Chapter 138 Limit Proof, Mathematicians' Amazement [Please Subscribe]

As Xu Yuan stepped down from the stage, the lecture was declared over, but the shock on the faces of many scholars remained, and they had a new understanding of Xu Yuan's mathematical talent.

Deligne had already stood up and was the first to greet him.

He asked Xu Yuan excitedly: "Is what you just said true?"

"In fact, the sieve method used by Professor Zhang originated from my sieve method for the Carmichael number problem, so the improvement was completed so quickly." Xu Yuan explained to Deligne somewhat embarrassedly.

I just mentioned this matter casually, but I didn't expect that it would make so many scholars present lose their guard.

It can only be said that his deep learning state, which is taken for granted, is a rare thing in the eyes of other mathematicians.

After all, once you enter a deep learning state, your quick thinking can generate inspiration more easily than usual.

Deligne knew very well that even though the screening method had the same origin, it would be impossible to improve it in a short period of time.

What's more, the number of prime number pairs less than 4200 million is directly reduced to the value of 246.

This is sufficient to prove the extent of the improvement in the screening method.

It is unimaginable that he could complete such a huge amount of calculations in just half a day. His mathematical talent is beyond imagination.

"Oh my God, this is a miracle."

After hearing Xu Yuan's answer, Deligne couldn't help but sigh, even though he tried to control his emotions.

Even Holt, the editor-in-chief of the Annals of Mathematics, who came over, had a bright smile on his face and was generous with his praise.

"Xu."

"You must be God sent to save mathematics."

"I'm so happy."

However, Professor Deva from Harvard University, who happened to be passing by, snorted coldly and stood still when he heard this.

Xu Yuan didn't even look at the other person, and immediately started talking to Holt.

"Mr. Holt, mathematics doesn't need anyone to save it. I just like mathematics."

The laughter and joy on their side formed a sharp contrast with the scholars waiting to leave in other areas of the lecture hall.

Bagev saw that Terence Tao had a complicated expression on his face, and after a slight hesitation he asked in English.

“Terry.”

"Do you want to go over and say hello to him?"

“He’s very talented.”

As scholars in the field of mathematics, we all know the horror of spending most of the day improving the sieve method. It would be a lie to say that we are not envious.

Tao Zhexuan was somewhat tempted when he heard this, but he took the idea back when the words were on the tip of his tongue.

"Let's forget about it today."

He casually said this and immediately followed the crowd out of the lecture hall.

Bagev looked at Xu Yuan who was talking to Deligne, and finally had to follow Tao.

-

Princeton University held a special party in the evening, and the scholars attending the conference all dressed up.

Lao Zhang was in a good mood because the report meeting ended successfully, so he wore a suit to attend the meeting.

At the party, I had a glass of red wine and chatted with other scholars.

On the other hand, Xu Yuan was in an awkward situation. Perhaps due to the large age gap between them, no scholar took the initiative to come and talk to him.

However, there was a girl who was performing and boldly invited him to dance with her.

But he rejected them all mercilessly.

After all, as a man with a girlfriend, you still need to pay more attention to ensure your safety when you go out.

But it's not his fault. He has a good-looking and elegant appearance, and he's wearing a suit. Compared with those other old men who are over 50 years old, he is naturally invincible.

It's quite normal to be liked by girls at the party.

Just as he was sitting there alone enjoying his meal, he saw Holt, wearing a black tuxedo, walking over. He looked a little more elegant than he had during the day.

"Xu."

"It's not gentlemanly to reject a girl like that."

“They’re both from Princeton University.”

When Xu Yuan heard what Holt said, he smiled and replied, "I have a girlfriend, so it would be gentlemanly to reject them."

"So that's how it is. You are such an outstanding man." Holt said with some surprise.

Then he tilted his head back and drank the red wine in the glass as an apology for misunderstanding Xu Yuan.

Xu Yuan's eyes were all on the food, and he was chewing lobster meat in his mouth. He didn't take the matter to heart at all.

