On the reporting table, the narrating voice stopped.
Under the report stage, thousands of listeners were also stunned for a moment.
Seeing Xu Chuan standing in front of the blackboard and staring at the calculations he wrote, many audience members who came to the exchange meeting were a little surprised.
Theoretically speaking, in today's report, the proof of the existence and solution of the Yang-Mills equation will not have any mistakes like other academic reports.
Not to mention that the reporter is a scholar who has made almost no mistakes since his debut. Even the verification of the general solution by various research institutions using supercomputers is enough to prove the correctness of the paper.
On the basis that the general solution is correct, theoretically there will be no errors in the paper and the proof process.
Although it is not unheard of that there are problems with the proof process and the results are correct, the probability is undoubtedly quite low.
While most of the audience was curious about Xu Chuan standing in a daze on the stage, a few scholars realized something.
Looking at the person on the stage, Terence Tao took a deep breath and stared at the blackboard.
Going to do it again?
Thinking about it, he couldn't help but have a trace of longing in his eyes that were staring at the blackboard.
It's really enviable. This is not the first time that I have gained inspiration and solved problems at a report meeting.
Is this time to address the remaining mass gaps? Or is it something else?
With a heavy breath, Tao Zhexuan looked at the lecture table longingly. For a scholar like him who has already stood at the pinnacle of the field of mathematics, every breakthrough and advancement is undoubtedly extremely difficult.
But when it comes to the person in front of me, it is as simple as eating and drinking.
Terence Tao was not the only one who realized this. Edward Witten, who was sandwiched between G. Faltings and Deligne in the front row of the auditorium, also realized what might happen next.
After all, he had seen this student deducing the unified framework theory of strongly correlated electronic systems on the lecture desk before.
This time, it does not seem impossible to solve the remaining problems of Yang-Mills's existence and quality gap.
If his guess is wrong, maybe he will see another miracle today.
Maybe this kind of thing is normal for the person standing on the stage, but at least it is for them.
Suddenly, just like Tao Zhexuan, Witten felt a ray of envy in his heart.
Being able to take a step forward on the academic road is undoubtedly the most desired thing for people like them.
...
On the reporting stage, Xu Chuan didn't care about the audience's reaction.
He stared at the equation he wrote on the blackboard. It was a differential manifold equation, and it was also the source of his deep thoughts.
These two formulas are the Yang-Mills equation, which is famous in both the mathematics and physics circles. Its description in the Millennium Problem defined by the Clay Mathematics Institute is as follows: "For any compact simple group G
, there is a quantum Yang-Mills field with mass (Yang-Mills field) with G as the gauge group on R?, and there is a mass gap? > 0."
This is a very interesting question. It is not only a differential equation in the field of mathematics, but also involves the description of the electromagnetic field in quantum mechanics.
Quantum mechanics treats the position and velocity of a particle as non-commutative operations acting in a Hilbert space.
Zi, whose ‘field’ is used to describe many natural phenomena.
For example, the electric field and magnetic field in Maxwell's equations, the gravitational field in Einstein's equations, etc. The gauge potential in gauge theory is mathematically described as a master-slave connection and is closely related to elementary particles and their interactions.
.
When explaining the interaction between fields and particles, the concepts of quantum field theory must be applied.
This is true for the Yang-Mills equation. When constructing the Hilbert space in which these operators act, traditional particles such as electrons are reinterpreted as quantizations of the Dirac field, and the difference between fields and particles disappears.
.
To understand it from a mathematical point of view, there is an arbitrary, compact simple group G, and the mass gap in the Yang-Mills field is greater than zero.
To put it simply, there is a group or number, and the value in a certain field is a positive number.
Although this understanding is not completely correct, for ordinary people, this should be the simplest language to understand the existence and mass gap of Yang-Mills from a mathematical perspective.
This extremely simple understanding, combined with the equations on differential manifolds on the blackboard, allowed Xu Chuan to capture that faint hint of inspiration.
"Relying on the micro-element construction method, maybe I can set a 'minimum' scalar field on the space-time manifold, and then press the two components of the group under the action of the gauge group U(2)x U(1)
Represents a change, the non-zero asymptotic constant of its vacuum state reduces the gauge group to a subgroup of U(1)..."
The ideas in my mind gradually became clearer, and a bridge that was wider than before was gradually built like building blocks on the Yang-Mills equation.
This is a brand new route that does not rely on the method of "invariant couplers with differentiable structures set on high-dimensional manifolds", and is simpler and more convenient.
He habitually picked up the brush from the blackboard in front of him, and just when he reached out to erase the calculations in front of him, Xu Chuan suddenly came back to his senses and remembered that he was still at the report meeting.
With a dumb smile, he put down the brush in his hand and continued writing along the unfinished formula on the blackboard.
It's not too late to wrap things up first. After completing this report meeting, it's not too late to sort it out. Anyway, the inspiration has been caught by him, and the ideas can't escape his mind, so he's not in a hurry.
As he continued to conclude his report on "Proof of the Existence and Solution of Solutions to the Yang-Mills Equation", the atmosphere in the auditorium gradually began to become lively again.
This chapter is not over yet, please click on the next page to continue reading! With some noise, many audience members were discussing what Xu Chuan had just been stunned at the reporting table.
"Professor Xu, was your train of thought stuck just now?" A middle-aged professor wearing gold-rimmed glasses curiously communicated with his friends.
"Maybe?" The friend in a suit and tie shrugged: "After all, everyone has bad situations, it's normal."
In a mathematics report meeting, it is normal for the presenter to get stuck in his thinking. No one can guarantee that he will be in the best condition when giving a report.
