his head and looked at Sergei Novikov and said:

"The above is the detailed proof process. I wonder if it has answered your confusion."

Upon hearing this, the latter looked unwilling, but still applauded.

Instantly, the entire auditorium erupted in thunderous applause. The first question had been perfectly answered, and many people enthusiastically raised their hands to ask more questions.

Wang Duoyu did not give his own people face, but gave the foreigners the opportunity to ask questions, just to see what tricks these foreigners had.

As a result, Wang Duoyu easily answered the questions of four people in a row.

All the questions were related to the theme of this report meeting, and there were many traps set, but they were of no use. Wang Duoyu was confident enough and knew very well what these foreigners were up to.

The relationship between us and the Polar Bear Empire is very bad now, especially after the war ten years ago, the relationship has reached a freezing point.

Now that we have begun to carry out reform and opening up, it is actually tantamount to betrayal. In the eyes of the Polar Bear Empire, this is a breach of faith.

On the contrary, the United States is extremely friendly. It is likely that it wants to gain our friendship and then deal with the polar bears together.

So judging from the many questions asked this time, the fact that people like Sergei Novikov were so enthusiastic about setting a trap for Wang Duoyu is enough to explain everything.

No matter what they thought, Wang Duoyu accepted everyone and resolved all crises.

As time went by, Kunale, who had not been called out, became unhappy. After not being called out by Wang Duoyu for the last time, he stood up and shouted loudly:
"Why don't you let me ask questions? Are you feeling guilty? Isn't China known as a country of etiquette? Why do you treat your guests like this?"

The English was full of curry flavor, which made Wang Duoyu want to laugh.

Zhu Ling turned back with a bit of worry, because Kunale's expression showed that he was here to cause trouble and was not a good person.

Wang Duoyu was not angered by the other party. He reached out to stop the others and said with a smile:

"Sir, whether I choose to ask questions depends entirely on my mood. You are so rude and reckless, I certainly don't want to talk to you, so please sit down."

"If I don't sit down, you're guilty. Your paper isn't supported at all. You're completely fabricating. There's no detailed supporting evidence in the entire paper. For example, pages 17 and 18, 23, 29, 35, and 67 are completely wrong and cannot be supported at all."

Kunale was furious and retorted directly.

Hearing this, Wang Duoyu laughed. "You haven't even understood my paper yet, have you? I've already analyzed it in my report. If there are any problems with the paper, do you think the Annals of Mathematics will publish it?"

After a pause, Wang Duoyu continued:

"What you just said is all relatively simple. I didn't state it in my paper. If I really needed to state it, it would be disrespectful and too simplistic."

"Although I don't know who you are, your question will become clear after you fully read the paper."

"Okay, let's stop wasting everyone's time. Sit down first, or I'll call security and let you go out and calm down."

The latter sentence is already very impolite.

Kunale's face immediately turned red, and he was so angry that he couldn't hold it in any longer. But he didn't have a chance to speak, because the classmate next to him had already pulled him down.

If they continue to make trouble, they will really lose face.

You haven't even understood the paper, so what's the point of asking questions?

After being disturbed by Kunale, Wang Duoyu no longer had the heart to continue answering questions.

Anyway, the report meeting was almost coming to an end, so I took the initiative to say:

"Well, this report concludes here. If you have any questions, please feel free to contact us at Harbin Institute of Technology. As long as you write to Harbin Institute of Technology, I will reply to you. Finally, thank you all and wish you all a wonderful day."

As soon as he finished speaking, thunderous applause broke out. Everyone clapped excitedly, and some even cheered.

Needless to say, even Zhu Hanting and the others were cheering, and even Jian Xianglan, Xue Xiaoling and other female comrades couldn't help but cheer along.

Wang Duoyu walked down from the podium with a calm expression, but he was still a little elated inside.

But at this moment, Qiu Chengtong couldn't help but walk towards him and stop him.

"Mr. Wang, a few days ago you mentioned using Ricci flow to construct geometric structures, transforming irregular manifolds into regular ones, and performing spatial changes to control these uncontrollable singularities. I have a new idea. It's like this..."

Before he finished speaking, Shing-Tung Yau quickly came to the blackboard and wiped it quickly. Before he had wiped off much, he started writing the system of equations.

This set of equations is actually the Ricci flow!

Qiu Chengtong had previously said that he had seen Hamilton studying Ricci flow in a seminar at Cornell University in early April.

At that time, Shing-Tung Yau had already realized that Ricci flow was of great help in constructing geometric structures and studying the properties of manifolds.

However, studying this Ricci flow takes time, and until there are any results, it is difficult to make any contribution to the Poincare conjecture in three-dimensional space.

But after arriving in Beijing and communicating with Wang Duoyu at the Jingxi Hotel, he also secluded himself for several days, which could barely be considered a burst of inspiration, so he now wanted to communicate with Wang Duoyu.

If possible, he still hopes to complete the proof process of the Poincare conjecture in three-dimensional space with Wang Duoyu.

In the auditorium, the applause gradually died down. The people who had stood up to leave also quieted down, sat down again, and looked at Qiu Chengtong and Wang Duoyu on the podium in surprise.

The latter said nothing, frowning as he watched the scene before him.

Wang Duoyu's eyes were a little dull, but if you looked closely, you would see that his eyes were staring at the blackboard in front of him with a sharp gaze, and his brain was working fast.

Hua Luogeng saw this and gave Chen Jingrun, who was standing next to him, a look: "Go and help wipe the blackboard."

At this time, the blackboard was densely covered with mathematical symbols, formulas, geometric structures, etc. written by Wang Duoyu before. If they were not erased, Qiu Chengtong would have no place to write next time.

As a result, before Chen Jingrun could stand up, the leader who had been sitting in the main seat suddenly stood up and said with a smile that he would wipe the blackboard.

Wow, let the leader wipe the blackboard?
This definitely won't work. Zhou Peiyuan took the initiative to step forward. Liu Deben, who was standing next to them and had been doing nothing, saw them scrambling to wipe the blackboard and wanted to help.

However, Su Buqing had already come over to stop him and said,
"Leader, Principal Zhou, you should just sit down first and let me do it. I know what can be erased and what cannot be erased."

Zhou Peiyuan heard this and said:
"It doesn't matter. Peking University can still provide a few blackboards."

This matter is just about wiping the blackboard. Is it necessary to make such a fuss?

Of course not!
However, Duan Xuefu had already stood up and asked several teachers standing at the door to help carry over some clean blackboards.

Soon, they brought in several new blackboards.

If it were somewhere else, it might not be possible to get so many blackboards, but at Peking University, this is not a big problem.

At this time, Smale, Robert Langlands and others had come forward to watch, while old guys like Chern Shiing-Shen, André Weil and others were sitting there, with no intention of disturbing them.

"Do they still want to prove the Poincare conjecture in three dimensions now?"

At this moment, Sergei Novikov, who was sitting in the audience, had this thought involuntarily in his mind.

Not long after this idea came to his mind, he immediately shook his head because he thought it was ridiculous and impossible.

If the Poincaré conjecture was so easy to prove, it would not have taken more than half a century, and we have only proven the Poincaré conjecture in four dimensions and above.

As for the Poincare conjecture in three-dimensional space and its final capping part, it is absolutely impossible to be proven so quickly.

"Kunale, maybe you should change your research topic again!"

PS: It’s the end of the month, do you have a monthly ticket?
(End of this chapter)