In the following time, after Xu Yuan had eaten and drunk his fill, he greeted and chatted with Deligne and Professor Witten and others. He returned to his hotel room alone before the party was over.

Continue to calculate and complete the subsequent proof formula of Qiu Chengtong's conjecture.

There were two lectures on the second morning, one by Professor Deligne and the Mozart of mathematics, Terence Tao.

Xu Yuan was undoubtedly looking forward to these two people and naturally would not miss the opportunity to attend their lectures.

……

It's about eight o'clock in the morning.

Xu Yuan arrived at the main lecture hall on time yesterday.

Looking around the scene, we can see that the number of people is almost the same as yesterday.

This alone shows Deligne's popularity in the mathematics community.

You should know that their report yesterday was the highlight, which promoted the research progress of the ultimate problems in the field of number theory.

As for what Deligne wants to talk about, it is possible that it does not belong to number theory.

After all, not all the participants in this conference are number theorists, so we also need to talk about other things as a foil.

Otherwise, it would not be easy to make full use of these three days.

"I am very happy to be here with you to discuss and exchange ideas in the field of mathematics. Today I will give a report on the existence of curvature metrics of Kähler manifolds, a core problem in geometry."

On the podium, Deligne had a smile on his face. After he announced the title of the report, he began to speak seriously.

Xu Yuan was sitting in the front row. He was a little stunned when he saw the title of the report. He didn't expect that Deligne's report was the question he had asked before.

No matter how you look at it, it seems that Deligne chose the content of the report specifically for him.

The thought stayed here, and I couldn't help but mutter to myself.

"Could it be that Professor Deligne is still paying attention to my question? It seems that I will have to listen to the end of today's report."

It turned out that his guess was not wrong. As Deligne continued to talk about Kähler manifolds on the stage, the related branches of mathematics in his mind began to intertwine, collide and combine.

Originally, he tried to prove the Yau conjecture with the help of differential geometry, algebraic geometry, and metric geometry of multiple complex functions.

By combining formulas, we try to find a solution to a class of fourth-order fully nonlinear elliptic equations.

If these branches of mathematics are regarded as the raw materials of gunpowder, then what Deligne talks about is the flame that can successfully ignite the fuse and cause an explosion.

Xu Yuan soon found himself in a special state.

Although he could hear Deligne's words normally, he was not isolated from the outside world.

But the formulas he had combined over the past few days kept appearing in his mind and were automatically arranged and combined.

It's like a computer executing an instruction on its own.

It was as if an electric current spread from the coccyx all the way up, eventually reaching the brain and making the body feel unprecedentedly excited.

"Solving a class of fourth-order fully nonlinear elliptic equations under the assumption of K-energy coercion or geodesic stability."

……

"Proof of the existence of a constant scalar curvature metric."

"and restrict it to the Kähler-Einstein metric..."

"Prove Qiu Chengtong's conjecture."

As he muttered to himself, his eyes became brighter and brighter, and he finally determined the complete proof of Qiu Chengtong's conjecture.

According to the original estimate, it will take some time to completely solve Qiu Chengtong's conjecture.

I didn't expect that after listening to this report today, I would get a burst of inspiration and accidentally figured out the key idea of ​​proof.

With a complete idea in mind, the next step is to write out the proof process and verify the conclusion.

If the verification is successful, it can be announced to the public that the Qiu Chengtong conjecture that the first Chern class is positive has been completely solved.

Soon after Deligne's one and a half hour report ended, Xu Yuan didn't even bother to greet him and immediately walked towards the hall outside the lecture hall.

In order to avoid his inspiration being interrupted, he did not even bother to go back to the hotel room to write the proof.

He went straight to the writing board in the hall, picked up the marker next to him and started writing quickly on it. Then, mathematical symbols appeared on the writing board one after another.

