Clay Institute of Mathematics, Cambridge, Massachusetts, USA.

Many people know this institute because of the famous Seven Problems of the Millennium, but what many people don't know is that this institute is actually not very old.

When the world was rewarded with the seven most difficult mathematical problems of the millennium, the institute had only been in existence for two years.

However, after all, this institute was funded by a mathematics professor at Harvard, and with Harvard's endorsement behind it, it still has great influence in the academic community. It's just that for the time being, it certainly can't be compared to the Institute for Advanced Study in Princeton.

Arthur Jeff of the Clay Institute learns that someone has solved the existential problem of the Yang-Mills solution.

Although a reward has been offered to the world, for the Clay Institute, it is natural that its own researchers will do corresponding research on the questions raised by itself.

Arthur Jeff is one of the mathematicians who has been working on the Young-Mills theory.

If it is really as Li Jiangao said before, if Qiao Ze proves the quality gap problem, only about twenty people in the world can read it for the first time, then Arthur Jeff is definitely one of these twenty people.

So when he learned that someone had proved the existence of a solution to the Yang-Mills equation, and that it had even been unanimously approved by the reviewers looking for by the Annals of Mathematics, the mathematician was surprised and annoyed.

"Professor Dugan, is that real? Has anyone really solved the existence of the solution of the Yang-Mills equation? ”

"You may be unhappy, but it's true."

"So I'm curious, why am I not one of the reviewers?"

"Hmm...... Have you ever won a Fields Medal? Or the Abel Prize? ”

"Lot!"

"Haha, okay, Arthur, just kidding, I just thought you weren't interested......

But then again, the five reviewers were all Fields Medal and Abel Medal winners, and I even excluded myself, you know, at least I'm in the PDE research direction. But you don't have to feel inferior, wait for a maximum of two papers, maybe half an hour, and they will be published on the official website. ”

“……”

"Alright, alright, another call is coming in, you see, I'm too busy today! So I'm sorry, I hung up first! ”

……

"Phew......" Lott Dugan hung up.

He really wanted to come to the door and "thank" Edward Witten.

It is because of this highly respected mathematical physicist that his phone has been busy today.

From the initial excitement, it is now almost numb.

There are those who inquire about the news, those who question it, and those who can't wait to see the papers.

Really, the editor-in-chief of the "Annals of Mathematics" is a little envious of the genius boy who is far away in China.

He wanted to share some news with Qiao Ze, but the other party turned off the phone!

However, counting the time difference, it is indeed very late in Huaxia.

But at this exciting time, how did that kid in Huaxia sleep?

Didn't he see the news in the background of the "Annals of Mathematics", which has been approved?

Well, even if Qiao Ze didn't see it, Edward Witten couldn't wait to spread the news to Huaxia, and Qiao Ze should know that his paper had passed the review, so shouldn't he raise a glass to celebrate at this time?

Lott Dugan was muttering in his heart when the phone rang again.

"Mr. Dugan, the editorial office has completed the final proofreading, and really, a paper of more than forty pages is so important...... Everyone didn't even take a break at noon. ”

"Haha, okay, let's publish it quickly! Don't worry, I'll help you claim a bonus. ”

"Yes, Mr. Dugan!"

Hanging up the phone, Lott Dugan put down the phone and smiled.

But thinking that Qiao Ze might be sleeping at this time, he felt very depressed, he really wanted to chat with Qiao Ze for the first time!

……

Qiao Ze was indeed sleeping at this time.

But he didn't sleep soundly, because he was dreaming, vivid dreams.

In the dream, he was confronted with a large and complex geometric configuration, which from a distance looked like a spiral structure, but if you look closely, you will find that each arc is composed of multiple lines, and countless curves are combined in a seemingly disordered but regular way, and finally become a complete structure.

What Qiao Ze did in his dream at this time was to observe the structure from all directions, and the equation composed of this line came to his mind.

"Ahh

The sudden sound of sneezing woke Qiao Ze from his dream.

