The train driver in the courtyard

This was the first time that Li Aiguo worked with his senior predecessors to overcome a difficult problem.

His biggest feeling was that these veterans were really hardworking.

Since starting work, Professor Qin has led the researchers to work at least eleven hours a day, and it is common for them to have dinner until one or two o'clock in the morning.

With this kind of work intensity, sometimes I have to eat 5, 6 or even 7 meals a day.

The original highland barley noodles and cabbage soup could no longer meet the needs of the researchers.

Some people experience altitude sickness, loss of appetite, and significant weight loss after using their brains intensively.

Professor Qin, the key member, couldn't eat for the whole day, and Zhou Xiaomeng, the computer, was so tired that she was gasping for breath.

But no one complained about the hard work, which is the norm in scientific research these days.

Due to the shortage of materials, the health of many older generations was ruined. The situation was not alleviated until the 1980s and 1990s, when the economy improved.

Seeing that there was no problem with the work progress, Li Aiguo sorted out his ideas and let everyone continue working.

He himself returned to the office.

What to do? Made two phone calls.

One call was made to the Beijing Meteorological Station, requesting the farmer to urgently dispatch a batch of supplies to support the Computing Institute of the Ninth Bureau of Factory 221.

On the phone, the farmer was a little confused: "Patriotic, the current research project of Factory 221 has nothing to do with our weather station."

Li Aiguo understood what the farmer meant. There were rules to be followed in the dispatch of materials within the country.

Even if the weather station is willing to provide help, it will be criticized if it easily provides supplies without sufficient reasons.

Everyone is having a hard time. Your Meteorological Bureau is supporting Factory 221 alone and not supporting them. Do you think they are not contributing to the country?
Li Aiguo was well prepared: "Teacher, don't worry, what the Ninth Bureau is researching this time is very related to our Meteorological Bureau. Maybe it can help us open up the situation in Lao Maozi's house."

The farmer couldn't understand what topological proofs had to do with meteorological work.

He also knew that if he asked Li Aiguo on the phone now, the boy would definitely not tell anyone.

Out of trust in Li Aiguo, the farmer notified the logistics department to urgently dispatch a batch of supplies.

Li Aiguo's second call was to Director Li.

"Brother, I need help urgently."

Before he finished speaking, Director Li said that the fishing team had made some gains and a batch of湟鱼 could be dispatched.

that's it.

The Beijing Meteorological Bureau sent small rice from Tianjin, peanuts from Shandong, and soybeans from the Northeast; the Ninth Bureau sent a batch of Huangyu.

Director Deng personally went to find the third company commander who was in charge of the canteen and asked him to prepare special meals for the researchers.

Seven or eight plates were served on the table every night, and the researchers' health conditions improved rapidly.

Looking at the excitement of those researchers, Li Aiguo felt that a foundation should be set up to collect supplies from all over the country, even from abroad, to ensure the problems of domestic scientific researchers.

However, this matter should be handled slowly and not in a hurry. Otherwise, you may end up doing something bad with good intentions, and be slandered by people with ulterior motives.

Since supplies became abundant, everyone often treated meals as seminars, continuing to discuss work while eating.

Most of the so-called work is knowledge of topology.

Topology mainly studies some properties of geometric figures or spaces that remain unchanged after continuous changes in shape.

It has important practical significance in the fields of condensed matter physics, high-energy physics, map making, path planning, etc. It is one of the few branches of mathematics that can directly promote the development of productivity.

Therefore, since the establishment of topology, it has become the focus of research for mathematicians around the world.

Although the research on topology started relatively late in China.

However, countless young people with patriotic enthusiasm and mathematical talent devoted themselves to the study of topology and achieved considerable results.

Professor Qin is one of the best among them.

The fact that he was chewing on a fish bone while talking about his peculiar ideas about the tile argument is enough to illustrate this point.

"The spherical structure is a three-dimensional sphere. If tiles form a sphere, we need to use tiles to form a three-dimensional space with a boundary. Every closed curve in this space can be continuously shrunk into a point."

Li Aiguo: "A three-dimensional special case of the Poincare conjecture?"

Professor Qin looked at Li Aiguo in surprise.

However, he soon realized that he was careless. The young man in front of him was no less knowledgeable than him in topology.

"Comrade Patriot, you didn't realize that if we want to calculate the exact number of tiles, there are two ways. One is to use pure calculation, which may produce errors, and the other is to start from the Poincare conjecture."

Professor Zhou waved his hand to interrupt Professor Qin: "Old Qin, I know you have always been thinking about the Poincare conjecture, but the difficulty of that conjecture is too high. Let's use the first method."

Professor Zhou is not belittling himself. The Poincaré conjecture is a conjecture proposed by the French mathematician Henri Poincaré.