"U(n)=O2(n)∩GL(n,C)∩So(2n)"

……

"h=g+iω"

……

When Xu Yuan was completely immersed in it, he quickly entered a state of deep learning.

There were so many complicated and difficult formulas, and there was almost no pause during the verification process.

There will be a break before the next report begins. You can see the situation in the hall without paying special attention when you come out of the lecture hall.

The writing boards placed in the hall are meant for people to use, after all, no one knows when inspiration will come.

So it's not surprising to see someone calculating in the hall.

Basically, I will look away after just one glance.

But because the person doing the calculation was Xu Yuan, the situation was completely different.

no way.

After making a major breakthrough in the twin prime conjecture, Xu Yuan has already made an impact in the mathematics community.

It can be said that anything you do about mathematics has the potential to cause major changes.

"Someone is calculating here live again. I don't know who got the inspiration. What a lucky guy."

“Inspiration can be right or wrong.”

“How many people claim to have found a way to prove a difficult problem, but the final result is wrong.”

"Don't you think that person is very young and looks familiar?"

Several overseas professors who were the first to see the situation in the hall expressed some sadness when they talked about it.

As they say, there is right and wrong inspiration.

Sometimes I feel like I’ve had a burst of inspiration and think I’ve found a way to solve the problem.

But after actual verification, I found that it was just a waste of time.

The hope of being a mathematician is only to generate the right inspiration and obtain conclusions that are not afraid of verification.

But it is too difficult to come up with such inspiration.

Therefore, they do not think that the person who does the calculations can obtain any mathematical results.

It's nothing but a waste of time.

Instead of wasting energy calculating these incorrect formulas, it would be more helpful to listen to reports to broaden your thinking.

It wasn't until someone suggested that the other person looked familiar that everyone paid more attention to him and tried to find out his true identity.

"It seems familiar."

"Such a young figure, but he shouldn't be a student of the Department of Mathematics at Princeton University..."

"He's the math genius who solved the twin prime conjecture. I just attended his lecture yesterday. I'm sure I won't mistake this familiar figure for someone else."

"I also saw him in Deligne's report just now."

At this moment, as everyone recognized Xu Yuan's identity, a thought suddenly emerged in their minds.

I was just listening to Professor Deligne's report, but now I ran to the hall to deduce formulas on a writing board.

Is it...

The thought stayed here, and several middle-aged overseas professors with silver hair walked towards Xu Yuan without any hesitation.

However, due to the consensus of the mathematics community, they did not approach Xu Yuan, but just stood behind and put on reading glasses to check.

In the mathematics community, what people hate most is being interrupted, especially at critical moments in deducing formulas.

So unless the person performing the simulation stops on his own initiative, everyone else can only wait patiently at a distance.

In their opinion, Xu Yuan is very talented in number theory, otherwise it would not have been possible to make a major breakthrough in the twin prime conjecture.

In this case, their subconscious reaction was that Xu Yuan was continuing to derive twin primes and wanted to improve the sieve method to reduce the positive value of twin primes. After all, this was the most reasonable analysis.

But after seeing the contents on the writing board, they couldn't help but be dumbfounded and looked shocked.

“Isn’t this a twin prime number?”

"Kähler manifolds related to geometry, what Professor Deligne just talked about."

"No, it seems there are multiple complex functions."

"Metric geometry is a branch of mathematics. What is this proving?"

After listening to Professor Deligne's report, it is indeed normal to borrow the writing board in the hall to conduct calculation research.

Besides, they all know that Xu Yuan has not made any achievements in the field of algebraic geometry.

When they come into contact with new knowledge, they try to find ways to consolidate it. I guess they would do the same if they were in their shoes.

But it is quite surprising that the formula also involves differential geometry, multi-complex functions and metric geometry.

Soon, other people noticed the special situation here, and out of curiosity they all moved over.

Soon, as more and more people gathered, someone with relevant research experience finally recognized Xu Yuan's purpose. Although he was worried about disturbing Xu Yuan, he still said something with great surprise.

