God's Crown

Let's be serious, everyone will definitely be very serious, after all, this matter must be taken seriously no matter what.

An Yan said that he had already solved the Yang-Mills equation, and now there are more and more formulas written on the blackboard, and everyone's expressions are becoming more and more cautious.

That's right, An Yan is already answering the core questions of the Yang-Mills equation on his mobile phone, and everyone is frantically recording the formulas on the blackboard.As for why An Yan wanted to disclose the Yang-Mills equation at this time, instead of submitting it to a journal after sorting it out, the reason is very simple.

Because when the International Congress of Mathematicians makes academic reports, there are meeting minutes.As long as there are meeting minutes, he is not afraid of someone plagiarizing or even plagiarizing his answering ideas and specific answering process.

Of course, if you think about it, how could someone copy the process and results of his Yang-Mills equation? Isn’t this just nonsense?At the International Congress of Mathematicians, especially a high-profile young mathematician like him, copied his academic achievements.Maybe this plagiarist's brain is not very good.

"This step..." Someone said softly, "It seems that something is not right, have you figured it out, what is going on?"

"This..." No one spoke, they just looked straight at the formula on the blackboard, to be honest.This has touched the heart of the Yang-Mills equation, and with the addition of Anyan abbreviated many things.It seems that, how should I put it, it seems that nothing is right.No, it's not that it's wrong to do anything, but this has touched the most essential thing.And they haven't been able to see anything in the most essential things.

The people behind have become more and more confused, and they don't even know what An Yan wrote. On the contrary, the group of mathematicians in front, frowning, looked at An Yan's formula and thought hard about An Yan. Does this solve the Yang-Mills equation.

No one is sure whether An Yan can solve the Yang-Mills equation, but according to the research results that An Yan is now writing on the blackboard.Obviously, that is, he has made some breakthroughs in the Yang-Mills equation, maybe even a breakthrough that shocked the mathematics world.

If he really solved the Yang-Mills equation, then it has to be said that he is probably one of the scariest mathematicians ever.

In one year, he solved three world-level mathematical problems in a row, which made all mathematicians feel dim in front of him.In addition, he is not a mathematics student, but a physics student. With this bonus, it is even more...

It's incredible!

"The Yang-Mills equation has not been solved yet." Deligne said in a deep voice, "but his theorem must be used, and this step is not yet the time to use the theorem."

Lance, behind Professor Deligne, looked at the young man who had been targeted by the New York laboratory.

At that time, although he was a little famous person in academia.But it was far from reaching such a terrifying level, and now, this young man has become a towering tree, a nightmare for the New York laboratory.

Thinking about it, he thought it was funny enough for those who were targeting them before.

Targeting such a guy is simply... hitting a stone with a pebble.

What a joke, he is an out-and-out math genius, a genius who solved three math conjectures crazily in a year.And the guys in the New York lab may be smart, but they're far from geniuses.

The distance between a genius and a smart person seems very close.In fact, it is like a natural moat, which cannot be crossed no matter what.

An Yan did not speak, but quietly continued to write the solution steps of the Yang-Mills equation on the blackboard.

"He has already achieved this step?" Faltings muttered to himself. When An Yan arrived at the Max-Planck Institute of Mathematics, he once asked An Yan how far he had achieved.On the Yang-Mills equation, An Yan at the time replied that he was in the core part. He still had a lot of things he didn't understand, and he couldn't touch the core part at all.

Originally, Faltings thought that An Yan had only made some achievements on a part of the Yang-Mills conjecture, nothing more.

But I didn't expect that he would go so far.It can be said that if the research continues, the Yang-Mills equation must be solved.Regardless of whether he now claims to have solved the Yang-Mills equation, Faltings believes that if someone solves the Yang-Mills equation, then that person must be An Yan, not anyone else.

God knows, this guy is really terrible.

I originally thought that such a terrifying math genius, no, he is simply the god of mathematics.It is impossible to exist. He rubbed his eyes vigorously. He was completely shocked by An Yan. There were more and more formulas on the blackboard, and the blackboard seemed a little insufficient. Fortunately, the conference was prepared. Less blackboard.

Handing over the blackboard, An Yan didn't care and continued to write.

After a while, he wrote the key points that he hadn't been able to understand before.

An Yan turned around, looked at everyone and said, "When I made this step, I thought about it for a long time."