Turning his head sideways, the window was already dark, and Chen Yiwen was crawling down from the bed.

"I'm sorry, I seem to have ...... rhinitis" Chen Yiwen, who climbed out of bed, took a special look at Qiao Ze, and found that Qiao Ze had opened his eyes and looked at him, and quickly apologized.

However, nothing happened to José.

His eyes were still looking at him directly, and his bright eyes made Chen Yiwen feel a little hairy in his heart.

"Forehead ......" Chen Yiwen just wanted to say something, but was suddenly interrupted by Qiao Ze.

"[ d_\mu f^{\muu} plus \alpha abla_\mu(\beta f^{\muu}) equals j^u ]"

"What do you mean?" Chen Yiwen touched his head, which was full of terms and sentences, which made him completely confused. The little heart is even more directly hanging into the throat, can't it? He shouldn't have sparked Qiao Ze crazy with a sneeze, right?

No, Qiao Ze can't be so timid?

So what went wrong?

"where (d_\mu) is the supercoil gauge covariant derivative, (f^{\muu}) is the supercoil field strength tensor of the gauge field, (j^u) is the source term of the gauge field, and (\alpha) and (\beta) are the curvature parameters of each line of this result."

"Huh?"

"But the definition of the supercoiled field strength tensor should include new dimensions and nonlinear relationships." Qiao Ze muttered to himself again.

"No, God Qiao, don't scare me!"

Really at this moment, Chen Yiwen was so panicked.

If Qiao Ze really had something wrong with his sneezing, he felt that Lord Dean might just kill him!

"Then the tensor of the supercoiled field strength of the gauge field should be equal to \partial^\mu a^u minus \partial^u a^\mu plus \gamma (a^\mu \ast a^u minus a^u \ast a^\mu)], where (\ast) represents the multiplication operation in supercoiled space algebra."

"No, Brother Qiao, God Qiao, what's wrong with you? Don't make a fuss, why don't you multiply? I really sneezed! Chen Yiwen was about to cry.

At this time, the other two who were sleeping were finally woken up.

Soon two heads poked out of the bed.

"It's only six and ten o'clock? Lao Chen, what are you muttering? ”

"yes, I'm sleepy."

"Sleepy fart, come down and see, there seems to be something wrong with God Qiao." Seeing the two wake up, Chen Yiwen hurriedly said.

"Huh?!"

"Bang ......"

Gu Zhengliang almost jumped off the bed directly, he was so flexible with a good figure, as for Zhang Zhou, he could only climb down the ladder step by step, rolled up the blanket and came to Qiao Ze's bed, the three men stood side by side beside Chen Yiwen, looking up at Qiao Ze.

Then I saw Qiao Ze's eyes, which seemed to be getting brighter and brighter.

"If you want to manipulate this structure now, you can define a manipulative field and transform the Yang-Mills equation into [ d_\mu f^{\muu} equals j^u + t^{u}], where (d_\mu) is the gauge covariant derivative, (f^{\muu}) is the field strength tensor of the gauge field, and (j^u) is the source term of the gauge field......"

The three of them began to look at each other.

Still incomprehensible, but they understood the words of the Yang-Mills equation transformation......

No one in the dormitory would think that Qiao Ze was pretending to be ......

But this time......

If this is the case, then the general solution formula of the manipulative field can be deduced first, and then this general solution can be brought into the Yang-Mills equation to obtain the general solution of the gauge field (a^\mu...... And then after spatial retransformation, we can get the solution of the Yang-Mills equation? ”

After speaking, Qiao Ze was stunned for a long time, and suddenly asked again: "How to derive the general solution of just the manipulation field?" ”

"Huh?"

The three men below looked at each other, then shook their heads at each other.

In the end, Chen Yiwen, who was the most daring, said tentatively: "We don't know!" ”

"What you don't know is that this is a whole new algebraic geometric configuration. I just dreamed about it when I dreamed last night, and it hasn't been proven yet. Qiao Ze explained, then silently got up from the bed and began to get dressed quietly.