"This is an attempt to prove the Yau conjecture that the first Chern class is positive. It's crazy."

As soon as these words came out.

Other scholars at the scene immediately started talking about it.

"Qiu Chengtong's conjecture is the last case of the Calabi problem. There has been no progress in decades, and it is not easy to prove it thoroughly."

"He is obviously very talented in number theory, but now he is suddenly studying algebraic geometry."

"It's just a waste of effort. He can't complete the proof at all."

……

Many of them have studied mathematics for half their lives and naturally have rich experience and knowledge.

It is precisely because of this kind of experience and knowledge that no one is optimistic about Xu Yuan.

Although Xu Yuan is very talented in number theory and was able to solve the twin prime conjecture that had been unresolved for a century, a person's energy is limited after all, and it would be very difficult for him to study other branches of mathematics.

Not to mention crossing branches to prove other difficult problems.

After all, it is not feasible to apply the knowledge in the field of number theory to algebraic geometry.

There is also the difficulty of Qiu Chengtong's conjecture.

As the case in which the first Chern class in the Calabi conjecture is positive, no one has been able to complete the proof of the Qiu Chengtong conjecture since it was proposed, and there has not even been any progress.

Even Qiu Chengtong himself couldn't prove it, let alone others.

The key point is that apart from hearing that Xu Yuan solved the Monge-Ampere equation and made some achievements in partial differential equations, they did not see any trace of Xu Yuan in other branches of mathematics.

It just so happens that Qiu Chengtong's conjecture involves multiple branches of mathematics.

In addition, some people also noticed that Xu Yuan was completely immersed in it and was not affected by the outside world at all.

It's like a state of enlightenment.

They expressed regret and felt very sorry about this.

"It is very rare to be able to concentrate deeply and immerse yourself in something. Most scholars may never have the chance to do so in their lifetime."

"In this state, the mind will be more agile and inspiration will be more likely to come."

"If he is working on the twin prime conjecture, maybe he can get a step closer to finding pairs of prime numbers less than 246."

"But he is trying to prove a difficult problem that should not be challenged. It is such a waste."

Upon hearing this, others also felt that wasting this hard-earned state was a complete waste of God's gift.

But what I feel more in my heart is envy.

I thought that if I could maintain this state of enlightenment, perhaps the problems that had been bothering me for years could be easily solved.

Just when the scholars attending the academic conference were about to fill up the hall, Professor Deligne and Professor Witten, who heard the news, finally rushed over.

When others saw this, they quickly gave up their seats.

Deligne was different from the other people around him. After he came behind Xu Yuan, stopped and saw the contents on the writing board, a relieved smile suddenly appeared on his face.

"This kid actually started proving it right here. Doesn't he know there's a special discussion room upstairs?"

Obviously, these words are supposed to express dissatisfaction, but they always sound like a doting tone.

It's like believing that Xu Yuan can complete the proof.

If it were anyone else, no one would think too much about it, but when facing Deligne, they couldn't help but reflect on it.

I wondered if I had really made a wrong judgment.

But before anyone else could ask, Witten, who was standing nearby, could no longer suppress his curiosity.

He immediately asked Deligne, "You knew he was proving Qiu Chengtong's conjecture?"

"On the morning before the official lecture, he came to me with questions." Deligne explained with a smile: "To be honest, when I first found out that he was also studying Qiu Chengtong's conjecture, my expression was similar to yours."

"Although the Qiu Chengtong conjecture is a problem of algebraic geometric stability, it is, after all, a Calabi conjecture with a positive first Chern class, and it also involves string theory."

"I don't think he can prove it here," Witten said, frowning. His field of research is string theory, so he is more aware of the complexity of proving the Calabi conjecture.

Even if only the first Chern class is positive, it is still not a problem that young scholars can solve.

Otherwise, Qiu Chengtong would have proved this conjecture himself long ago.

Others may not know about Xu Yuan's research on algebraic geometry, but Deligne knows it very well.

