Clay Mathematics Institute, Cambridge, MA, USA.
Many people know this institute because of the famous Seven Millennium Problems, but what many people don’t know is that the history of this institute is not very long.
The institute had only been around for two years when it offered bounties to the world for the Seven Millennium Mathematics Puzzles.
However, after all, this institute was founded with funds raised by Harvard mathematics professors, and with the endorsement of Harvard, it still has great influence in the academic world. It’s just that it certainly can’t be compared to the Institute for Advanced Study in Princeton for the time being.
It was in the afternoon that Arthur Jeff of the Clay Institute learned that someone had solved the problem of the existence of Yang-Mills theoretical solutions.
Although a reward has been issued to the world, for the Clay Institute, its own researchers will naturally conduct corresponding research on the questions it raises.
Arthur Jeff is one of the mathematicians who has been studying Yang-Mills theory.
If it is true as Li Jiangao said before, if Qiao Ze proves the quality gap problem, only about twenty people in the world can understand it immediately, 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 it was even unanimously recognized by the reviewers sought by the Annals of Mathematics, the mathematician was surprised, but his first feeling was anger.
"Professor Dugan, is that true? Has anyone really solved the existence of solutions to the Yang-Mills equation?"
"You may not be happy, but it's true."
"So I'm curious, why am I not one of the reviewers?"
"Hmm... have you won the Fields Medal? Or the Abel Prize?"
"Lot!"
"Haha, okay, Arthur, just kidding, I just thought you weren't interested...
But then again, the five paper reviewers are indeed Fields Medal and Abel Prize winners. I even excluded myself. You know, at least I am also in the research direction of pde. But you don’t have to feel inferior. The paper will be published on the official website after waiting for at most two, maybe half an hour. "
"..."
"Okay, okay, another call came in. Look, I'm too busy today! So I'm sorry, I'll hang up now!"
…
"Huh..." Lot Dugan hung up the phone.
He really wanted to come and "thank" Edward Witten.
Just because of this respected mathematical physicist, his phone has been busy today.
From the initial excitement, now I am almost numb.
Some are inquiring, some are questioning, and some can’t wait to see the paper.
Really, the editor-in-chief of "Annual Review of Mathematics" is a little envious of that genius kid far away in China.
He wanted to share some news with Qiao Ze, but the other party turned off his phone!
But after calculating the time difference, China time is indeed very late.
But at this exciting time, how could that boy from China sleep?
Didn't he see the news from the backstage of "Annals of Mathematics" that it had been approved?
Well, even if Qiao Ze didn't see it, Edward Witten couldn't wait to spread the news to China. Qiao Ze should also know that his paper has passed the review, so shouldn't he raise a toast at this time? ?
While Lot Dugan was muttering in his heart, the phone rang again.
"Mr. Dugan, the editorial department has completed the final proofreading work. Really, the paper of more than 40 pages is so important... everyone didn't even take a break at noon."
"Haha, okay, let's publish it quickly! Don't worry, I will help you apply for a bonus."
"Okay, Mr. Dugan!"
After hanging up the phone, Lot Dugan put down the phone with a smile on his face.
But thinking that Qiao Ze might be sleeping at this time, he felt very depressed. He really wanted to chat with Qiao Ze as soon as possible!
…
Qiao Ze was indeed sleeping at this time.
But he didn't sleep well because he was dreaming, a vivid dream.
In the dream, he was facing a huge and complex geometric configuration. From a distance, it looked like a spiral structure. But if you look closer, you will find that each arc is composed of multiple lines, and the countless curves resemble a spiral structure. They are put together in a disorderly but regular way, and finally become a complete structure.
At this time, what Qiao Ze was doing in his dream was to observe the structure from all directions, and the equations composed of these lines emerged in his mind.
"Ah sneeze!"
The sudden sound of sneezing woke Qiao Ze from his dream.
He turned his head and glanced, it was already dark outside the window, and Chen Yiwen was climbing down from the bed.
"I'm sorry, I think I have rhinitis..." Chen Yiwen climbed out of bed and took a special look at Qiao Ze. He found that Qiao Ze had opened his eyes and looked at him, and quickly apologized.
However, Qiao Ze didn't react at all.
Her eyes were still looking straight at him, and her shining eyes made Chen Yiwen feel a little scared in her heart.
"Uh..." Chen Yiwen was about 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. The terms were all so confusing that he was completely confused. My little heart was lifted directly into my throat, couldn't I? Could it be that his sneeze scared Qiao Ze crazy?
No, Qiao Ze can't be so timid?
So what went wrong?