This is, this one still hasn't figured out how to do this step?But looking at the questions on the blackboard, indeed, if this step can be done, wouldn't it mean that this guy has proved the existence and quality gap of Yang Mills.Think about it, this person has made great contributions and breakthroughs in this area, and even made great contributions to theoretical physics.

It is no exaggeration for such a genius to be called the world's top mathematician.If he can really solve the Yang-Mills equation, it seems that there is nothing wrong with saying that he is the greatest mathematician of the 21st century.No matter in terms of the speed at which he solved the puzzles or the quality of his solutions, the title of great mathematician is absolutely uncompromising on An Yan, without the slightest bit of moisture.

"For about half a month, I have been stuck on this step." An Yan said calmly, "I have thought of many ways, and I seem to have fallen into an endless loop."

Speaking of which, this guy hasn't been able to solve the Yang-Mills equation, has he?

For some reason, many people at the scene let out a breath of foul air slowly, as if something had been let go of their hearts.This was their instinctive reaction, probably because An Yan was already dazzling enough.Putting on a layer of halo, it is simply impossible to look directly at, like a god-like existence.

Who wants a guy like a god to appear at this time?

Isn't this crazy?Modern mathematics has already improved a lot compared to previous mathematics.And many theories of modern mathematics come from people in the past, if this person has reached the level of a god.It can be said that what everyone needs to study in the future is probably the contribution of this person.

It's just... It's hard to imagine how sour it would be.

What a joke, modern mathematical classification is detailed enough.An Yan is just plugging in casually, and let other researchers live?

Which first-class or top-notch master in mathematics does not want to leave a name in the history of mathematics.

This An Yan's achievement is already a person who cannot be bypassed in the history of mathematics. There is no need to do such a great job, and build all future research on his foundation, right?

Is this going to kill them all?What's even more frightening is that this guy is not only ready to do everything in mathematics, he doesn't even want to let go of theoretical physics.

The previous theory is obviously intended to be applied to gauge field theory.

Although the vast majority of mathematicians have no interest in studying physics, they just don't have an interest, not because they don't know anything about physics.You must know that there are many mathematical formulas that physics needs to use, and every mathematician has some understanding of physics.

Let them do physics topics, especially theoretical physics topics, and they may all do well.

It's as if An Yan, a theoretical physicist, was able to win the highest award in the mathematics world. In the field of mathematics, mathematicians who can achieve world-class and top level, usually, physics is not too bad.

Can you believe that the mathematics of Einstein who came up with the theory of relativity is extremely poor?How can it be.

"However, I figured it out later." An Yan said with a smile, "Although it is a one-hour academic report meeting, it is obvious that the time is not enough. I ask the organizing committee of the conference to give me as much time as possible. Although I've only gotten so far before, but I'm confident I can solve the Yang-Mills equation."

"what?"

"Is he crazy?"

"He wants to solve the Yang-Mills equation on the spot of the academic report?"

"No way, how arrogant is this guy?"

"Oh my God, I can't believe this is happening."

Members of the organizing committee of the International Congress of Mathematicians were present, but he did not speak.He is a mathematician himself, thought for a while, "Professor An, I need to discuss this request with other people."

"Thank you." An Yan smiled slightly, and after bowing, he stood still, waiting for the member of the organizing committee to speak.

He stood up, walked out of the academic lecture hall, took a mobile phone to call the chairman of the conference, and reported the current situation, "You see, Professor An needs more time now, and I am afraid that it is impossible in the No. 1 academic lecture hall." moveable."

"Professor An, why does he need more time?" The chairman of the conference was a little confused. Why did Ann, the winner of the Fields Medal, need more time to make his academic report? Does not conform to the general assembly system.

"He wants to solve the Yang-Mills equation in the lecture hall."

"What?" said the conference chairman in surprise. "He wants to solve the Yang-Mills equation here?"

"That's right, it was to solve the Yang-Mills equation at the academic report meeting of the International Mathematics Conference."

"Are you sure you heard right?"

"I'm sure I heard right."

"Okay." The chairman of the conference said in a deep voice, "The academic lectures arranged in the 1st academic lecture hall will be twisted to the 6th academic lecture hall. I'm looking forward to it."

"Like you, I am also very much looking forward to whether he can untie it."

