Before Lot Dugan left the town of Princeton for China, he had already made an appointment with Qiao Ze for today's meeting.
This is due to the experience of attending Qiao Ze’s report conference last time in China.
It's not like they will definitely be able to meet Qiao Ze if they come to support him.
If he didn't make an agreement in advance, this little guy would probably use various reasons to shut out all the old guys like him.
Yes, this guy can really do this kind of thing.
This is very infuriating.
Even if we don't mention the tradition of respecting the elderly, the world's academic community respects old guys like him. Especially in Asian countries, except for Xilin, no matter where he goes, especially countries like Dongben and Beixian Island, if he wants to meet a junior in academia, he does not need to come in person.
He only needs to stay in the most prosperous city, and then make a casual phone call, and people will come over.
Especially on Higashimoto Island, the rules of respect and inferiority are very clear. The younger generation of scholars even left their mentors and had no resources to start research independently.
But then again, although Qiao Ze is a little willful, in Lot Dugan's view, this is understandable.
People who are capable are often more tolerant.
Even the old dean who has never had trouble rubbing his eyes has learned how to make excuses for the other party after being rejected countless times.
For example, this child wants to make progress after all, but his temperament is dull and he has higher requirements for communication. Maybe he is really busy... and so on.
Well, to put it bluntly, the almost unlimited increase in his tolerance threshold in Qiao Zeli is ultimately caused by the mismatch between supply and demand.
He needs to be able to understand the strange but extremely useful knowledge in Qiao Ze's mind, and even dreams of bringing this young scholar, who is too young but already occupies an important position in the world's academic circles, to Princeton.
But Qiao Ze didn't need much help from him.
He even ignored the many resources he could get for this little guy.
That’s why you can just disappear without thinking.
Lot Dugan understood this very well. He didn’t want to waste the hard-earned opportunity to meet, so he came to talk to Peter Schulz about his ideas first, so that he could make full use of the opportunity for face-to-face communication later and get more opportunities. Qiao Ze squeezed out some useful things from his mind.
This little guy is a real pain in the ass.
He doesn't even have the competitive ideas of young people.
Lott Dugan knew that the Institute for Advanced Study in Princeton specifically posted the research progress on superspiral space algebra on its official website.
Anyone, even an old guy like him, would probably be proud to see the theory he created being put on the official website of the world's top research institutions for discussion and research by scholars around the world, and would definitely give a response.
Even if the relationship between the two parties is not good, they may not be able to help but tell them whether there are any problems with the research direction by not limited to public announcements, or show off some ideas for solving the problem to prove how impeccable their theories are. .
At least Lot Dugan put himself into Qiao Ze's perspective and thought that he would definitely do this. Even if it will help the other party deepen their understanding of this new theory.
Which theoretical mathematician doesn't want to see his theory carried forward during his lifetime?
This is the lifelong pursuit of this profession!
But Qiao Ze is really different.
Lot Dugan didn't know how this young man could hold back. For a whole quarter, except for occasionally publicly posting a few related topics, he never said a word about Princeton's research progress in any public or private setting. Character.
He just watched silently as a group of scholars discussed the theoretical framework he had already built.
Horribly cruel.
Is this something that a normal mathematician can do?
When occasionally communicating with Qiao Ze through video, he also raised relevant questions, and often even asked Qiao Ze implicitly what he thought of the research on the Princeton official website, but Qiao Ze dealt with it with a few words.
He can even memorize Qiao Ze's common expressions.
"Not bad.", "Deserves recognition.", "Very good.", "The theorem is very simple."...
This was also the reason why he cherished this face-to-face communication with Qiao Ze.
He was afraid of being recorded in the video and couldn't completely lose face.
But when it comes to communication, he can temporarily put aside his old face and ask everything he wants to know.
This is very important, because Qiao Ze's defense meeting today really inspired him a lot. He has a feeling that if he can learn from Qiao Ze, it can greatly simplify the calculation amount of the project he is currently researching.
This is an n-body project.
If he can succeed, maybe he can train another Fields Medal-winning student.
Yes, Lot Dugan may be a stubborn little old man. Many times, his attitude towards students is not friendly, and he may even assign extra homework to those poor students because he is in a bad mood.
But from the perspective of pure academic training, Lot Dugan is actually a very good and excellent mentor.
For example, he would neither hide his secrets when teaching, nor would he snatch the honors that belonged to his students. He was even willing to take the blame for the students' minor mistakes that were innocuous.
If Qiao Ze were to give him an evaluation, he would probably be a very pure scholar.
…
At seven o'clock in the evening, Lot Dugan brought Peter Schulz to the yard of Xilin Institute of Mathematics on time.
