Yuan Zhengxin carefully browsed through Qiao Yu's questions and Pan Jingyuan's answers. When he looked up at his professor, he realized that Professor Pan's eyes were very dark today. He couldn't help but smile subconsciously and said, "Little Pan, Thanks for your hard work."

Pan Jingyuan smiled bitterly and said: "Mr. Yuan, you have really worked hard. I feel like I have never worked so hard when doing the project. The angle of this guy's questions is very tricky. I had to think carefully before I dared to answer him at night. As a result, he has not been able to answer the questions. He kept asking questions, and I thought about not replying, but I was afraid of dampening his enthusiasm...

Just as he was talking, the phone started to vibrate again. Pan Jingyuan subconsciously picked it up and took a look at it, and then immediately complained: "Good guy, here we go again." Then he took the phone and handed it to the old man for a look.

"Will the isomorphism relationship in this part of the proof be very dependent on the specific choice of G? So G will also cause the properties of certain geometric objects to change, which may lead to the failure of this isomorphism relationship? Hmm... this question ?」

The old man looked at Pan Jingyuan and asked curiously: "Is this a question in your paper?"

Pan Jingyuan nodded, took a deep breath and said: "Yes, the question he asked involves the local system LocSys and the global differential homology IndCohNilpglob. The purpose of this part of the proof process is to analyze the geometric objects on the algebraic curve. Represents geometric data related to automorphic forms to describe global uniformity.

The old man continued to ask: "Is his question reasonable?"

Pan Jingyuan replied: "It does make sense, but in our proof, we imply the global nature of the local system and also indicate possible failures under specific circumstances, such as the presence of singularities."

"Oh." The old man nodded, a little confused. He also couldn't figure out what Qiao Yu wanted to cause trouble.

????????????

He previously expressed his intention to recommend Qiao Yu to join the research group. Of course, he only wanted to work as a handyman to get a feel for the atmosphere of the world's most cutting-edge research. But he decisively rejected it. Now he has downloaded Qiao Yu's paper and can't wait to analyze it piece by piece.

etc..

"Does he understand?" The old man suddenly reacted and looked at Pan Jingyuan.

Pan Jingyuan sighed in his heart, time is not forgiving...it was only then that Mr. Yuan came to his senses.

So he nodded naturally and replied: "Not only did he understand it, but I felt that he was trying to find loopholes in the paper. Every question raised was very targeted, and there were even two questions that we didn't know at the time. I thought about it."

Yuan Zhengxin nodded slightly, thought for a while, and asked, "What do you think?"

Pan Jingyuan immediately said: "What I mean is, why don't we just let him come to Huaqing to stay for a few days, and I will spare some time to explain to him specifically. The efficiency of WeChat communication is really too low."

Whether it was selling face to an old man or selling face to Qiao Yu himself, Pan Jingyuan never resisted having more in-depth academic exchanges and discussions with Qiao Yu. But he couldn't stand being bombarded with all kinds of questions on WeChat.

No one can stand it if it changes.

If they were all nutritionally insignificant questions, that would be fine. He could just fool around with them, but the questions Qiao Yu asked were obviously carefully thought out and to the point.

He needs to think carefully before answering.

The result is that Qiao Yu's last question last night was indeed a little too much. After he answered it, Qiao Yu politely told him that he was going to rest and asked him to rest early.

But people who often work at night will know that if their brain has just been thinking intensively and then they can't fall asleep at all in bed, they still feel a little sleepy even now.

etc.

Pan Jingyuan suddenly picked up his mobile phone and carefully read the questions raised by Qiao Yu again. He suddenly felt a little uneasy. "He may not be free during this period... huh? What's wrong with you?" Yuan Zhengxin suddenly asked.

Pan Jingyuan replied subconsciously: "I suddenly feel a little unsure. When we deduce the global nature, we require that each ridge E on the C curve corresponds to the unique representation of the Lie group G. If BunG, that is, G Any change in the structure of the bundle space during the proof process may indeed lead to the invalidation of the isomorphism relationship."

This answer made Yuan Zhengxin stunned. He looked at Pan Jingyuan with a deep look and asked: "This should be considered an obvious loophole, right? You didn't fully discuss and self-examine it internally before publishing the paper?"