When he discussed the relevant content with Xu Yuan that day, even though he had been studying in the field of algebraic geometry for many years, he couldn't help but praise Xu Yuan's proof process of combining formulas from multiple branches of mathematics.

Even he was inspired and temporarily changed the title of the report.

At that time, he believed that Xu Yuan could prove Qiu Chengtong's conjecture, it was just a matter of time.

Now that Xu Yuan has been fortunate enough to enter a special state, it is very likely that he can complete all the proofs on the spot.

His thought stayed here. He did not directly refute Witten, but just threw out a mysterious sentence.

"Then let's wait and see."

However, just as he finished speaking, he heard an inappropriate voice suddenly in his ear.

"The more talented a person is, the more conceited he is. He thinks that he can easily solve difficult mathematical problems just because he has made some progress on the twin prime conjecture."

"He will certainly pay for his ego and become the biggest joke in the mathematics world this year."

When Deligne and Witten heard the voice, they turned their heads to check. When they found that it was Professor Deva from Harvard University, they immediately understood what was going on and chose not to respond.

They had heard something about what happened between Professor Deva and Xu Yuan.

Since the Annals of Mathematics announced a major breakthrough in the twin prime conjecture, I have been reluctant to agree with it.

Publicly stated that it would overturn the conclusions in the paper.

They also contacted several professors from the school's mathematics department to jointly verify Xu Yuan's paper, trying to find errors and logical loopholes in the paper.

Unfortunately, they found nothing in the end, but had to admit that there had been some progress in the twin prime conjecture.

This result is normal. After all, the twin prime conjecture paper has been verified by many mathematicians at the Institute for Advanced Study in Princeton. If it is really overturned by the other party, wouldn't it seem that the mathematicians in the Institute for Advanced Study are not worthy of their reputation?

In addition, Deva is collaborating with another top journal in the field of mathematics, so it is not surprising that he questioned the Annals of Mathematics.

Deligne naturally knew that Deva was intentionally targeting Xu Yuan, but he did not take the initiative to refute.

Because when a result that is not recognized by the other party becomes a reality, it is the most powerful counterattack.

However, Zhang Yitang, who was also attracted, once again supported Xu Yuan and refuted Deva.

"I believe Xu Yuan can complete the final proof."

Although Lao Zhang knew that Xu Yuan was studying Qiu Chengtong's conjecture, he was not sure about the actual situation.

However, when he thought of how Xu Yuan improved the sieve method and reduced his result of less than 4200 million prime number pairs to 246 prime number pairs in half a day, he became full of confidence in Xu Yuan.

The bearded Deva just glanced at Lao Zhang and didn't say anything else.

Anyway, in his opinion, Xu Yuan's proof would not produce any results, and he would have to accept the failure silently.

Pay for your own ego.

As time passed, no matter how much people disbelieved it, their eyes were always fixed on the formula on the writing board.

After careful study, it was found that many of the formula steps are very sophisticated.

To put it simply, it is a perfect combination of algebraic geometry, differential geometry, and metric geometry of multiple complex functions, and an innovative application of proof methods.

It is no exaggeration to say that even if the conjecture is not ultimately proven, this method is equivalent to providing a new tool for exploring the unknown in mathematics.

It is of great significance and high value.

Faced with such unexpected changes, many people's initially firm beliefs began to waver.

Even some very bold ideas came to my mind.

Could it really be possible to prove Qiu Chengtong's conjecture?
And this thought became stronger and stronger and could not be shaken off my mind.

Another ten minutes passed.

Among the onlookers, there was more praise for Xu Yuan's proof process.

"This formula is really great. It simplifies complex problems a lot."

“Why didn’t I think of that when I was researching it before?”

“It’s really exquisite!”

"God willing, I hope to see a difficult problem solved."

As for Deva, who was still waiting to see the show, his face became increasingly gloomy.

It seemed as if water was about to drip out.