Originally, he planned to come alone, but after discussing with Peter Schulz, he found that it was indeed necessary to bring the young mathematician with him, so that he could think more carefully when discussing the problem.
The only bad thing is that one more person may see this old guy acting like a rogue, which will have a big impact on his face.
But thinking that this might be an opportunity to solve a problem he had been studying for many years, after weighing it, he still felt that face was not worth much money.
Facts have proved that this is a very correct decision.
Because when he arrived for the appointment on time, he discovered that this conversation was not between two people.
"Ha, Qiao Ze, I finally see you again! You know, it's so difficult to meet you face to face like this. It's a pity that you still refuse to go to Princeton. Really, if you are willing to go and see it, You will definitely like it there.”
When meeting and greeting, it is still very old-fashioned.
The same goes for online video.
When Lot Dugan saw Joe Ze, he would always start with the beautiful environment or strong academic atmosphere of Princeton.
Even if he is rejected every time, he never gets tired of it.
Anyway, it was just a casual remark. If Qiao Ze agreed on a whim, it would be an unexpected surprise.
Unfortunately, I still got the same reply today: "Xilin Research Institute is very good, you can come."
"Haha, okay, you know, I can't leave. Oh, by the way, Peter Schulz, we met last time. Um... Also, who are those people?"
Lot Dugan glanced at the figures guarding the yard and asked.
"Bodyguard?" Qiao Ze said uncertainly.
Since the director surnamed Du came to talk to him last time, the team codenamed "Tinder" that had been following him silently before simply moved into the courtyard of the institute and directly moved the junk piled on the first floor. A room in the property was cleared out and became their stronghold.
I often wander around the yard and even check the garbage in the institute.
Fortunately, these things did not have any impact on Qiao Ze's work and life, so he went with these people.
In fact, it is beneficial to say so.
It was as if he had made an appointment to chat with Lot Dugan early this evening. Qiao Ze also knew that Su Mucheng was definitely not interested in what they were talking about. Then Xiao Nizi followed the arrangement that Director Du agreed to arrange last time. Two young women went shopping.
He also brought Lu Xiuxiu with him.
Today is just his Ph.D. graduation, but the two women closest to him are as excited as if they were celebrating a holiday.
Qiao Ze's answer also made Lot Dugan stunned. His eyes flickered around the faces of the people in the courtyard before he said: "Oh, okay... forget it, you'd better take a look first. This, you know, I've been working on n-body problems.
Your report today gave me a lot of inspiration. I talked a lot with Peter Schulz in the afternoon, and everything that came to mind is here. Take a look first, and then be sure to give me some advice. "
As he spoke, Lot Dugan handed over the manuscript he had written after discussing with Peter Schulz in the afternoon.
"It's a PhD graduation defense."
Joe Ze corrected Lott Dugan's slip of the tongue, took Lott Dugan's manuscript, and glanced at it carefully, feeling a little surprised.
It is obvious that the content in the manuscript uses the formula he just talked about today, involving concepts beyond geometry.
A mathematical tool derived from a new mathematical direction and idea often means that it can solve many mathematical problems. It is as if calculus has become the most basic tool for studying mathematics in this century.
But Lot Dugan was inspired by his doctoral defense. Even Qiao Ze did not think of using transcendental geometry to solve the n-body problem.
And it seemed that this idea was indeed interesting and even gave him some inspiration.
Sure enough, Su Mucheng was right, these old people were still very capable, it was just that they had not been exposed to them before.
But really speaking, the difficulty from 0 to 1 is far more difficult than from 1 to 100.
After spending about ten minutes reading the contents of the manuscript, Joe Ze raised his head and glanced at Lot Dugan, who looked expectant. He thought quickly in his mind, and after a while he said: "It's better to be bolder."
"Be bolder? What do you mean?" Peter Schulz, who had been silent until now, tilted his head and asked.
"Do you have a pen?" Qiao Ze glanced at Peter Schulz and asked.
Before Peter Schulz could react, Lot Dugan quickly took out a pen from his pocket and handed it over.
Qiao Ze picked up the pen and started writing on the manuscript, explaining casually: "Instead of indirect conversion like this, it is better to directly introduce transcendental geometry to describe the position of the object."
Lot Dugan stretched his neck to look at what Joe Ze had written, while Peter Schulz beside him said, "Is this okay?"
"Of course, but a new coordinate system based on transcendental geometry is needed, expressing the position of each object as a transcendental number."
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"Wait, I don't quite understand. Wouldn't this make the calculation more complicated?"
"No, on the contrary, this actually allows us to describe the interaction between objects more accurately. Especially when the objects are very close, we can approximate the interaction force by performing a series expansion on it. And more than just The classical n-body problem can also be extended to the relativistic n-question."