Pan Jingyuan replied: "Yes, but no one seems to have raised this issue. After all, we have conducted sufficient partial verification work, which occupied most of everyone's energy. And as you know, Professor Schultz also expressed doubts about our conclusions. Very satisfied.

Moreover, in a paper of more than 800 pages, BunG is an extremely important content, occupying a lot of space in each paper. If all were verified, it would probably take more than a year to be published. And this cannot be considered an obvious loophole, right?

Yuan Zhengxin nodded. Of course he could understand this situation. It was nothing more than utilitarianism.

If the paper is delayed for more than a year, it will definitely not be discussed at next year's World Congress of Mathematicians.

Five systematic papers of more than 800 pages are the most cutting-edge mathematical propositions, and it will take more than a year for the world's mathematical community to demonstrate them.

It is now only one year and four months before next year's World Congress of Mathematicians. To be honest, this time is already extremely tight. This makes Yuan Zhengxin unable to even say anything critical.

Physicists don't care. As long as you live, no matter how old you are, you can win the Nobel Prize, the top prize, if you produce results. But once a mathematician reaches the age of forty, he will miss out on the most dazzling top prize.

If it takes one more year to verify, indeed many people will not be satisfied.

Even if he was young, he would probably make the same decision. This can't be blamed on anyone, especially Pan Jingyuan, who is not even the leader of the team.

So Yuan Zhengxin did not make an evaluation, but said with a smile: "Haha, you can share Qiao Yu's thoughts with the team, and you can start self-examination first. If the problem can be found, then you have to thank Qiao Yu."

Pan Jingyuan nodded seriously and replied: "Well, I will discuss this issue with the instructor later. By the way, what did you just say?"

Yuan Zhengxin replied: "I mean Qiao Yu has been unavailable for a while. The first phase of this year's IMO training camp will start tomorrow. At least in the next nine days, he will complete the training content at Yanbei University in accordance with regulations."

Pan Jingyuan was stunned, and after a long while he asked in confusion: "Qiao Yu? He still wants to participate in IMO? Why is he participating in IMO? Can his mind come to his mind?" As someone who has participated in IMO and won the championship, Pan Jingyuan naturally has Qualified to say this.

To put it bluntly, no matter how difficult the IMO questions are, they still test the ability to apply elementary mathematics knowledge at the high school level. How to put it bluntly, it can only be said that the mathematics you are exposed to before college and the mathematics you are exposed to after college are two completely different subjects.

The knowledge of the former is all concrete, with only basic concepts and basic formulas.

The latter knowledge begins to be abstracted, that is, from this time on, students may be exposed to mathematical questions that do not have a single number, but only various symbols and letters that refer to them.

The depth and abstraction of knowledge determine qualitative changes in the way of thinking and the nature of the subject.

To put it bluntly, high school mathematics is at a stage where hard work can make up for one's weakness. As long as you are willing to work hard and study hard every day, even if you are not talented, you can get a good score just by relying on your intuition. At most, it will be the last. It will be a little confusing to raise the questions.

But even at this stage, mathematics alone can screen out many people who are not suitable for advanced research.

It's even more different when you get to college. Just answering questions can no longer support you to learn this subject well. It's even exaggerated to the extent that you may not understand the examples in the textbooks after the teacher explains them over and over again. The reason is abstraction.

Mathematics does not explore phenomena that can be seen in reality. It can play freely within the scope allowed by the theoretical framework.

High dimensions are difficult to imagine in the physical world, but they are everywhere in the mathematical world and are even indispensable. Just like in N-dimensional Euclidean space, mathematicians can discuss spaces of any dimensions and study their geometry. characteristic.

It happens that the most difficult thing for people to imagine is something they have never seen, but there are always people with extraordinary talents and sufficient imagination to do these things that are beyond the reach of ordinary people. For example, Poincarai's exploration of high-dimensional manifolds is still regarded by nearly Perfect proof.

But why would such a person go to IMO? What’s the point of him going to IMO?

Yuan Zhengxin explained: "Well, I think so too. This will indeed cause trouble to many people. Especially when he goes to participate in IMO, his article on Ann.Math may have been published. This makes him even qualified to sit At the judges' table.