Hang up the phone and walk into the academic lecture hall.There was still some commotion at the scene. Everyone was probably intimidated by An Yan. Is he really going to solve the Yang-Mills equation?

This guy must be crazy!

Even the first-class mathematicians and top mathematicians sitting below were all frowning, not knowing what they were thinking.

He returned to his seat and said to An Yan, "Professor An, you can continue your academic report, and you have been allowed to continue the academic report meeting. After that, the academic report meeting in Hall 6 will be moved to Academic Room 6." Lecture Hall, if you are interested in other academic reports, you can go to Hall [-]."

"Thank you." An Yan smiled.

The members of the organizing committee gave up and made such a big move.

If An Yan had not been able to solve the Yang-Mills equation, he would probably have been laughed at for a long time.Of course, no one can deny that An Yan is already at the top level in the world in mathematics, but such an arrogant person is still rare.If he could solve the Yang-Mills equation, Anyan's name would be widely circulated in the mathematical community.He is a well-known scholar now, but there are still some people who don't know him well.

People might call him a great mathematician, but Anyan would have screwed up if he hadn't been able to solve the Yang-Mills equation.His academic reputation may be affected to a certain extent, and he will definitely be ridiculed when he goes out.

Of course, no one dared to negate this person's position in mathematics indiscriminately.It's just that compared to mathematicians of the same level, An Yan may be the most shameless one.

This can be regarded as a battle of conferred gods, if he can solve it, then everyone will be happy.An Yan, he will become the most powerful mathematician, bar none.At least for now, but if he hadn't been able to untie it at the colloquium.The consequences are hard to predict, besides, the man himself is a professor at Princeton University.

You must know that the group of students at Princeton University is not a worry-free guy. Maybe after returning to school, he will be booed by the students and coaxed off the stage when he goes to class.

Very interesting, isn't it?Members of the organizing committee frowned.

An Yan turned around, "Since I have obtained permission, I will start the next steps now. The unnecessary steps omitted in the previous ones are due to the time of the conference. There is no time limit now, and the latter part is very difficult, and I will not Some steps will be omitted.”

"Next, I need to introduce the theorem I said earlier."

"It turned out to be like this..." Deligne suddenly realized, and he knew that this theorem should be used in the Yang-Mills equation.But he also thought that An Yan was doing gauge field theory, and maybe he was going to quote it on gauge field theory, so he mentioned it at the academic report.

He suddenly understood everything, "So..."

"Sure enough!" Faltings' eyes lit up with a gleam of light, and he knew that An Yan would definitely not do anything thankless.

Now it is even more proven.

The theorems he proposed at the beginning were intended to be applied at this last time.

Professor Witten squinted his eyes, as if he was thinking about something.

After a while, the formulas on the blackboard were filled again, and everyone looked at the formulas written by An Yan on the blackboard without blinking.I'm afraid that if I miss a little bit, I won't be able to keep up with An Yan's rhythm.

Indeed, the pace of An Yan is very fast.

If you are not careful, and you don't even have time to think about this question, all the following questions will no longer be able to keep up with An Yan's rhythm.

Everyone's eyes were straightened, and An Yan's calculations became smoother and smoother.This is also the first time An Yan has done this. He never calculated on the scratch paper, but he didn't seem to think much, just kept writing these formulas and calculations on the scratch paper. It seems to be calculating while thinking, but it seems to start after thinking well.

Everyone was wondering whether An Yan had already thought about what to do or whether he really solved it at the academic report meeting.

Of course, there are still many people here who can't understand what An Yan wrote, but they don't think they should leave if they don't understand.

At least it can be seen through the expression whether An Yan has really solved the Yang-Mills equation or not.

After watching for a while, the group of mathematicians below seemed to be constantly calculating whether the formula written by An Yan was wrong, but no one raised any objections.Just seeing that everyone kept looking at An Yan's formula, the group of students above began to whisper, "Do you think An Yan can really solve it?"

"

What nonsense, An Yan is one of the world's top mathematicians.Such things as nonsense should not happen to him, right? "

"You mean, is it possible for him to actually solve the Yang-Mills equation?"

"Who knows." The student spread his hands and said, "I am not him, how could I know whether he can solve the Yang-Mills equation."

"According to my observation, Professor An should have really created the Yang-Mills equation."

"Why do you think he really made the Yang-Mills equation? Why do you think so?"