"Wherein, (d_\mu) is the superhelical gauge covariant derivative, (f^{\muu}) is the superhelical field strength tensor of the gauge field, (j^u) is the source term of the gauge field, (\alpha ) and (\beta) are the curvature parameters formed by each line of this result."
"ah?"
"But the definition of the superhelical field strength tensor should include new dimensions and nonlinear relationships." Qiao Ze said to himself again.
"No, God Qiao, don't scare me!"
At this moment, Chen Yiwen was really panicking.
If something went wrong with Qiao Ze because of his sneezing, he thought the dean might just beat him to death!
"Then the superhelical field strength tensor 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 superspiral space algebra."
"No, Brother Qiao, God Qiao, what's wrong with you? Just stop making trouble, okay? What about multiplication and not multiplication? I really just sneezed!" Chen Yiwen was about to cry.
At this time, the other two people who were sleeping were finally woken up.
Soon two heads popped out of the bed.
"It's only six-ten? Old Chen, what are you muttering about?"
"That's right, I'm so sleepy."
"You're so sleepy, come down and take a look, there seems to be something wrong with God Qiao." Chen Yiwen said quickly when he saw the two of them waking up.
"ah?!"
"boom……"
Gu Zhengliang almost jumped off the bed. His figure was so flexible. As for Zhang Zhou, he could only climb down from the ladder step by step. He rolled up the blanket and came to Qiao Ze's bed. The three men stood side by side in front of Chen Yiwen. Beside him, he looked up at Qiao Ze.
Then he saw Qiao Ze's eyes seeming to get brighter and brighter.
"If you want to operate this structure now, you can define a manipulation 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, (j^u) is the source term of the gauge field..."
The three people began to look at each other.
They still don’t understand, but they understand the words Yang-Mills equation transformation...
No one in the dormitory would think that Qiao Ze was showing off...
But this time...
"If this is the case, then you can first derive the general solution formula of the manipulation field, and then bring this general solution into the Yang-Mills equation, and you can get the general solution of the gauge field (a^\mu)... and then re-transform it through space , can we get the solution to the Yang-Mills equation?"
After saying that, Qiao Ze was stunned for a long time, and suddenly asked: "How can we derive the general explanation of the control field?"
"ah?"
The three people below looked at each other, then shook their heads.
In the end, Chen Yiwen, who was the boldest, said tentatively: "We don't know!"
"You must not know that this is a brand-new algebraic geometry configuration. I just dreamed about it when I was dreaming last night. It has not been proven yet." Qiao Ze explained, then silently got up from the bed and started Quietly put on clothes.
There are still traces of the complex structure of lines in yesterday's dream in my mind, and if it takes a while, I will probably forget them all. But he has just analyzed some of the structures in the dream in his mind, and he will basically never forget them.
I just don’t know if this can really be a direction to solve the Yang-Mills solution.
Qiao Ze even had a vague feeling that if he could really find the solution to the Yang-Mills equation in this way, he could also use this method to prove the existence of the mass gap, and even use this unconventional mathematical structure to explain many things. Micro issues.
It’s just that pure number theory issues such as the highly relevant Riemann Hypothesis 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 words "dream" once again made all three of them feel bad.
We are all young people, so it is understandable that we have erotic dreams, but which normal person can dream about a bunch of incomprehensible formulas and algebraic geometric configurations?
"Hey... I think about it every day and dream about it at night? Qiao Ze, have you been thinking about the Yang-Mills equation recently? So you don't even let go of this problem in your dreams?" Zhang Zhou asked with a sigh. .
He originally thought that he worked hard enough, but now it seems that there is no comparison!
Anyone who can dream is doing scientific research.
Qiao Ze nodded slightly and said, "Maybe. In the past, if I thought about a problem very concentratedly and for a long time, I would occasionally have similar dreams. But dreams are just dreams after all, and they may not really solve the problem. "
"No, Brother Qiao, have you really solved problems by dreaming?"
"Well, when I was studying the principles of mathematical analysis by myself in the second grade of elementary school, I often encountered problems that I couldn't solve that day. I solved them while dreaming, and then I understood them when I got up the next day. But later this situation became very common. not enough."
Qiao Ze, who was already dressed, nodded, answered casually, and then got up from the bed.
He wanted to record all his thoughts.
Then study carefully whether this method can really be used to find the general solution to the Yang-Mills equation.
If possible, just find the general solution and then throw it to the supercomputer for verification. If the verification is successful, it means that this method is correct.
However, this paper will probably be very long. After all, it involves a new spatial structure and an unconventional mathematical configuration.
Simply put, it's all new.
Just to discuss and make people understand and accept these new mathematical tools requires a long description. It's far from as simple as the few formulas he just extracted.