Hearing Qiao Ze's words, Peter Schulz couldn't help but stand up, approached Qiao Ze and began to read his calculations on the manuscript paper.
"Is this an elliptical model?"
"Yes, let's first presuppose a three-body problem and express the position of each object in the three-body system as the solution of the elliptic function."
After speaking, Qiao Ze wrote three more formulas on the manuscript.
[x_i(t)= a_i \cos(\omega_i t +\phi_i),]
[y_i(t)= b_i \sin(\omega_i t +\phi_i),]
[z_i(t)= c_i \cos(\omega_i t +\phi_i),]
Then he explained: "Where (a_i, b_i, c_i) are the semi-major axis, semi-minor axis and semi-maximum axis of the ellipse respectively, (\omega_i) is the angular frequency of the ellipse, (\phi_i) is the initial phase."
Lot Dugan first showed a look of surprise, then frowned and asked: "But how does this affect the calculation of the interaction force?"
"Approximate the interaction force through series expansion. For example, if we first consider the gravity between objects (i) and (j), then define the interaction force as..."
While talking, Qiao Ze wrote another series of formulas on the manuscript.
[\mathbf{f}_{ij}=-g \frac{m_i m_j}{|\mathbf{r}_i -\mathbf{r}j|^2}\hat{\mathbf{r}}{ij} ,].
Then he said: "(g) is the gravitational constant without explanation, (m_i, m_j) are the masses of objects (i) and (j) respectively, (\hat{\mathbf{r}}_{ij}=(\mathbf{ r}_j -\mathbf{r}_i)/|\mathbf{r}_j -\mathbf{r}_i|) is the unit vector.”
"How to do series expansion? It goes beyond geometry and involves mechanical calculations?"
"Transcendental geometry allows the use of item-by-item approximation technology, which can be used for series expansion. Specifically, it can be obtained..."
[\frac{1}{|\mathbf{r}_i -\mathbf{r}j|}=\sum{k=0}^{\infty}\frac{\psi_k}{r^{k+1} },]
"By the way, (\psi_k) is the coefficient."
Looking at the formulas on the manuscript that were gradually becoming fuller, Peter Schulz suddenly felt a little bad. He frowned and said: "No, this will cause a truncation error in the series expansion. This error is uncontrollable, right?" ?”
"There is a way. Have you forgotten how I solved it when I explained the paper today? Set a truncation parameter n and only consider the first n terms of the series expansion. As long as the value of n is large enough, the model mathematically approaches Exact solution.
Of course, when it comes to calculating the position of celestial bodies, we don't need such high accuracy. We can directly consider the performance of the supercomputer and the required accuracy to set the truncation parameters. At least the amount of calculations is less than solving high-order differential equations. many. "
Lot Dugan subconsciously raised his hand and gestured twice, and couldn't help but ask: "During this iterative solution process, we will encounter the problem of numerical instability. How to solve it?"
"Um?"
Qiao Ze wrote the last stroke casually, looked at his derivation process carefully, then handed the pen back to Lot Dugan, and said: "I remember there is an adaptive step size numerical integration algorithm. Coupled with the superiority of transcendental geometry in solving such complex problems, it should be possible to ensure that the numerical solution remains stable when the distance between objects is small.
Of course, you can also use numerical stability analysis to adjust the parameters of the algorithm. In short, there should be many methods, but if I were asked to solve this problem, I would definitely choose this idea. In addition, if you want to calculate a relativistic n-body problem, use Einstein's field equations instead of the traditional Newton's law of gravity. There is probably no change in the idea. "
After speaking, Qiao Ze handed the manuscript and pen back to Lot Dugan.
Lot Dugan stupidly took the manuscript handed over by Joe Ze and looked at the content on it, his expression changing rapidly.
Really, after studying n-body problems for so many years, it was the first time that he felt that his ideas were so clear.
The most important thing is that he finally realized Qiao Ze's boldness in solving mathematical problems.
Or how flexible his thinking is. Of course, it may also be because he has a deeper understanding of transcendent geometry.
In short, the ideas he gave are completely subversive.
Of course, the effect will ultimately need to be verified by supercomputers, and the specific algorithm will also need to be designed by his team.
Although Qiao Ze didn't say it explicitly, Lot Dugan knew very well that it was a great honor for Qiao Ze to talk about his ideas to this extent. If all the problems can be solved in just a few minutes, the n-body problem would be too simple...
More importantly, when a paper is published in the future, whose name will be written on it?
…
Three people in the small courtyard on the other side also gathered together and chatted casually.