There is still a trace of the intricate line structure in yesterday's dream, and if it were a while, it would probably be all forgotten. But just now, he had already analyzed some of the structures in the dream in his mind, and basically he would not forget it.

I just don't know if this can really be a way to solve the Yang-Mills solution.

Even Qiao Ze had a vague feeling that if he could really find the solution of the Yang-Mills equation in this way, then he could also prove the existence of mass gaps in this way, and even use this unconventional mathematical structure to explain many microscopic problems.

It's just that pure number theory questions such as the highly correlated Riemann conjecture have to be slowed down again......

Seeing that Qiao Ze's actions began to become normal, Chen Yiwen finally breathed a sigh of relief, but Qiao Ze's sentence "dreamed" once again made the three of them feel bad.

Everyone is young, and it is understandable to have spring dreams, but what normal person can dream of a bunch of formulas and algebraic geometric configurations that he can't understand?

"Hey...... Thinking about it day and dreaming at night? Josser, have you been thinking about the Yang-Mills equation lately? So you can't even dream about this problem? Zhang Zhou asked with a long sigh.

He used to think that he had worked hard enough, but now it seems that there is no comparison!

Anyone who can dream of doing scientific research.

Qiao Ze nodded slightly, and said, "Maybe, I used to think about a question, if I think about it very attentively and for a long time, I will occasionally have similar dreams. But dreams are just dreams after all, and they don't necessarily really solve the problem. ”

"No, Brother Qiao, have you really solved the problem by dreaming?"

"Well, when I was learning the principles of mathematical analysis on my own in the second grade of elementary school, I often encountered problems that I didn't know how to do that day, and I solved them when I dreamed, and then I got up the next day and understood them. But then this has been rare. ”

Qiao Ze, who was already dressed, nodded, replied casually, and then got up from the bed as well.

He was going to write down all the thoughts he had just thought.

Then take a closer look to see if you can really use this method to find the general solution of the Yang-Mills equation.

If you can, just find the general solution and throw it to the supercomputer verification, if the verification is successful, it means that the method is correct.

However, this paper will probably be very long, after all, it will involve a new spatial structure, as well as a mathematical configuration that is not known to be conventional.

To put it simply, it's all new.

Just talking about and making these new mathematical tools understandable and acceptable will require a long description. It's far from being as simple as the few formulas he just distilled.

After two presentations at Yanbei University and Huaqing University, Qiao Ze has found that the comprehension of mathematics in others is worrying.

Even those who are known to be smart.

Qiao Ze's words once again silenced the three people in the dormitory.

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Started teaching yourself mathematical analysis in the second grade of primary school? And then start solving the problem while dreaming?

Sure enough, there is a reason why some people can touch on mathematics.

At this time, everyone couldn't sleep, everyone began to get dressed silently, and after Qiao Ze went to the bathroom to wash up first, several people rushed into the bathroom together.

"I started teaching myself the principles of mathematical analysis in the second grade of primary school, damn it, I suddenly forgot what we learned in the second grade of primary school mathematics? Anyway, who remembers that they started learning geometry in the second grade? ”

"Phew, you want to learn geometry in second grade? You think you're a math genius too! I remember that the chickens and rabbits in the same cage only started to learn in the fourth grade. ”

"By the way, you remember the first day José came, we went to dinner together, and he said that he seemed to have taught himself the principles of mathematical analysis of Ludin! , I'm in the second grade of elementary school, and I'm teaching myself Ludin's book? It's pure math in it. I've heard that this textbook is written by Ludin for undergraduate honor-level analysis courses at universities in the United States. ”

"No, did you two get the point? The point is, in what grade did Qiao Shen start learning the principles of mathematical analysis? The point is that you can still learn while you are dreaming? ”

Chen Yiwen directly interrupted Zhang Zhou and Gu Zhengliang's words and emphasized.

He was so impressed by that scene just now.