After two lectures at Yanbei University and Huaqing University, Qiao Ze has discovered that other people's understanding of mathematics is worrisome.
Even those guys who are considered very smart.
Qiao Ze's words once again caused the three people in the dormitory to fall into silence.
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Start teaching yourself mathematical analysis in the second grade of elementary school? Then start solving problems while dreaming?
Sure enough, there is a reason why some people can understand mathematics by analogy.
Now everyone couldn't sleep, and everyone began to put on their clothes silently. After Qiao Ze went to the bathroom to wash up, several people rushed into the bathroom together.
"I started to teach myself the principles of mathematical analysis in the second grade of elementary school. Damn it, I suddenly forgot what we learned about mathematics in the second grade of elementary school? By the way, who remembers that we started learning geometry in the second grade?"
"Bah, you want to learn geometry in the second grade? Do you think you are also a math genius? I remember that the chicken and the rabbit in the same cage didn't start learning until the fourth grade."
"By the way, do you remember that when Qiao Ze came here on the first day, we went to have dinner together, and he said that he seemed to have learned Ludin's principles of mathematical analysis on his own! Damn it, in the second grade of elementary school, that book about Ludin's self-study? Mathematics. I heard that only honor-level undergraduate analysis courses in universities in the United States use this textbook compiled by Ludin."
"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, can you still learn while dreaming?"
Chen Yiwen directly interrupted Zhang Zhou and Gu Zhengliang's words and emphasized.
The scene just now left a deep impression on him.
Really, God knows how uneasy Chen Yiwen felt when Qiao Ze suddenly spit out a bunch of formulas that he couldn't understand at all.
In fact, I felt like I was almost going crazy with fear.
"Actually, I seem to have been in this situation before. When I was in high school, I couldn't solve a Mathematical Olympiad problem in the middle of the night. Then I just took a nap and suddenly solved it the next day. But did you have any dreams that night? , I really don’t remember.”
Zhang Zhou scratched his head and said.
"Ha... Then you can do research even in your dreams? The Yang-Mills equation, you can explain it to me in your dreams." Chen Yiwen squinted at Zhang Zhou's white and fat face and said disdainfully .
"No, you have to let me understand that equation first. What nonsense do you think I don't understand?" Zhang Zhou complained.
Gu Zhengliang echoed from the side: "Yes, yes!"
Chen Yiwen was too lazy to talk nonsense with these two people. After washing up quickly, she walked back to the dormitory and asked Qiao Ze who was already sitting in front of the computer: "Qiao Shen, didn't you dream yesterday that you could solve the Yang-Mills equation?" Have you found out all the solutions?"
"No, it's just a method. I'm not sure if it will work." Qiao Ze responded casually.
"Oh, that must be useful. By the way, do you want me to bring you breakfast in the morning?"
"No, Cheng Zi will bring it to me."
"Old Chen, I need you to bring me three fried dough sticks and a cup of soy milk..."
"I want five steamed buns, stuffed with pickles and vegetables, um, and two cups of soy milk."
"Haha, you call me daddy first!"
"Bah, Shi Ke can't be killed. I only have one father in the dormitory, and that's our Brother Qiao!"
"me too."
"Go to hell!"
Chen Yiwen was too lazy to deal with the two shameless guys and walked out of the dormitory.
After thinking about it, regardless of the fact that it was not yet seven o'clock, I took out my mobile phone and made a call.
Xu Dajiang asked him that if Qiao Ze made any new mathematical discoveries, and if Chen Yiwen happened to know about it, he would inform him.
Chen Yiwen also agreed.
Anyway, the dean who is on Qiao Ze's side will not be disadvantageous to Qiao Ze.
"Hello, Dean Xu."
"Chen Yiwen, what's wrong with Qiao Ze?"
The voice on the other side sounded tired.
"It's nothing, it's like this. Didn't you specifically tell me yesterday that Brother Qiao had any new ideas and let you know in time? It's just that Brother Qiao had a dream yesterday, and I heard him say that he seemed to have found a new idea in his dream. A method that can directly find solutions to the Yang-Mills equation."
"What? Dreaming?"
"Well, that's right. Anyway, that's the situation. You can just ask Brother Qiao directly. I don't know much about this aspect."
"...Oh, okay, thank you, classmate Chen."
"Well, you're welcome. Working hard to build our School of Mathematics at Xilin University of Technology is the common responsibility of all students in the School of Mathematics."
"..."
"Then I'm dead, Dean Xu."
"Um."
…
After hanging up the phone, Xu Dajiang felt confused for a moment.
After studying mathematics all my life, I seem to have heard of people getting inspiration while dreaming. But they are all biographies that have been processed in various ways.