"What are the two foreigners talking about with Qiao Ze? Zhou Shun, your English is the best. Please translate for us."
"My English is definitely fine, but the English they speak is useless. They seem to be discussing some celestial calculations or something like that? It seems like Qiao Ze provided them with an idea for solving the problem."
"Nonsense, if you say that, I can see from the expressions of those two foreigners that they have benefited a lot. Aren't you very good at speaking English when you are on a mission? Why did you lose track at the critical moment?"
"No, Brother Lu, they are full of words that I have never heard of. There is a kind of English called academic language, which is not accessible to ordinary people, okay?"
"Hey, I said let's not discuss this. I think Qiao Ze doesn't seem to be so patient with professors in China. Could it be that he was really persuaded by that old man to go abroad? That would be a big trouble. This If this young master gets into trouble, I always feel that I can't bear it."
"That's not the case. I understood what they said when they first met and said hello. The old man wanted Qiao Ze to go to Princeton, and Qiao Ze said that Xilin was very nice to let him come. In short, the two of them were the same as in the previous video, always like this Pulling back and forth.”
"Hey... I'm so tired! If you ask me, this kind of one-sided communication should be canceled directly."
"Ahem, someone else reported it. Although we don't understand it, didn't I say it during the meeting that the achievements of theoretical mathematicians benefit all mankind..."
"Okay, stop talking nonsense, just put things in order and submit them on time. You two are the only ones talking too much."
"No, Brother Lu, it seems you were the first to chat..."
…
After the three people on the other side discussed the questions raised by Lot Dugan, Peter Schulz asked Joe Ze for some questions about superspiral space algebra.
The biggest inspiration for him from today's report is probably that he can combine superspiral space algebra with transcendental geometry to start thinking about similar problems.
Unfortunately, the questions he prepared did not seem to arouse much interest in Qiao Ze.
Or maybe the communication about the three-body problem just now made Qiao Ze finish everything he had to say for the day, and returned to his usual taciturn self, only answering a few simple sentences.
Well, at least there is still something to gain.
A question that I had been thinking about for a long time without an answer was solved with Qiao Ze’s suggestion.
But this also made Peter Schulz even more depressed.
After struggling for a moment, he simply said directly: "Dr. Qiao, I think we should do what I said last time about researching and promoting superhelical algebra. In fact, we are already doing it, but the progress is a bit slow."
"Well, it's indeed slow." Qiao Ze nodded, agreeing with Peter Schultz's statement.
"So, you can actually join in. Even if you are in Xilin, we can always keep in touch by email."
Qiao Ze thought for a while and said: "I promised others that I would form a research team for research and promotion. If you want to join, you can wait until the 28th to take the exam."
"take an exam?"
"Yes, exam."
"Are you saying that you plan to form a team at the institute to specialize in the research of superspiral algebra and transcendental geometry? The recruitment of team members will be in the form of examinations?"
"right!"
"Can foreigners also join?"
"Yes, it must be in Xilin."
"Must be in Xilin? Not remotely?"
"right."
Listening to the conversation between the two, Lot Dugan came back from thinking about the n-body problem and suggested: "Is it possible to cooperate with your Xilin Institute of Mathematics in the name of the School of Mathematics and the Institute for Advanced Study of Princeton University? , jointly promote this project?”
Qiao Ze looked at Lot Dugan and said, "The resident professor you appointed can join."
"Well, actually we have already produced a lot of research results."
"Yes, the progress is just too slow." Qiao Ze nodded in approval.
There's no way to refute, so there's no point in talking.
Sure enough, if some opportunities are missed, it is really difficult to get them back.
Lot Dugan shook his head, and then suddenly remembered what he was going to say, and asked quickly: "By the way, will your doctoral thesis still be submitted to our "Annals of Mathematics"?"
"Do you accept Chinese papers?" Qiao Ze asked.
"Huh?" Lot Dugan was stunned.
It seems that Chinese papers have not been included.
"Our institute plans to launch a journal that will include both Chinese and English." Qiao Ze explained.
"This...don't you plan to publish your doctoral thesis in English?" Peter Schulz asked in an incredible tone.
He originally thought that Qiao Ze's answer in Chinese today would be too brilliant, and the time was limited, so he couldn't wait to announce it...
"Well, there are too many new terms and explanations that are very tiring to translate." Qiao Ze nodded.
"You can leave this to me and I'll find someone to translate and compile it." Lot Dugan said quickly.
"Oh, thank you."
"Uh...then..."
"I'm tired, let's stop talking today." Qiao Ze said.
It's not an excuse, Qiao Ze does feel a little tired.
Especially during today’s doctoral defense, I talked too much, and my throat felt a little sore.
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