He was similar to Deligne, and his main research branches in mathematics were number theory and algebraic geometry.

He could naturally find some good points in Xu Yuan's proof process, but the voice in his heart kept convincing himself.

This strengthened my belief that Xu Yuan could not prove the conjecture.

Even if the other party creates a new branch of mathematics, the conclusions obtained will not be able to solve the Qiu Chengtong problem.

-

As the saying goes, some people are happy and some are sad.

Just as mathematicians gathered in the lobby downstairs to witness Xu Yuan's attempt to prove Qiu Chengtong's conjecture, Tao was looking at the empty main lecture hall with a look of surprise on his face.

Even fell into self-doubt.

"What about people?"

"There are more than 200 well-known mathematicians. It's impossible that no one is here?"

"Could it be that no one is paying attention to me anymore..."

It was decided early on that he would give the second report in the morning.

For this reason, he did not even attend Professor Deligne's lecture, but stayed in the room upstairs to carefully perfect what he was going to say.

He thought that even if he was not as popular as Xu Yuan, he had to maintain his reputation as the Mozart of mathematics.

Turns out what he saw.

When he arrived at the main lecture hall, he found that there was not a single other person in such a large space except himself.

It's a bit beyond my understanding.

Even if there are more talented mathematical geniuses in the mathematics world, the attention paid to him should not be lost so completely.

After briefly preparing himself mentally, he decided to find the organizer's staff first.

Ask for specifics.

Just as he was about to walk out, he ran into his colleague Bagfu.

Just as I was about to ask him, the other party's voice came into my ears, and there was obvious excitement and agitation in the tone.

"Terry, go to the hall quickly. Xu Yuan is trying to prove Qiu Chengtong's conjecture there."

“Everyone is watching and waiting for the results.”

The information on the report in Bagev's words was so shocking that Tao Zhexuan was unable to react for a while.

After extracting and repeating the main information, I was dumbfounded.

"On-site proof?"

"Qiu Chengtong's guess?"

To solve every math problem, mathematicians have to spend a lot of time and energy, plus a little bit of inspiration, to come up with so many theorems in textbooks.

But Xu Yuan is an exception.

Spending most of the day improving the sieve method and proving the value of the twin prime conjecture from less than 4200 million prime pairs to less than 246 prime pairs can be called a miracle in the field of number theory.

It is an existence that cannot be replicated.

But now Xu Yuan has to prove a mathematical problem on the spot, which is the Calabi conjecture that the first Chern class is positive.

This made him feel like he was living in the other person's shadow.

No wonder no one listened to his report.

Now that things have come to this, there is no need for this report to continue without an audience.

The thought stayed here, and he immediately said: "Let's go over and take a look at the specific situation."

Yes.

No matter what, he had to know what the result of the on-site evidence that ruined his report was.

Bagev was already showing signs of becoming a keen fan of Xu Yuan. Upon hearing this, he quickly walked downstairs to the lobby without waiting for Tao.

-

As soon as Terence Tao saw the situation in the hall, he couldn't help but gasp.

I was still shocked by the scene before me.

The crowded hall, which was home to at least a hundred people, was clearly separated from Xu Yuan, who was surrounded and struggling to write the proof. It was obvious that everyone was trying their best to control their emotions and make as little noise as possible for fear of disturbing Xu Yuan's rhythm.

It is obvious that Xu Yuan's proof of Qiu Chengtong's conjecture should have come to an end.

Just as Terence Tao squeezed into the crowd, Xu Yuan was seen with a smile on his face, his right hand hanging naturally and he finally stopped proving.

The many mathematicians who were watching the whole process stood there in shock for a few seconds when faced with this scene.

Then the whole hall suddenly became noisy.

"This class of fourth-order fully nonlinear elliptic equations has actually been solved."

"It's unbelievable."

"My God, I am so lucky to see the Calabi conjecture solved before my death."

"There should be no problem with the proof process. He really put a belated end to the Calabi conjecture."

