When the formula for the general solution was displayed on the big screen, the audience was stunned at first, and then there were endless exclamations in various languages. Then countless mobile phones were taken out. Looking down from the reporting table, everyone began to look at Qiao Take a picture of the results given by Ze.
If this is the surprise Xu Dajiang said, then this surprise is a little too big.
The young man on the stage actually directly solved the general solution of the Yang-Mills equation?
So is this still far from completely solving the mass gap problem?
In the first row, after Mr. Yang stared at the general explanation result given by Qiao Ze for a long time, he turned his head and looked at Li Jiangao beside him in astonishment and asked: "Do you know?"
Li Jiangao shook his head blankly, feeling no less surprised than anyone else present.
He only knew that Qiao Ze had been in retreat recently, and he really didn't know what he was studying in retreat.
Behind him, Edward Witten had already taken a photo of the formula, edited it and sent it to his mailbox, and then made a phone call.
"Hey, Neo, I just sent the general solution to the Yang-Mills equation to your email. Please use my dedicated channel to verify it immediately."
"Um? Mr. Witten? What did you just say? The general solution of the Yang-Mills equation?"
"Yes, you heard it right. I thought that when I came to China this time, I was just going to listen to a report on the existence of solutions, but who would have thought that at the beginning of the report, the kid would directly give the general solution."
"Is that so? It's amazing! Well, Mr. Witten, although I have gone home now, for the sake of solving the Yang-Mills equation, I am willing to work overtime."
"Thank you, Neo, check your email."
After saying that, Edward Witten hung up the phone, and several people around him immediately started talking to him.
"Edward, do you think Qiao Ze's general explanation is correct?" Lott Dugan still had a strong sense of surprise in his tone.
Edward Witten curled his lips and replied: "I don't study mathematics, let alone PDE, so you are wrong to ask me. Maybe Daniel understands."
These words directly shocked Lot Dugan. He was speechless for a moment, and then glanced at Daniel who was still in a daze next to him...
Ever since Edward Witten called the supercomputer, this guy has been in a daze, and it seems that there is no hope. Too lazy to pay attention to the two people around him, Lot Dugan turned around and saw the young European mathematician Peter Schulz staring at the screen, and his eyes lit up.
"Hey Peter, do you think this is right?"
"Huh?" This young man who is recognized as the most likely to solve the problem of unification of mathematics glanced at Lot Dugan blankly, then curled his lips and asked: "Professor Dugan, are you serious?"
"What's the meaning?"
"Do you think someone's brain can match that of a supercomputer?"
"Forehead……"
"Professor Dugan, this is not something that mathematicians can do. We have to let those who work on computers do it."
"Of course I know, I mean intuition...Has your mathematical intuition failed?"
"Haha... Who dares to have intuition about this problem? Not to mention that there is no proof process yet. However, thinking from another perspective, if I have not verified whether the result is correct, I will definitely not dare to directly announce the general solution on such an occasion. "
…
At the same time, almost all the professors in the front row who could contact the supercomputer were busy.
Fortunately, many professors were from the same school, so one representative called and the others started the discussion in a tacit understanding.
Among the professors at Yanbei University, it was Zhang Hongcai who called back immediately.
"Has the school started verification?" Qian Yuhai asked quickly.
"Well, the instructions have been given. The programming will be completed within half an hour, and then it will be immediately connected to the supercomputer. By the way, it will be verified with the Tianhe-1 of the Chinese Academy of Sciences." Zhang Hongcai replied concisely.
Yanbei has its own supercomputing platform, but its speed is certainly not as fast as those of several national supercomputing platforms.
In addition, Huaqing, Harvard, Columbia, Clay Research Institute...
All units capable of verification spread the news as soon as possible.
As for those scholars and students who are unable to mobilize supercomputers, they are not idle either.
Social media and question-and-answer websites such as Twitter, Facebook, domestic Moments, Weibo, and Dahuhu have become the main sites.
"God, you guys absolutely can't believe what I saw. The general solution to the Yang-Mills equation! I actually saw it for the first time! If the result is correct, do I participate in history?!"
"It's crazy, it's crazy! Don't say we can't sit still, even those big-name professors in front can't sit still!"
"Big news, Xilin Qiaoze gave the general solution to the Yang-Mills equation at the beginning of his thousand-person lecture conference. No one among the academic leaders at the scene dared to question it!"
"I'm so excited, and I hope this general explanation is correct, because after I listen to Qiao Ze's explanation, my doctoral thesis will have a direction!"
"Excuse me, how can I verify this thing? I cried to death, undergraduates have no human rights! I went to study the Yang-Mills equation yesterday and found that I couldn't understand it. I saw this general solution today and still don't understand it!"