Especially for some older scholars, it is normal for them to forget what they said a second ago when they are speaking.
After all, as we grow older, the decline of brain memory is a very serious matter, especially for a scholar who does academic research. He must remember those formulas and theorems as he grows older, and clarify his thoughts.
It's even more difficult.
While others were chatting, Terence Tao frowned and looked at the reporting table.
He just saw Xu Chuan holding a blackboard eraser and preparing to erase the calculations on the blackboard, but he stopped for some reason.
Have you not sorted out the inspiration and thoughts in your mind?
As the thought passed by, Tao Zhexuan breathed a long sigh of relief and shook his head slightly.
It seems that he doesn't say he can do it every time.
In fact, in the long journey of academic career, inspiration is not too lacking for a scholar. Many times, the key to the truth is hidden behind the ignorant ideas.
But for a scholar, it is extremely difficult to grasp those hazy inspirations that happen by chance, let alone transform them into feasible theories and ideas and sort them out in such a short period of time.
.
If he could really do it every time, he would even be tempted to suspect that the brain of the person on the stage was made of a quantum computer, and would want to cut it open and take a look.
.......
"...by setting up an invariant coupler with a differentiable structure on a high-dimensional manifold, a bridge is built between mathematics and physics. By stepping on this bridge, we can get the Yang-Mill
The general solution to the Sri Lankan equation can also provide a deeper understanding of the interaction between microscopic particles and the form of their existence or movement."
"Not only from a physical sense, but also from a mathematical point of view, we can preliminarily confirm that the behavior of elementary particles can be determined by the non-Abelian Lie group and the unified core electromagnetism and weak force (i.e. U(1)
xSU(2)) and the strong force of quantum chromodynamics theory (based on SU(3))."
"The above is all my report today."
The moment the words fell, thunderous applause erupted in the auditorium of thousands of people. The applause spread like a tide from the front row to the back row, and instantly filled the entire report conference.
“A very exciting report meeting!”
Sitting in the front row of the venue, Tillman Lunt applauded and said with emotion.
Even though he had quite complicated emotions because of some things, he had to admit that this report on the solution of the Yang-Mills equation would be extremely exciting.
Before coming to China, he naturally also studied Xu Chuanfa's paper on arxiv. Whether it was the existence of solutions to the Yang-Mills equation or the general solution, he studied them carefully, and even had special discussions with some mathematicians.
.
But after all, he is not a mathematician, and he still has many problems with his understanding of the application and details of mathematical formulas.
However, these questions have now basically been answered.
At least, he was able to understand the paper and how to understand these things mathematically.
Sitting next to him, Frank Wilzek also applauded. He smiled and agreed: "It was indeed a wonderful lecture. He explained many theories to me that I didn't understand before."
"But...compared to these things, I am now more curious about what he was thinking about when he was sitting in front of the blackboard."
"Huh?" After hearing this, Tillman turned to look at him curiously: "What are you thinking about?"
Vierzek smiled and said, "Haven't you heard of it?"
"Have you heard anything?"
"Whenever Professor Xu stops speaking on the lecture platform and starts to be in a daze, it means that he must have new inspiration and harvest, and this inspiration may be the answer to a world-class conjecture!"
Hearing this, Tillman laughed and said, "Is it such an exaggeration? Maybe he just got stuck in the report meeting and forgot what he wanted to say for a while?"
Frank Wilzek said enthusiastically: "Want to make a bet? I bet he will have new inspiration during today's report meeting, and it will definitely be very important!"
Tillman Lunt glanced at him and asked, "Do you think so highly of him?"
In the world of physics, making a bet is not a rare thing. Especially for Wilzek, who is keen on betting on various things, inviting people to bet is not a very strange thing.
Wilzek smiled and said: "A few years ago, in 15 or 16 years, when he was still studying at Princeton, he went to CERN to work and research."
"At that time, I made a bet with Edward Witten, betting that he could win both the Fields Medal and the Nobel Prize before we left this world and create a new history."
"The result was obvious. I won. Only a short time later, he won both the Fields Medal and the Nobel Prize in 2018."
"For this reason, Witten also lost to me a thousand meters of gold and the request to play a real-name guest role in my next book, although I haven't figured out how to write about him yet."
"So, do you want to make a bet with me?"
Hearing this, Tillman's mouth twitched slightly.
Poor Witten.
"No, I'm not interested in such things as betting."
After thinking for a while, although he felt that it would be difficult to get inspiration for a world-class conjecture problem at a report meeting, Tillman still declined the invitation to bet.
He has no interest in being written into a book by this guy. God knows how he will fabricate himself.
"It doesn't matter, this time we will only bet one thousand meters of gold." As if knowing that he would refuse, Wilzek quickly chased after him and said.
After looking at him, Tillman thought for a while and asked curiously: "Then how do you plan to prove that he was not in a daze just now but was thinking about a certain problem and gained inspiration?"
Wilzek grinned and said with a smile: "Of course I have my own way, and the results will be available today, so do you want to come?"
"If it's just one thousand meters of gold, I also want to see if what you said is really that magical."
Tillman shrugged and replied that one thousand meters of gold was nothing to him.
Moreover, his curiosity was aroused by Wilzek's words.
In such a major mathematical proposition, in front of thousands of mathematicians and physicists, just to withstand such huge pressure and complete the report perfectly is already very good.
If you can still get inspiration for world-class conjecture problems at a report meeting, no one will believe it if you tell me this. It is too unbelievable.
"OK, then it's settled!"
Wilzek clapped his hands, raised his right hand with a smile, and looked at Xu Chuan, who was announcing the question-and-answer session on the reporting table.