At least no one around him could solve a mathematical problem in his dreams.
He wasn't even sure whether Chen Yiwen was making fun of him.
The kids seemed to have less respect for him as the dean these days.
Forget it, Qiao Ze is already up anyway, just call and ask and he will find out.
Xu Dajiang was not afraid that Qiao Ze would know that it was Chen Yiwen who called him.
In fact, this was approved by Qiao Ze.
At that time, Chen Yiwen was still a member of the group intelligence research team. Xu Dajiang mentioned that the research team could talk to him about anything. For some issues that Qiao Ze felt were not important, he asked Chen Yiwen to call him.
But later, Chen Yiwen directly quit the group intelligence research group, without any source of information.
As for his beloved disciple...
Forget it, Xu Dajiang gets angry when he thinks of Liu Chenfeng.
Ignorant of knowledge and skills, really ignorant of skills. Although he got into Qiao Ze's research group, he couldn't help with important topics. He couldn't even get into the second work, that's all. He couldn't even find out the news. arrive.
Even though Qiao Ze made such an important proof, he didn't even get the slightest bit of information.
Recently, Qiao Ze sent two sophomore undergraduate students to do a project...
It’s useless!
What made Xu Dajiang depressed was that when he called Qiao Ze, his phone was still turned off.
Hey, after thinking about it, he still got up from the bed.
Yesterday, I discussed with Dean Fan from the School of Physics until midnight and didn't sleep for a few hours.
Another early morning wake-up call from Chen Yiwen made him unable to lose his temper.
but……
Xu Dajiang did not wash up, but rushed directly to the study room and opened the official website of "Annual Review of Mathematics".
After a while, all the decadence was gone.
Sure enough, at 4:10 yesterday morning, Qiao Ze's paper was posted on the homepage of the official website of "Annals of Mathematics".
Looking at the large font title of the paper "proof of the existence of solutions to the yang-mills equation", Xu Dajiang smiled and became more energetic, especially the "school of mathematics, xilin" in the column of the author's affiliation. university of technology", no matter how you look at it, it will please your eyes.
After all, the Mathematics Academy is in his hands, Xu Dajiang, and has launched a charge towards the top Mathematics Academy in China!
Who dares to dissent?
Looking at the country, even Yanbei, who can publish three "Annual Review of Mathematics" in two months? Who can easily challenge the millennium problem? Who can publish nine papers in top international journals in half a year?
Alas, Yanbei Shuyuan is nothing more than mediocre and has an empty reputation.
It's the Institute of Mathematics of the Chinese Academy of Sciences, that's all.
The future of Huaxia Mathematics still depends on the Xilin Institute of Mathematics under his control!
After quietly appreciating the title and abstract of the paper, Xu Dajiang downloaded and printed five copies of the paper, and then left the study to wash up.
He didn't plan to read the paper, he didn't have that much time. But you must print out a few copies first and put them in the office later. Anyone who comes to visit recently must give a copy. Five copies are definitely not enough. The others can wait until the school and ask people to print more.
After finishing all this, Xu Dajiang called Qiao Ze again.
This time it finally got through.
"Hello."
"Qiao Ze, it's like this. I heard Chen Yiwen say this morning that you found a method to calculate the solution to the Yang-Mills equation in your dream? Is it true or false?"
"uncertain."
"uncertain?"
"It may be a direction. First, we need to prove that the constructed spiral field has the same gauge symmetry as the Yang-Mills equation, and then prove the mathematical consistency. Next, there is a difficulty. We need to find a general solution to the manipulation field and then convert it."
"Spiral field?"
"Well, an unconventional mathematical structure. Contains some hypothetical mathematical objects with unconventional symmetries"
Xu Dajiang felt that his brain was a little weak.
But it sounds reasonable, since it's abstract enough.
If it weren't so abstract, this problem wouldn't have bothered everyone for so long.
"Then do you think this method can solve it?"
"uncertain."
"Oh...well, I understand, but if I figure it out..."
"I remember."
"Okay, okay, you go ahead and do your work, I'll just take care of you."
"Oh, hung up."
"good……"
"Dududu..."
Xu Dajiang didn't care about the busy signal on the phone.
This wasn't the first time that Qiao Ze hung up the phone, and it wasn't specifically targeting him.
It's already a big honor to answer his call.
Children may not even answer the phone calls from the great professors at Yanbei Institute of Mathematics.
But Xu Dajiang planned to record this matter.
If in the future Qiao Ze really uses the method he thought of in his dreams to calculate the solution to the Yang-Mills equation, children in future generations will have another legendary story of a mathematician. Of course, this is the second one. This awesomeness will be enough for him to brag about until the day he dies. .
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