……

As the voices rang out one after another, Deva finally broke down and shouted at the top of his voice: "The conclusion has not been verified yet. Before this, it is still unknown whether Qiu Chengtong's conjecture has been truly proved." After that, he went straight to the hall to find draft paper and pen to prepare for verification.

This sentence undoubtedly reminded others, and the next second no one wasted any more time.

They all followed Xu Yuan's example and verified their conclusions by doing calculations on the spot.

Some people even tore off the posters and squatted on the ground to count on the back of them.

He didn't care about his image at all.

Everyone wants to be the first to verify the result so that they can officially announce to the mathematical community that the Calabi conjecture that the first Chern class is positive has been completely solved.

Tao Zhexuan looked at the people around him who were starting to take action, and at this moment he felt mixed emotions.

Judging from the current situation, Xu Yuan should have really proved Qiu Chengtong's conjecture on the spot.

Given the rigor of Xu Yuan's previous papers, there should be no problem even if so many people on site collectively verify it. Such an amazing mathematical talent is truly enviable.

"It turns out that the gap between him and I is so big."

He sighed secretly, and then he also found a place to try to verify the research.

Xu Yuan was naturally confident in his own proof process and was not worried at all about other people verifying it.

Speaking of which, even he himself could hardly believe it. He did not expect that he would finally choose this method to prove the conjecture. At this moment, he was still somewhat excited.

It’s just that because I stood for so long and was in deep learning state throughout the whole process, my energy consumption was quite high.

As his legs felt a little sore, he simply sat on the ground, with a smile on his face the entire time.

The spiritual world has been satisfied unprecedentedly.

"I knew you could do it, but I was really surprised to see you prove it this way." When Deligne was communicating with Xu Yuan, he knew that all these processes were feasible and he didn't need to verify anything. He walked straight to Xu Yuan and said this, waving his hand and saying, "You don't have to get up."

Witten next to him did not hide the excitement on his face at all, and generously praised Xu Yuan.

"I admit that at first I didn't think you could prove and completely solve the Calabi conjecture that the first Chern class is positive, even though Deligne had full confidence in you."

"Now I understand why Deligne has such confidence in you. You have the best mathematical talent I've ever seen."

The moment he finished speaking, he continued:
"Solving a class of fourth-order fully nonlinear elliptic equations was like an invisible curtain wall blocking mathematicians before, but you found a breakthrough without any warning, not only finding the solution to the equation, but also establishing a systematic method to study this type of equation."

“It is foreseeable that this paper will become a classic in this field.”

Xu Yuan listened to Witten's words and was immediately delighted to be praised by such a famous mathematician in the mathematics community.

However, facing the two big guys in front of him, he was still a little shy and spoke modestly.

"I have to thank Professor Deligne for this. Without his guidance, I would not have been able to prove Qiu Chengtong's conjecture so quickly."

Deligne smiled and said, "Even without me, you will be able to solve this problem sooner or later."

But after he finished speaking, there was some regret on his face.

"It's a pity that you broke away from that special state of high concentration so quickly. If you continue to deduce the twin prime conjecture, perhaps you can reduce the positive value further."

When Xu Yuan heard this, he felt a little amused. He didn't expect that Deligne was regretting this.

So he immediately explained: "I call this state of high mental concentration the deep learning state. It can improve my efficiency a lot when studying and doing exercises."

"Can you get into this state during your normal studies?" Deligne suddenly raised his voice and asked.

Xu Yuan wondered: "Is it difficult to enter this state?"

After the words were spoken, Deligne and Witten fell silent. As masters of mathematics, they actually felt very hurt.

Thousands of words finally come together into one sentence.

"It's good to be young!"

The scholars around who also heard Xu Yuan's answer finally understood why Xu Yuan was able to successfully improve the sieve method and reduce the value of the twin prime conjecture from 4200 million to 246 in just half a day.

It turns out that people didn't say anything nonsense yesterday.