The conjecture is: any simply connected, closed three-dimensional manifold must be homeomorphic to a three-dimensional sphere.

Since the Poincare conjecture was proposed, it has been considered a proposition of fundamental significance in topology.

This attracted countless topologists to study the Poincare conjecture, and it later became one of the seven "Millennium Problems".

It was not until the 20th century that the Poincare conjecture was proven.

In his previous life, Li Aiguo had paid attention to the Poincare conjecture.

It’s just that the proof process was too complicated and I can’t remember some of it clearly. I only remember the three-dimensional form of the Poincare conjecture - the proof idea of ​​the geometrization conjecture.

But that's enough.

After all, the spherical structure of the big mushroom is a three-dimensional structure.

If the geometric conjecture can be solved, it will not only resolve the tile problem, but also elevate the level of domestic topological research and make one's name famous in history. Li Aiguo felt that the steamed buns were even sweeter.

He did what he said. After lunch, Li Aiguo immediately started writing the proof of the geometric conjecture.

Although it was just to prove an idea, it was extremely complicated and took me an entire afternoon to write.

Zhou Xiaomeng brought dinner, which consisted of a steamed bun and a fried fish, which was considered top-notch food in those days.

****
The next morning at 8:30, in Professor Qin’s office.

Professor Qin had just assigned a calculation task and returned to his office when Li Aiguo flashed in and placed a document on Professor Qin's desk: "Old Qin, this is my opinion on the three-dimensional Poincare conjecture. Please give me some advice."

After speaking, Li Aiguo handed over a cigarette.

Professor Qin was feeling depressed because he was stopped by Professor Zhou. When he heard that it was related to the Poincare conjecture, he immediately became interested.

"Pour the water yourself."

He sat on the chair without even lighting a cigarette.

Professor Qin picked up the material. There was a line of words written in blue ink on the cover, "On the feasibility of proving that [a three-dimensional manifold can be split into submanifolds with one of the eight standard geometric structures. It is an analogy of the monovalent theorem of two-dimensional surfaces on three-dimensional manifolds]"

"It seems to be a variation of the Poincare conjecture?"

Professor Qin thought this thing was interesting, so he opened the cover and saw that it had a lot of pages.

The first page begins with the words [Three red flags fluttering in the wind, guiding us in the direction of progress! In order to better fight the American empire, the proletariat better master scientific weapons]

Reading further down, Professor Qin couldn't help smacking his lips. These little words were so comprehensive.

What about "destroy resolutely, thoroughly and cleanly", "promote production, promote work and promote construction!", "emancipate the mind, seek truth from facts, unite as one and look forward!", "be indomitable and forge ahead courageously!".
If Professor Qin had not known in advance that the material was a scientific research paper, he would have thought it was a conference.

I turned another page and found a complete proof idea in the document, from the analysis of dimensional characteristics to the constructive proof method and then to the linkage between conditions and conclusions. The whole idea was very detailed.

Even at the end, there is a multidisciplinary cross-validation.

“Geometry conjectures may be influenced by physical phenomena such as wave propagation and turbulence. By mathematically modeling the structural characteristics of these phenomena, we can provide an intuitive basis for rigorous proof.”

Professor Qin couldn't help but light up a cigarette when he saw this: "Well, that's good. Although the previous content is a bit debatable, the multidisciplinary cross-validation at the end is something that even I should learn. Many old professors have never heard of it."

In fact, Li Aiguo also knew that the proof process was too complicated and obscure. If he wanted to quickly gain the trust of others, he had to come up with something that people could understand at a glance.

"I just figured it out myself. I'm sorry to make you laugh."

Professor Qin shook off the cigarette ash, held the material and read it carefully again.

"I think I understand a little bit. But how can we regard a three-dimensional manifold as a geometric object that evolves over time?"

Professor Qin pointed his finger at the third page of the material, and his brows were twisted into knots.

As a first-class mathematician, he immediately realized the key part of the entire proof.

The reason why the Poincare conjecture had not been proven for hundreds of years, but was quickly proven after the geometric conjecture was proved, was only because a new tool was used in the geometric conjecture - "Ricci flow".

This is a differential geometry research tool that describes the evolution of space.

In differential geometry, a "Ricci flow" is an intrinsically geometric flow that diffuses heat in a formally metric-similar manner to the deformation of a Riemannian manifold, smoothing out irregularities in this matrix.

Of course, according to the first-come, first-served basic law of crossing, the name of "Rich Flow" should now be called "Li Aiguo Flow".

Li Aiguo smiled and said, "Professor Qin, I have introduced a new type of tool here. Well, let's temporarily name it Li Aiguo Flow."

"Li Aiguo and his ilk?" Professor Qin felt a little annoyed.

None of the theories and proofs that can be given names have any significant effect. This guy came up with it without saying anything?