"Brother, let me remind you, the guy on the stage is also an undergraduate. He seems to be in his sophomore year!"
…
Qiao Ze on the stage ignored the bursts of noise from the audience.
I just waited silently in my heart for ten minutes to pass.
Then he picked up the pen and walked to the first blackboard.
The cameras at the scene immediately began to move with Qiao Ze and projected the blackboard that Qiao Ze was walking towards on the big screen.
Otherwise, except for the people in the first five rows, no one behind will be able to clearly read the content written on the blackboard.
"The Yang-Mills theory describes the dynamics of the gauge field, which is specifically expressed as an equation that is satisfied by the field strength tensor of the gauge field. It is extremely difficult to solve it directly, whether it is the existing mathematical tools or what I have proved before. The segmentation method for the existence of solutions to the Yang-Mills equation is not enough to complete this task, so we can only find another way.
To this end, I designed a relatively special algebraic structure, which I named superspiral space algebra. The first step I took in order to be able to solve it successfully was to reinterpret the dynamics of the gauge fields in superhelical space algebra.
So next I need everyone to understand these basic concepts, the superhelical gauge covariant derivative, the superhelical field strength tensor of the gauge field, the source term of the space gauge field, and several important curvatures that only take effect in superhelical space. parameter……"
He did not deliberately silence the scene. When Qiao Ze walked to the blackboard and started writing on the blackboard, and began to introduce his latest research results, the noisy scene immediately became quiet, and everyone's eyes were focused on the big screen. .
Especially the big guys in the front row...
At this moment, I feel like my brain is exploding!
really!
It's the new math!
Of course this seems reasonable.
Because any known mathematical tool, a group of mathematicians attracted by this proposition have already tried it, it is impossible to solve this problem.
But superspiral space algebra?
Is this span too big?
"Okay, now that we understand these mathematical concepts, we can change the Yang-Mills equation, just like the familiar Fourier transformation. This step is very simple. The original Yang-Mills equation is in superspiral algebra The variations in space are as follows:
[ d_\mu f^{\muu}+\alpha abla_\mu(\beta f^{\muu})= j^u ]. "
…
All the math experts in the audience stared blankly at the derivation process on the big screen.
Many of them seem to be rediscovering the feeling they had when they were in school.
The only problem is that most people have passed the age of learning, and their ability to accept new knowledge has significantly declined. Qiao Ze on the stage has no idea of taking care of these elderly people. Not only can he write quickly, he can also speak in one sentence. He didn't bother to add anything more to what he had finished.
As for the many students attending today, their brains are still very young and they should be able to keep up with the pace. The problem is that their knowledge reserves are seriously insufficient.
Although superspiral space algebra is a brand new algebraic field, this algebraic field is based on previous knowledge of algebraic geometry.
Without a deep understanding of Hibbert space, Hamiltonians describing systems in quantum mechanics, topological physics, topological insulators and other subjects, it is also difficult to understand these so-called "simple concepts" in superspiral space algebra.
Especially regarding ultra-high-dimensional computations, performing high-order multiplication operations in superspiral space algebra is extremely abstract.
Unfortunately, Qiao Ze may be an extremely good scholar, but he is obviously not a competent professor. He didn't even care whether the people in the audience could understand what he said.
"Next are several important formulas about superhelical space algebra. The first is the Taylor expansion of superhelical derivatives. We assume that (d) is the superhelical derivative operation in superhelical algebra space. Then for any smooth function (f), The Taylor expansion of the superhelical derivative can be written as:
[ f(x +\delta x)= f(x)+ df(x)\delta x +\frac{1}{2} d^2f(x)(\delta x)^2 +\ldots ]
Here (d^2) represents the second order of the superhelical derivative. From this, we can calculate the superhelical expansion of the field strength tensor:
Consider the gauge field (a^\mu) in the superhelical algebraic space, and its field strength tensor is (f^{\muu}= d^\mu a^u - d^u a^\mu). Then the superhelical expansion of the field strength tensor can be expressed as:
[ f^{\muu}(x)= f^{\muu}_0(x)+ d f^{\muu}_0(x)\delta x +\frac{1}{2} d^2 f^{ \muu}_0(x)(\delta x)^2 +\ldots ]
Here, (f^{\muu}_0) is the initial field strength tensor of the gauge field. Next is the curvature tensor expansion of the superhelical space. Consider the curvature tensor (r) of the superhelical algebraic space, which can be expressed as the commutator of the superhelical derivative. Then the expansion of the curvature tensor can be written as:
[ r(x)= r_0(x)+ dr_0(x)\delta x +\frac{1}{2} d^2r_0(x)(\delta x)^2 +\ldots ]
Here’s the key point, (r_0) is the initial curvature tensor of the superhelical algebraic space. The next step is to perform differential operations on the superhelical field according to these formulas to obtain this result:
[ df(x)=\lim_{\delta x o 0}\frac{f(x +\delta x)- f(x)}{\delta x}]......"