Really, God knows how apprehensive Chen Yiwen felt when Qiao Ze suddenly spit out a bunch of formulas from his mouth that he didn't understand at all.

It really felt like I was almost going crazy.

"Actually, I seem to have had this situation, that is, when I was in high school, there was an Olympiad problem, so that I couldn't solve it in the middle of the night, and then I simply fell asleep, and the next day I suddenly solved it. But I don't remember if I had a dream that night. ”

Zhang Zhou scratched his head and said.

"Huh...... Then you can do research even if you dream? Young-Mills equation, you dreamed of solving it for me. Chen Yiwen squinted his eyes and glanced at Zhang Zhou's white and chubby face, and said disdainfully.

"No, first of all, you have to make me understand the equation. I don't even understand something, what a fart! Zhang Zhou complained.

Gu Zhengliang echoed on the side: "That's it, that's it!" ”

Chen Yiwen was too lazy to talk nonsense with these two people, and after washing up quickly, he walked back to the bedroom first, and asked Qiao Ze, who was already busy sitting in front of the computer: "God Qiao, didn't you dream yesterday that you found the solution to the Yang-Mills equation?" ”

"No, it's just a method, I'm not sure if it works." Qiao Ze replied casually.

"Oh, that must have worked. By the way, do you want me to bring you breakfast back in the morning? ”

"No, I'll bring the oranges."

"Lao Chen, I need, help me bring three fritters and a cup of soy milk......"

"I want five steamed buns, plum cabbage and meat filling, well, two cups of soy milk."

"Hehe, you call Dad first!"

"Phew, you can't be humiliated, I only have one father in the dormitory, it's our Brother Qiao!"

"Me too."

"Die!"

Chen Yiwen didn't bother to pay attention to the two shameless guys, and walked out of the bedroom,

After thinking about it, it didn't matter that it was less than seven o'clock at this time, so I took out my mobile phone and dialed it.

Xu Dajiang asked him, if Qiao Ze made any new discoveries in mathematics, if Chen Yiwen happened to know, he would definitely inform him.

Chen Yiwen also agreed.

Anyway, the dean, who is on Qiao Ze's side, will not be unfavorable to Qiao Ze.

"Hey, Dean Xu."

"Chen Yiwen, is there anything wrong with Qiao Ze?"

The voice on the other side sounded tired.

"It's nothing, that's the case, didn't you tell me yesterday that Brother Qiao wants to have any new ideas and tell you in time? It was yesterday that Brother Qiao had a dream, and I heard him say that in the dream, he seemed to have found a way to directly find the solution of the Yang-Mills equation. ”

"What? Dream? ”

"yes, yes. Anyway, this is the situation, you can ask us directly Qiao Geha, I don't know much about this. ”

“…… Oh, okay, thank you, Mr. Chen. ”

"Well, you're welcome, working hard to build our School of Mathematics of Xilin University of Technology is the common responsibility of all students of the School of Mathematics."

“……”

"Then Dean Xu, I'm hanging."

"Hmm."

……

Hanging up the phone, Xu Dajiang only felt very dazed for a while.

I've studied mathematics all my life, and I seem to have heard of someone who gets inspiration when they dream. But they are all biographies that have undergone various processing.

At least no one around him can solve a mathematical problem when he dreams.

He wasn't sure if Chen Yiwen was joking with him.

These kids don't seem to have much respect for him as a dean lately.

Forget it, Qiao Ze has already gotten up anyway, just call and ask.

Xu Dajiang was not afraid that Qiao Ze knew that it was Chen Yiwen who called him.

In fact, this was originally agreed by Qiao Ze.

At that time, Chen Yiwen was still one of the members of the group intelligence research group, and Xu Dajiang mentioned that the research group could talk to him about anything, and there were some questions that Qiao Ze felt were not important, so he asked Chen Yiwen to call him.

It's just that Chen Yiwen directly withdrew from the group of group intelligence, and there is no source.

As for his beloved disciples......