Li Aiguo took out the second set of materials from the canvas bag and handed it over.

"Take a look first."

He turned around, poured a glass of water, and sat opposite Professor Qin. Professor Qin was already skeptical, so he took it and opened it directly. His eyes lit up, and he lit another cigarette and read it carefully.

There was only one line of words on the cover of the second document: "Three Manifolds with the Positive Li Aiguo Flow"

Professor Qin looked at it for two hours very carefully, and wrote and drew with a pencil from time to time.

Li Aiguo was not in a hurry and just sat there waiting.

Li Aiguo flow is a deformation process that aims to smooth large-scale or global irregularities in complex spaces or surfaces. The theory is very abstract and obscure.

However, Li Aiguo used the Li Aiguo flow to prove the first long-term existence theorem.

The proof of the theorem makes the existence of Li Aiguo and his ilk very convincing.

After carefully studying for two hours, Professor Qin took off his glasses, closed his eyes and thought for a full ten minutes before speaking: "Young people are formidable, patriotic comrade, how did you come up with these ideas?"

Li Aiguo lit a cigarette: "Once, I was driving a train and saw the trees on the roadside moving backwards at high speed. Then I heard the sound of the train wheels hitting the rails. I wondered if the sound was caused by the train. I was on the train and saw the trees moving backwards. Is there a mathematical connection between the sound and the trees? If so, how can we describe their states?"

Hearing this, Professor Qin was stunned. After a long while, he sighed and said, "My teacher once told me that mathematics is a highly abstract field, but it provides us with a framework to help us understand and describe the real world. Now it seems that you have achieved this."

"As a front-line worker, everything I do is based on experience gained from work," Li Aiguo said modestly and continued.

"Although we now have the theory and ideas, if we want to fully prove it and use it to solve the problem of the number of tiles, we still need you to step forward."

Professor Qin couldn't wait any longer. This was a great opportunity to reach the pinnacle of mathematics. He nodded and said, "I will immediately arrange for someone to solve this problem together. However, the tile calculation..."

Professor Qin stopped and looked at Li Aiguo.

His meaning was very clear. Should we suspend the calculations and allocate personnel to focus on solving the geometric conjecture?
Li Aiguo pondered for a moment and said: "The calculation work of tiles cannot be stopped. We can then use the calculation results and the proof results to cross-verify each other."

Mathematical research and proof are not like building airplanes and cannons, and they cannot be used to employ human wave tactics.

Professor Qin naturally understood this principle: "Then I will select three researchers from the same department, and the four of us will form a team."

Li Aiguo slapped his thigh and said, "That's great!"

Professor Qin finally made the decision: "Let's do this."

Then he thought for a while and began to select specific candidates: "Professor Chen is a mathematics professor at Jingcheng University and a member of the organization. He graduated from West China Union University with a bachelor's degree in science. He has done mathematical research at the University of Paris and has insights into topology.

Professor Liu once taught at the University of California, Berkeley. He is a member of the Jiusan Society and has very positive ideas, so he can also be counted.

With these two people, our group's research capabilities are unmatched.

Now we have to choose someone to handle logistics."

Professor Qin looked up at Li Aiguo and said, "How about Comrade Zhou Xiaomeng? She is one of the few scholars of the younger generation who has done research in topology, and she is also a lesbian."

Li Aiguo knew clearly that Professor Qin had two intentions. One was to support young people, and the second was that there were relatively few female comrades engaged in mathematical research and they should be supported more.

Only when female comrades achieve results in scientific research can they encourage more female comrades to leave their homes and devote themselves to scientific research.

The nature of this practice is similar to the establishment of a 38-pack crew in the locomotive depot.

It's not really political correctness.

Li Aiguo nodded in agreement.

Professor Qin picked up the phone and was about to notify a few people, but suddenly stopped: "Aiguo, you have to be the one to call this handsome guy. This is the rule. I can't take the credit from you."

Li Aiguo had never thought of this. Seeing Professor Qin refuse, he did not refuse and picked up the phone to inform the three people.

Professor Liu and Professor Chen are both the main forces in the room, and they were not surprised when they learned that they were selected.

Zhou Xiaomeng was so frightened that her heart started beating fast.

She knew that even as a waiter, it was an honor to be able to work with these big guys.

"Team Leader Li, don't worry, I will definitely do my best to do my job well."

Li Aiguo nodded unequivocally and handed over a document: "Go over the basic knowledge first, and then join the group after you have mastered it."

His meaning was very clear. Zhou Xiaomeng had to rely on her own abilities to prove that she was capable of doing the job, rather than just being a tea server.

Zhou Xiaomeng also understood this and took the information excitedly: "Team Leader Li, don't worry!"

After the work was arranged, two days passed uneventfully.