Swish, swish, swish...
When Qiao Ze quickly wrote a series of expansion formulas on the blackboard, the audience finally became no longer quiet.
"God...I want to protest! Can't you speak slower?"
When the first person started shouting suddenly, there were many echoes immediately.
"No, it's not a matter of speaking fast or slowly! If you want people to understand this new mathematical system, you shouldn't use such difficult examples directly! You should go from easy to difficult!"
"Yeah, can't we use a few simple examples first? Why analyze the Yang-Mills equation directly? Why can't we start with the single-variable nonlinear equation?"
Some people roared directly regardless of the rules, while others took this opportunity to whisper.
"Daniel, do you understand?"
"I feel like such a report would be unfair to people our age!"
"Okay, so...Edward?"
"There is only a thin line between understanding mathematics and not understanding it. My suggestion is to take pictures of these processes first."
I must admit that this answer is very rigorous.
"No, I will ask the organizing committee for a copy of the video. I believe it will not be difficult."
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"Hi Peter, you're the youngest among us..."
"Hmm... I seem to understand a little bit. I suggest you start with the characteristics of space to understand what he said."
"Okay! But I think the most important thing is the results! If the results are correct, these will only make sense!"
"I seem to have a feeling about this, and the result seems to be right!"
"Oh? Phew..."
Later, a group of professors from China were also in the discussion stage.
"Lao Zhang, I feel like we shouldn't have come!"
"hehe."
"Yeah, when we got back, someone asked us what we gained from this visit. I was embarrassed to speak."
"Indeed...it's a bit too much."
"Fortunately, I don't study PDE."
"Sorry, this is actually out of the scope of PDE, at least out of the scope of PDE that we are currently studying."
Further back, the people who had been keeping quiet and dared not speak became active at this time.
"Huh... do you understand even a little bit?"
"Well, are you talking about a new algebraic form? At least I know. He solved this problem using a method called superspiral space algebra."
"Pfft... what about other than that?"
"Don't ask me, this math is different from what I've learned before."
As for those students...
"Well, we actually learned fake math, right?"
"Don't belittle yourself like this. Listen to the roars of those big guys in front! I doubt they can understand either."
"No need to doubt it! Isn't it obvious?!"
"Haha, it turns out that today we enjoy the same treatment as the big guys! It turns out that Taylor's formula can be calculated in this way. Although I don't understand it at all, it seems to make sense! It's just not beautiful at all."
"No, what are you so happy about? Qiao Ze is only a sophomore this year! Speaking of which, we are one grade above him!"
"Please don't open any pot or pick up any pot!"
…
Principal Chen in the front row could not sit still.
Ever since Qiao Ze directly announced the general solution formula, he didn't expect to understand what Qiao Ze was talking about.
But what the hell is the sudden breakdown in venue discipline?
We are all decent people and intellectuals. How could we suddenly start shouting in the middle of a report meeting?
Just when Chen Yuanzhi was still thinking about how to get this report meeting back on track, Qiao Ze had already turned around and began to face the audience. That young face was three parts serious, three parts puzzled, and three parts Partly annoyed and partly troubled...
"Everyone..."
The audience gradually became quiet.
"This is just the most basic expansion part of supercoil. It is far from the most difficult part of solving the Yang-Mills equation. If you don't understand what is going on here, I suggest you leave directly.
I never like stupid people, but stupid here does not specifically mean lack of IQ. So please don't make any noise. There will be half an hour of Q&A time in today's report. If you don't understand now, please don't disturb those scholars who can understand to follow my derivation steps. "
After listening to Qiao Ze's words, Chen Yuanzhi felt that cold sweat had broken out on his forehead.
"stupid?!"
Fifty percent of the scholars sitting in the front row have won Fields Medals, and 25% are Nobel Prize winners. As for the remaining ones, they have also won various other awards. International awards, or editors of top international journals, are the group of people recognized internationally as the most academically influential.
Not to mention that there are many Chinese academicians present today.
Qiao Ze's words could probably offend at least 90% of them, right?
After all, judging from the reaction in the front row just now, it seems that there are really not many people who can understand and follow Qiao Ze's discussion.
However, before Chen Yuanzhi racked his brains to come up with a way to smooth things over, Qiao Ze felt that the audience had quieted down, and he turned his head with satisfaction and continued his deduction.
"Okay, the above operation has come to an end. Next we need to do the first difficult analysis, deriving the field equation suitable for superspiral space. Then we can bring it into the Yang-Mills equation for solution. First we need to construct a Lag Langian density, please note that the nonlinear terms of its field strength tensor must be taken into account when constructing it, so we can get:
[\mathcal{l}=-\frac{1}{4} f^{\muu}f_{\muu}+ext{nonlinear term}(a^\mu)]......"