Forget it, thinking of Liu Chenfeng, Xu Dajiang became angry.

If you don't learn and don't know, you really don't learn and don't know, although you are mixed in Qiao Ze's research group, but there are important topics that he can't help, and he can't even mix a second work, and he can't get the news.

Even Qiao Ze made such an important proof, he didn't even hear the slightest news.

Recently, I was sent by Qiao Ze to take two sophomore undergraduates to do a project......

There is no use for fart!

It's just that what makes Xu Dajiang depressed is that when he calls Qiao Ze, his phone is still turned off.

Hey, after thinking about it, he still got out of bed.

Yesterday, I discussed with Dean Fan of the School of Physics until the middle of the night, and I didn't sleep for a few hours.

was woken up by a phone call from Chen Yiwen early this morning, and he couldn't lose his temper yet.

But......

Xu Dajiang did not wash, but rushed directly to the study first and opened the official website of the "Annals of Mathematics".

After a while, the decadence of the body was swept away.

Sure enough, at 4:10 a.m. yesterday, Qiao Ze's paper was hung on the front page of the official website of the Annals of Mathematics.

Looking at the title of the paper in large font "Proof of the Existence of Solutions to the Yang-Mills Equation", Xu Dajiang smiled happily and became more energetic, especially the "School of Mathematics, Xilin University of Technology" in the column of the author's unit.

After all, the School of Mathematics is in the hands of Xu Dajiang, and it has launched a charge against the top mathematics academy in China!

Which one dares to disagree?

Looking at China, even if it is Yanbei, who can publish three "Annals of Mathematics" in two months? Who can challenge the millennium puzzle casually? Who can publish nine papers in the top international journal in half a year?

Hey, Yanbei Academy, but Er'er, it's just a false name.

It's the Institute of Mathematics of the Chinese Academy of Sciences, so be it.

The future of Huaxia mathematics still depends on the Xilin Academy of Mathematics under his hands!

After quietly appreciating the title and abstract of the paper, Xu Dajiang casually downloaded and printed five copies of the paper, and then left the study to wash.

He didn't plan to read the paper, he didn't have that much time. But you have to print out a few copies first, and then put them in the office, and everyone who has recently visited, you have to send a copy. Five copies are definitely not enough, and the others can wait until the school to get more printed.

After all this was done, Xu Dajiang called Qiao Ze again.

This time it finally got through.

"Hey."

"Qiao Ze, that's right, I heard Chen Yiwen say this morning, you found a way to calculate the solution of the Yang-Mills equation when you were dreaming? Really? ”

"Not sure."

"Not sure?"

"It may be a direction, first to prove that the constructed spiral field has the same gauge symmetry as the Yang-Mills equation, and then to prove the mathematical consistency, and then there is another difficulty, which needs to find the general solution of the manipulative field, and then convert."

"Spiral field?"

"Well, an unconventional mathematical structure. contains some hypothetical mathematical objects with non-traditional symmetry"

Xu Dajiang felt that his brain was a little insufficient.

But it sounds reasonable, it's abstract enough.

If it weren't so abstract, this problem wouldn't have bothered you for so long.

"Do you think this method can solve the problem?"

"Not sure."

"Oh...... Well, I see, but if I do the math......"

"I remember."

"That's okay, that's okay, you get busy first, I'll take care of it."

"Oh, hang up."

"Good ......"

"Doodoo ......"

Xu Dajiang didn't pay attention to the busy tone on the phone.

It's not the first time that Qiao Ze has hung up the phone quickly, and it's not specifically for him alone.

Willing to answer his phone is already very face-saving.

The calls of the big professors in Yanbei Institute of Science and Technology may not be willing to answer the children.

However, Xu Dajiang plans to record this incident.

If Qiao Ze really used the method he thought of in his dream in the future to calculate the solution of the Young-Mills equation, the children of later generations would have one more legendary story of a mathematician, of course, this is still secondary, this awesome enough for him to blow until the day of his death.

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