Because of Li Aiguo's clear division of labor at the beginning and the analysis of the proof ideas, the group's work went smoothly.

Three days later, Zhou Xiaomeng had read and mastered all the basic information.

Professor Qin tested her and nodded: "Aiguo, this girl is more talented than I expected."

Li Aiguo was also a little surprised. Could Zhou Xiaomeng become a great mathematician in the future?

"Then let Zhou Xiaomeng take care of the proof of the second step. Three days. After three days, I want to see the result."

Li Aiguo picked up a document and handed it to Zhou Xiaomeng.

****
A week passed in busyness.

To be honest, this is the busiest week for Li Aiguo since he came to this era.

However, in this era, as long as you work hard, you will reap rewards.

In the afternoon, Li Aiguo was sorting out materials when Professor Qin and Zhou Xiaomeng came in happily, holding a stack of draft papers.

"We succeeded! We succeeded! We are patriotic, we have proved it." Professor Qin was very excited: "We have proved the three-dimensional special case of the Poincare conjecture!"

Li Aiguo stood up and went to Professor Qin: "Professor Qin, what about the number of tiles? Have you proved it?"

Professor Qin suppressed his excitement and nodded heavily: "We used the proof of the three-dimensional special case and substituted it into the mathematical model of growing mushrooms. Finally, we proved that the number of tiles needed is 32, not 36 as the Russians told us."

Li Aiguo secretly breathed a sigh of relief when he heard the result.

It seems that his efforts have not been in vain.

In the previous life, it was because the Russians provided 36 tiles that the mushroom-growing business was delayed for nearly half a year.

Now we have found the correct number of tiles and solved the proof of the three-dimensional case of the Poincare conjecture, which can be said to be killing two birds with one stone.

Li Aiguo now wants to have a drink to celebrate.

However, he still had to be cautious: "Professor Qin, it's too early to celebrate now. We still need to wait for the calculation results of the calculation team."

Professor Qin also understood the importance of data verification and nodded, "I just met Lao Zhou, they still need at least three days."

After saying that, Professor Qin looked a little strange, and tilted his head towards the person next to him: "Aiguo, should we report this to Director Li?"

As he spoke, he handed all the draft papers to Li Aiguo. His meaning was very clear: this was a great achievement, you are the team leader, you should report.

Li Aiguo was feeling impressed that Professor Qin's ideological awareness had improved a lot, and he felt a little amused after taking the draft paper.

"Let's go, the four of us."

The meaning is very clear, the credit goes to everyone.

Professor Qin told the two professors the news, and both professors were very happy.

After all, who doesn’t want to show up in front of their boss?

Of course, the draft paper cannot leave the room.

Li Aiguo took a document and the four of them, accompanied by a confidentiality officer, came to Director Li's office and knocked on the door and went in.

There was another person sitting on a chair in Director Li's office, and he seemed to be reporting to Director Li.

When Director Li saw the men coming in, he pointed at the man and introduced him to Li Aiguo: "This is Liu Xingnian, the captain of the fishing team. It's almost Chinese New Year, and the fishing team is planning to organize a large-scale fishing event."

"Hello, Captain Liu."

"Commissioner Li, we meet again." Liu Xingnian extended his hand.

Li Aiguo took a closer look and recognized that Liu Xingnian was the guard who had gone fishing with them at the river.

Director Li sent his guards out to fish. It seems that he really cares about the fishing team.

Liu Xingnian knew Li Aiguo's identity, and when he saw that the others had something to discuss, he left.

After closing the door, Director Li asked, "Are there any results for the project to calculate the number of tiles?"

Li Aiguo handed the materials to Director Li: "There is indeed a result, but it uses a new method."

When Director Li heard this, he asked, "A new method?" Director Li had followed the tile project before, and he looked at Professor Qin in surprise and said, "Isn't there only one method?"

Professor Qin said proudly: "No, no, there was indeed only one method at the beginning, but now under the leadership of Team Leader Li, we have developed a new method, and this new method has also solved part of an international mathematical problem."

Director Li didn’t understand what the new method meant, but he was very sensitive to “international mathematical problems”.

"What's going on?"

Professor Qin looked at Li Aiguo, who nodded and said, "Old Qin, you should introduce them."

Professor Qin nodded gratefully. He picked up the materials and explained the whole story of the new project.
He also explained the general ideas to Director Li one by one.

Director Li listened for a long time, looked at the materials for a long time, and after smoking three cigarettes, he only understood one thing: if this thing really exists, it is a large satellite.

"Old Qin, are you sure this problem is international?" Director Li interrupted Professor Qin and got straight to the point.

Professor Qin puffed out his chest and said, "Director, although the geometrization conjecture is only a part of the Poincare conjecture, it is definitely a worldwide mathematical problem. Once this result is announced, it will shock the entire international mathematical community."

(End of this chapter)