"Why?" The man murmured, "It should be based on his confident eyes. Haven't you noticed that this big guy's eyes are actually very confident?"

"Yes, is there?"

"When the organizing committee of the conference gave him a little time just now, he was so confident."

Not only the students below were talking nonsense, but the mathematician sitting in the front row was also very shocked, "I should have thought a long time ago that An Yan's theory should not be so simple."

"I had guessed before that he might be substituting into the Yang-Mills equation, but he didn't do it for the most difficult point in such a long time. I thought he wouldn't. Unexpectedly I was waiting for this opportunity at the end..." The person next to me said dumbfounded, "But I have to say, this is a genius idea, at least I can't have such an idea."

"That's right, I'm really surprised that he was able to calculate to such a degree. Even if he didn't prove the existence and quality gap of Yang-Mills in the end, I don't think anyone would laugh at him."

"That's right, such a powerful mathematician, who else do you think would laugh at him?"

"Huh? What do you think he is?"

"A master of mathematics, isn't he?" The man shrugged, "Don't you think he is a master of mathematics now? Shouldn't he be called a master of mathematics for his achievements in mathematics?"

"You may be right, but his age actually seems to be called a master, which is a bit unreliable."

"Fuck the age of X, if age can be regarded as academic achievement, I believe many people's academic achievement is only age, isn't it?"

"That's right. Mathematics itself is a subject of genius. It's just that I'm shocked now. Geniuses in mathematics are indeed more terrifying than ordinary people. Even ordinary people may not be able to accomplish one thing that geniuses accomplished when they were young." .”

"It's a pity, doesn't it?"

"Yes, unfortunately, at least I don't think I am qualified to be a Fields Medal winner before the age of 30."

"This is probably why there are only a few geniuses and ordinary people are the majority."

Everyone was chatting non-stop, but An Yan had no intention of slowing down at all.Faster and faster, there are more and more formulas on the blackboard, so many that people don't even have time to see whether the formulas on the blackboard are right or wrong.

After a while, An Yan stopped.With his back to them, he began to think.

He has written a lot of calculation formulas smoothly, and he has been very smooth until this step.At least in his opinion, he is very smooth.

It's just why after this step, it seems that everything has been messed up, and there are still some things that I can't understand.

The people below looked at An Yan's back without moving, and waited first.They thought An Yan was thinking and shouldn't disturb her.Everyone didn't speak, they were all quiet.

But the waiting time passed little by little, and An Yan stood there motionless like a sculpture.This made everyone lose patience, and it was some students who lost patience at first.They frowned and discussed in a low voice, "Why doesn't Professor An continue to write?"

"What's going on here? Professor An can't continue writing, can he? Or, let's go to other academic lecture halls to see other academic lectures? It's not a thing to be exhausted here."

"Let's go."

Just as they were talking, some students had quietly left the academic report meeting.

When they walked across from An Yan, they looked back.At this moment, An Yan's expression was indescribable. Professor An, who was frowning slightly, looked very delicate and pleasant, but why did he have a particularly weird feeling?It's like... I don't know what words to use to describe the current Professor An Yan.

I feel that his current appearance has never appeared in their impressions.

A little embarrassed!That's right, embarrassment.

After a while, the group of mathematicians who participated in the International Congress of Mathematicians seemed to be a little restless.

"Is An Yan stuck? Why haven't you started the formula below?"

"I looked at the above formula and roughly calculated it. It seems that there is nothing wrong. Of course, it is only a rough calculation, but after this step, I don't know how to calculate it later."

"I'm afraid this person has really encountered a problem."

"Just now this guy was so swaying, why is he motionless now. It doesn't look like his style..."

"Maybe I was really trapped by the last few steps."

The mathematics professor next to Professor Li Bo seemed very excited. He took a deep breath and said in a low voice, "Professor An, what's wrong? This is clearly about to be proved, why is it stuck? It shouldn't be. .”

"I don't know." Professor Li Bo shook his head, and said with some confusion, "The last few steps don't seem to be easy to do. So far, An Yan has been the closest to proving the Yang-Mills equation, but want to Getting him to make the last few steps, I think there are still a lot of difficulties."

"I can't, this...why can't I do it yet. I think it's infinitely close to the proof..."