Principal Chen let out a sigh of relief...
Fortunately, there was no farce where the big guys in the front row left the venue one after another!
And the discipline at the venue seemed to have gotten better, but many people silently took out their mobile phones.
All right……
No matter what, today should be a successful report meeting.
What Principal Chen didn't know was that Xu Dajiang, who was standing far away at this time, was completely stunned after Qiao Ze said those words!
He knew that today's report would be exciting, but he didn't expect it to be so exciting!
Xu Dajiang was the only person in this report meeting who knew that the general solution derived by Qiao Ze had not been verified by supercomputing.
If the results of the super calculation the next day are correct, everything will be easy to say...
If Qiao Ze is wrong, just based on what he said just now...
Xu Dajiang no longer dared to think further.
At this time, it seems that he can only believe that Qiao Ze must be right!
Damn, this is so wrong!
…
The discipline in the venue has been maintained, except for the occasional whispers, but it is no longer enough to affect Qiao Ze's blackboard writing and deductions on the stage.
But soon another question was placed in front of Xu Dajiang.
Qiao Ze's report meeting timed out!
It was originally scheduled that the morning report meeting would start at nine o'clock and end at eleven o'clock.
Then most people go directly to the lobby arranged by the hotel to eat the buffet.
In addition, ten private rooms were booked to entertain some distinguished guests.
But it's already half past eleven.
Yu Chenggong had already made two calls to ask if the food was served.
Yes, Yu Chenggong was responsible for all the contacts with the hotel this time.
But the blackboard used for writing was already full of five words, but Qiao Ze had no intention of stopping.
This is crazy...
Xu Dajiang felt like bubbles were coming out of his mouth again...
There was no other way, so he simply bent down and walked to Principal Chen, leaned down and whispered: "Principal Chen, look, it's already dinner time, what should I do?"
"This... yes, it's time to eat." Chen Yuanzhi did not expect this situation to occur, and subconsciously glanced at Mr. Yang next to him, but actually looked at Li Jiangao next to Mr. Yang.
"Hey... don't be in a hurry. It's the same thing if you eat later. It's best to disturb the children at this time." After hearing what Chen Yuanzhi said next to him, Mr. Yang turned his head and said with a smile.
"Oh, that's okay. You tell the hotel to wait until we notify you when the food is served." Chen Yuanzhi immediately said to Xu Dajiang.
"That's okay." Xu Dajiang nodded, and then prepared to go out and call Yu Chenggong.
He was full of tangles in his heart. It was all his fault. Qiao Ze should have told him the time before he came on stage.
Of course, what he didn't know was that Qiao Ze actually knew the time all along.
He didn't stop just because the fuss just now made him too lazy to postpone today's blackboard writing process to the afternoon.
Speeding up a little, finishing speaking in the morning, answering some questions in the afternoon, and the time for his report meeting has passed.
Finally, at one o'clock in the afternoon, Qiao Ze had filled eight blackboards.
"...The next step is the most important step. We have obtained the general solution in the superspiral space. After conversion, we can obtain the general solution of the Yang-Mills equation. However, in this step, there is a place where it is easy to make mistakes. , everyone must pay attention.
That is (g(xy)) is the Green's function in four-dimensional space-time, and its function is to describe the propagation of the Yang-Mills equation. In other words, we construct the gauge field through the convolution of Green's function and external source terms. Therefore, in the process of solution conversion, more complex mathematical structures and mathematical principles must be considered. "
Finally, Qiao Ze wrote again on the blackboard the general explanation that had just been projected on the big screen.
Then he put down his pen and faced the audience again.
"The above is the solution process of the entire Yang-Mills equation. We completed the solution by introducing superhelical space algebra and manipulation fields. This method allows us to develop a mathematical method for special energy band structures.
The next step for me is to use this complete set of tools to prove the mass gap problem and try to mathematically explain the formation of mass gaps in matter. I welcome any scholar who can understand today's proof process to join this work.
Okay, now it's lunch time, everyone can think about any other questions. Since this is a newly introduced algebraic form, I believe some people may have many questions. Therefore, the Q&A time in the afternoon has been extended by one hour. "
After saying that, Qiao Ze bent down slightly, then turned around and walked towards the back of the field.
It was at this time that everyone in the front row let out a long sigh...
The back row even let out a long sigh...
…
"Fuck, wake up, go eat! Why the hell did you fall asleep?"
"Um...is it over?"
"Well, it's over!"
"Huh... damn, I will never come to Qiao Ze's report meeting again. If I do, I'll be a dog!"
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