But Qiao Yu said that this is what he promised his alma mater, so he must do it. I don’t think I can veto a child’s commitment to his alma mater. Otherwise, how should I discuss the concepts of trustworthiness and gratitude with him in the future? "

Pan Jingyuan opened his mouth but said nothing. This reason is indeed invincible.

From a purely mathematical perspective, there is really no need for Qiao Yu to participate in IMO.

A paper that can get into Ann.Math is more than enough for him to lead the team to participate in IMO this time.

There are so many mathematics professors in Huaqing, but they cannot guarantee that their independent research results will be published in professional mathematics magazines every year. Not to mention that Qiao Yu's achievement can be said to be a very important achievement.

But if you want to repay your alma mater...

Yuan Zhengxin added: "Oh, you may not know that Qiao Yu did not go to a key middle school. His alma mater has not produced an IMO champion. No, it has not produced a student who can enter the national training team. So if

If Qiao Yu can win an award at the IMO this time, it will be a breakthrough for his alma mater."

Pan Jingyuan shook his head and said with a wry smile: "Even if he wants to participate in IMO, he doesn't need to participate in the training camp, right? Why is he going to the training camp? Can't we just give him an exemption?"

"Hey." Yuan Zhengxin sighed and said, "It's hard to teach a child like him. Of course it's okay, but he has a very out-of-touch temperament. If you really want to give him this kind of privilege, who knows what he's going to do after he gets used to it.

What else could happen? The age of sixteen is when a person’s worldview takes shape, and he must be given a sense of rules.”

Pan Jingyuan suddenly realized that since the discussion with Qiao Yu yesterday afternoon until now, he had probably subconsciously regarded Qiao Yu as the same person as him, and he did not realize that this little guy was still in the stage of personality formation.

The strong plasticity means that adults will have many scruples when interfering with his ideas at this time. The old man is probably afraid that Qiao Yu has no sense of rules, which will lead to the higher he climbs and the harder he falls, right? He really doesn't know how to do this in this regard.

What can I say, it just feels weird and weird when I think about it.

"That.."

"Then you have to work hard for another day. Please excuse me, Xiao Pan. He will go to the training camp tomorrow. This is something he has volunteered to participate in. I think he will take it seriously." The old man said with a smile, with a hint of pleading.

smell.

Pan Jingyuan was startled and said quickly: "Mr. Yuan, you are too polite. To be honest, I also like this child Qiao Yu." Yes, who doesn't like children with high intelligence?

..

Yanbei International Mathematics Research Center.

Qiao Yu still maintains his state of seriousness and selflessness. What is a peak showdown?

Of course, you have to put in 100% effort to defeat your opponent.

Mountain climbing is a long process, and those who claim to be able to reach the top of Mount Tai in one hour would be happy if they could see the gate of the scenic spot. Qiao Yu did not have this illusion, but he had to take every step steadily.

So he was very serious, more serious than he had ever been when dealing with difficult problems.

The geometric Langlands conjecture is a very complex proposition. Just like Schulz's quasi-complete space theory, it is characterized by the complexity of the theoretical framework. This makes it difficult for people to understand the paper, so he raises many questions.

At this time, his mathematical intuition is often more useful

Many of the to-the-point questions he raised were really based on mathematical intuition. For example, the question he just sent to Professor Pan. There are many technical obstacles when dealing with homology theory and spectral sequences related to the geometric Langlands conjecture.

This makes the selection and construction process of the model very complicated, and it is difficult for BunG not to be affected in this process. Any small technical mistakes will lead to imprecision in the paper, leading to failure of the proof. This is like a spaceship in space.

The docking between China and the space station is very similar.

Ordinary people understand that the space station is always suspended in space. The spacecraft only needs to slow down slowly, then align the interface, touch and lock it. But the actual situation is that the space station and the spacecraft are actually moving at high speed during the docking process.

.

The docking work must be completed at high speed, and any small mistake will lead to docking failure or even collision. The process of asking Professor Pan questions is the process of materializing these possible problems.

Qiao Yu has saved these into a directory in his mind. The next main task is to deduce and verify the possible situations in the directory, and then find the loopholes in the proof.

This is a very large project. Even the fourth and fifth papers total more than 300 pages.

But if he succeeds, it will be an even bigger project for the team studying this proposition.

Again, mathematical proof requires 100% correctness. If there is any inconsistency in logic, you need to find a way to make up for it.
To be continued...