"No way, who can be sure about things like inspiration?" Professor Li Bo spread his hands and said helplessly, "He is already very good at doing this, isn't he?"

"Yes..." The mathematics professor had to admit that he would have to study for many years before he could achieve the step An Yan is taking in his lifetime.

However, An Yan obviously started to study after unraveling Hodge's conjecture. In a few months, he was infinitely close to the final proof, and even surpassed the problem of the weak Yang-Mills existence and quality gap.It can already be said that Professor An is very powerful.It's just that he might have expected too much from Professor An, or he always felt that Professor An could be better.

He didn't know if his thinking was wrong, but he was very anxious now.

He wasn't the only one who was anxious, the bosses in front were all a little anxious.

"What the hell is Ann doing?" Faltings muttered, frowning.He admitted that at this point, no one can do it now.However, if An, who has achieved this step, can't do it, it seems a little unreasonable.

At least he thought that An could do it, but he didn't expect that An could not make the last step, which was a bit embarrassing.

"Is he probably thinking about something?" Professor Deligne was also a little uncertain.

A member of the organizing committee pondered and said, "Professor An's thinking time is a bit unreasonable." He took out his watch and looked at the time for a while, "It's been 5 minutes, and Professor An still hasn't been able to solve this formula. .”

"Wait." Professor Deligne leaned on the chair, "He is still thinking, there is no need to tell him to stop at this time."

"Of course." A member of the organizing committee nodded and said, "I will definitely not tell him to stop at this time, but I am thinking that whether Professor An can solve the Yang-Mills equation may need to be verified."

"Isn't he solving it now?" Professor Deligne chuckled, "Don't forget, you can't even do what Ann did before."

The member of the organizing committee said without blushing, "Of course I know I can't do it myself, but Professor An said that he can solve the Yang-Mills equation. I never said such a thing, Isn't it?"

"So, you want to attack him with what he said?" Professor Deligne narrowed his eyes and looked at the member of the organizing committee.

"No." A member of the organizing committee hastily stopped and said, "I think you have misunderstood. Even if Professor An failed to solve this problem, I think he is still a well-deserved top mathematician, isn't he?"

"But it's a pity that it's just a little distance away from the master of mathematics. I don't know how long it will take to reach the apex of this distance."

"I believe he is very clear about what you said." Professor Deligne rubbed his eyebrows, "How should I put it, I think An Yan is now a master of mathematics. At least, I think so .”

The members of the organizing committee chuckled, as if they didn't care what Professor Deligne said.

Professor Witten said quietly beside him, "I think, given him a little time, he can solve the Yang-Mills equation."

"Oh?" The members of the organizing committee turned their heads, looked at Professor Weiteng and said, "Professor Weiteng, why do you think so?"

Professor Witten smiled, "There is no reason why I think so, it's probably just a kind of intuition. My intuition tells me that he must be able to do it."

"Really?" A member of the organizing committee smiled dispensably, "I'm looking forward to it, and it's been 10 minutes now. I think many people behind have become a little impatient."

"Actually, if you think that it is impossible for An Yan to solve the Yang-Mills equation, you can stop at any time. But you don't seem to have done so."

"Why did I do this." He said with a smile, "I also want to know what Professor An can do. I am also very curious."

The sweat on An Yan's forehead had already begun to drip down bit by bit, under the fine beads of sweat, An Yan's expression was very solemn.After doing this, his brain seemed to be completely short-circuited.For a moment, I can't think of anything, I can't remember anything.

How to say this question, my mind suddenly went blank.Those formulas that have been thought of before, those things that can be answered seem to be useless, and it seems that nothing is right.

I froze for a while.

He didn't know how long it had passed, it could be 1 minute, 10 minutes, half an hour, or an hour.All in all, he remained motionless, combing his thoughts over and over again, but there was still nothing he could do.

It is too difficult, it is too difficult!He didn't know how to proceed at all.

The following voice reached his ears——

"Whether Ann can continue, I thought that using his theory could solve the Yang-Mills equation, why am I stunned now."

"Keep your voice down, everyone heard you."

"But if he continues like this, do we have to wait for him for several days? At this point in time, it's almost time for dinner, right?"

"It's still a little early for dinner, but to be honest, if Ann continues like this, I think that this academic report can be ended at any time. Although he failed to solve the Yang-Mills equation, he also gave We have provided a lot of new things, maybe we can solve it after researching and researching?"