However, this also made them more convinced that Xu Yuan had indeed completely proved Qiu Chengtong's conjecture after the twin prime conjecture.

at the same time.

While many mathematicians in the hall were actively verifying Xu Yuan's proof process, Holt, the editor-in-chief of the editorial board, was leading his men hurriedly over here.

He did not attend today's report meeting, after all, there are things to deal with at the Mathematical Yearbook every day.

He thought that yesterday's report on the twin prime conjecture was over and nothing special would happen.

It doesn't matter whether you show up or not.

Who would have thought that Xu Yuan would quietly do something big again and actually try to prove Qiu Chengtong's conjecture on the spot.

When he received the news, he rushed over without saying a word and even specially found a photographer.

I thought about filming the proof process to record this important moment in mathematics.

Even if it is not successfully proved in the end, it can become an interesting thing in the mathematics community if it is publicized.

"Hurry up, it will be too late later."

Holt walked quickly in front, and from time to time he did not forget to urge the photographers following behind him, for fear of missing this rare moment.

After all, not every mathematician has the confidence to challenge difficult problems in front of so many people.

Soon, as Holt and the photographer walked into the hall, when the scene in front of him came into view, he was stunned for a moment and felt that his brain was not enough.

The mathematician, who was originally dressed in a suit and tie, was now squatting on the ground and calculating seriously without caring about his image.

Looking more closely, I found that the draft paper used was actually a torn poster.

As for Deligne and Witten, two big names in mathematics from the Institute for Advanced Study at Princeton, they were also squatting on the ground and talking to Xu Yuan who was sitting on the ground.

I'm afraid that no one who sees this scene will associate it with a high-end mathematics academic conference.

The photographer barely maintained his own perspective, swallowed his saliva and asked Holt beside him:

"Mr. Holt, do we still need to film this?"

"Shoot." Holt gritted his teeth and uttered a word firmly.

Although he didn't know what had happened, he rushed over here and couldn't give up halfway.

Fortunately, after entering the hall and inquiring about the situation, he received good news that was worth celebrating: Xu Yuan successfully completed the proof of Qiu Chengtong's conjecture.

Although other mathematicians are still verifying it, he is full of confidence in Xu Yuan's proof process.

Thinking that the Annals of Mathematics was about to announce that a difficult problem had been solved, he, the editor-in-chief of the editorial board, could not suppress his excitement.

Just like this, more than an hour passed. As someone shouted out his or her verification result, it was like a powder keg had been ignited and more people continued to respond.

"My verification was successful. The stability of algebraic geometry has been proven."

"Qiu Chengtong's conjecture has been thoroughly proven."

"It not only proves Qiu Chengtong's conjecture, but the method used in it is also applicable to solving such equations."

"We now have a new tool for exploring unknown mathematical worlds."

"After several decades, the first Chern class was finally solved for being positive, and the Calabi conjecture came to a successful conclusion."

……

Professor Deva of Harvard University looked at the results of his own verification and kept repeating that he couldn't believe it.

“The verification was actually successful.”

"How is it possible that I can't even find one mistake?"

I thought the result was a sure thing, but in the end it turned out to be the same as the situation when I tried to overturn the twin prime conjecture. I suddenly collapsed to the ground like a deflated ball.

On the other hand, Xu Yuan was surrounded by many mathematicians, and everyone was congratulating him.

Witnessing Xu Yuan solving the Qiu Chengtong conjecture with my own eyes, no matter what I think in my heart, I have to admit that there is a mathematical master who is growing rapidly in the mathematical world.

Holt, who successfully squeezed in, grabbed Xu Yuan's arm and couldn't hide his excitement.

"When will the paper proving Qiu Chengtong's conjecture be published? Please submit it to our Annals of Mathematics."

There are so many mathematicians on the scene helping with verification, and he can publish the paper directly after receiving it. He must get his hands on this rare classic paper.

……

(End of this chapter)