"It's not wrong to say so, but I always feel that his theory is still a bit insufficient. Whether he can solve the Yang-Mills equation is still in the works."

Wait, An Yan raised his head while pondering.

"It moved, he really moved, this guy, isn't he going to continue to solve the Yang-Mills equation?"

But when they saw An Yan's actions, they were a little disappointed.It turned out that An Yan did not continue to solve the Yang-Mills equation, but looked at the formula that he had written on the blackboard before.

Everyone was a little confused about what An Yan wanted to do, and looked at An Yan in confusion.

"What exactly does this guy want to do? I don't understand what he wants to do."

"With this action, does he want to solve the Yang-Mills equation, or does he not want to solve the Yang-Mills equation? Do you want to continue to solve the equation? Let me tell you something. Now I am so straightforward. What does it mean?"

"I don't understand. He has been in a daze for more than half an hour, right? Now look at the previous equation again. What exactly does he want to do?"

"Maybe it's because he talked too much just now, isn't he a little embarrassed now? If it were me, I would definitely be embarrassed too. I talked so full, but I couldn't do it in the end."

"I now hope that Ann can cherish her academic reputation and not mess around."

"That's true. If An Lunlai claims to have solved the Yang-Mills equation, I will definitely be disappointed."

"Don't think about it, there are so many mathematicians on the scene, it's impossible for Ann to act foolishly."

"Oh, how long do we have to wait?"

After looking at his own formulas for a while, An Yan recalculated these formulas in his mind very quickly.But in the eyes of this group of people, An Yan remained motionless.

This is - stuck again?No way, what's going on with this top mathematician? How can there be so many accidents in an academic report meeting? It's not like his style at all.

Has this guy been dropped?It's not right, if this guy is swapped, the previous formulas can't be written at all.However, at this point, if An Yan can't do it, it's good to just say it.Such a silent attitude is actually quite difficult to accept.

They don't even know what words to use to describe the embarrassing scene at the academic report meeting. The students from Han Country are almost gone.Those who stayed were to watch the excitement.Some students from other countries also left, probably thinking that this academic report would be meaningless.

It was the first time to see this academic report, but this one was stunned.

He was really stunned, how embarrassing this group of students must be.Although they couldn't understand the content on the blackboard, they were stunned when they saw An Yan. This was a great blow to those who admired An Yan.

Not to mention them, even Faltings said strangely, "What does he want to do?"

"Yeah, what exactly does he want to do?" Everyone was very puzzled, and now An Yan has not started writing, and has been looking at the previous formula, what exactly does he want?

It's better to honestly admit that I can't figure it out, so that they can go to the next academic lecture hall.

Listening to other people's academic reports, they did learn a lot at Anyan, but that's just a lot of things. It's okay to listen to other people's academic reports and learn more. .

An Yan was so dumbfounded that he was not only wasting their time, but also consuming others' enthusiasm for him.

Professor Li Bo couldn't figure out what An Yan was going to do. He could only see from his back that An Yan was motionless again.

"What's going on?" The mathematics professor next to him said dumbfounded, "Is Professor An not in the mood today?"

As soon as he finished speaking, An Yan, who turned his back to everyone, showed a meaningful smile.

Very good, very interesting, he finally understood why he got stuck just now.

The pen in the hand kept writing on the blackboard, and everyone stared straight.

After nearly an hour, An Yan continued to move.Although I don't know if An Yan can do it, but this academic report meeting is really-enough to go back and forth.

Everyone focused on An Yan's answer. It didn't matter if they could solve the formula. What mattered was that An Yan was writing again.

"That's right. Why didn't I think of doing this?" Someone muttered to himself, "So that's why he got stuck just now, it turned out to be here."

"My God, when he calculated that step, he could obviously continue to do it, but he was stuck for so long. I thought what was going on. This guy took one step, how many steps did he see?"

"I can't, is this guy really going to solve the Yang-Mills equation? It's really too tough."

"My God, Ann is horrible."

An Yan's pen still didn't stop, Faltings raised his eyebrows and looked at the formula on the blackboard.He didn't calculate, and he doesn't need to calculate now.Only one result is needed. If An Yan can solve it, he will definitely have to calculate it.If An Yan can't solve it, he expresses his regret, and he will collect An Yan's answers before answering.