The End of Technology

There was a lot of commotion outside and Chen Yonggang couldn't answer all the calls, but Ning Zi's office seemed particularly quiet.

Having learned from the previous experience that Ning Zi had to sit down when receiving distinguished guests in a small room in the doctor's building, the school's logistics department was very attentive to the layout of Ning Zi's suite.

There is not only a large long sofa that can comfortably seat three people, but also two independent leather sofas surrounding a high-end solid wood coffee table, placed diagonally on both sides to facilitate everyone to sit together and discuss.

This also made it easier for the four of Cisco to sit around the coffee table.

Two foreign professors, Dominette Duncan and Conan Lamar, sat at both ends of the long row of sofas, while Lu Zhengyue and Ning Zi occupied separate sofas on both sides.

The three of them were browsing the paper they had just received. Ning Zi was sitting on the side with March in her arms, occasionally answering a question or two that someone asked when reading the paper. About an hour later, Lu Zhengyue was the first to put down his thesis, took off his reading glasses, and looked at Ning Zi while stretching, as if he was looking at a monster.

"Ning Zi, when did you start working on the subject of NP problems?"

Although he had only read the paper briefly, Lu Zhengyue had already announced that he had given up the idea of ​​reading the paper in a short time.

Firstly, this is not his research direction, and it is not convenient for him to comment; secondly, as he gets older, his thinking really cannot keep up. After reading the literature immersed for a while, he feels lack of energy.

However, although Lu Zhengyue has not specifically studied NP problems, mathematics is similar in terms of optimization. It’s not that he can’t read it at all, at least he can understand the impact this article may have on the world of number theory.

"I have considered doing this topic before. I talked about this issue with Professor Duncan when he first came to China." Ning Zi replied.

Try to make this time period as long as possible so that it does not appear so abrupt, but even so, it is enough to make Lu Zhengyue speechless.

After all, Dominique Duncan has not been in the sports university for a long time. He came at the beginning of last summer vacation, which is still more than half a month away from the full year. If the mathematical community in this last article cannot find too many problems, it means that Ning Zi has spent one year taking the first of the seven millennium problems proposed by the Clay Institute and has taken a big step forward. It can even be said that We are only one step away from proving that P≠NP, but the subsequent verification and calculation work is extremely cumbersome.

But there's obviously more to it than that.

Because during the entire proof process, Ning Zi once again proposed many interesting mathematical methods. In Lu Zhengyue's opinion, these methods are very inspiring for the development of mathematical induction and functional analysis for studying mathematical problems in the quantum world.

In fact, the advancement of mathematical problems by mathematicians is a process of enriching the mathematical tool library. For example, calculus can be understood as a mathematical method for solving a type of problem. This is true for the famous Taylor formula and Fourier transform. By finding rules and formulas for solving problems, mathematicians make it easier for people to solve practical problems through mathematics.

This also includes Ning's paper on solving NS equations, and even designed a turbulence algorithm for this purpose, which also solved specific problems. There is also the now famous Ning's segmentation method. Nowadays, as long as mathematicians who study the popularity of Xinzi, Xin's expansion surgery, or Gromov-Witten invariants, almost all use Ning's Ning's segmentation method.

This is the embodiment of the status of mathematics.

Ning's division method has now become a compulsory course for graduate students in this field of research. In the future, as long as mathematicians doing research in this area, they will not be able to avoid Ning Ji's name. Just like learning physics, you must know Newton, and learning communication, you must know Ning Ji's name. It is almost the same reason not to use Shannon or Fourier.

The only problem is probably that the research on this mathematical problem is relatively niche.

But Lu Zhengyue felt that after Ning Zi’s paper was interviewed, Ning Zi’s name would probably be unavoidable in many disciplines in the future, which happened to include quantum physics and communications, and of course the extremely popular computer science, etc. .

Of course, this is still just a feeling. If it is really to be realized, this paper needs to be reviewed with extreme rigor and prudence.

What made Lu Zhengyue even more considerate was that the manuscript of the paper given to him by Ning Zi was in Chinese. The entire paper, except for the formulas and some professional vocabulary, was in Chinese. Although the manuscript of the paper for Dominette Duncan and Conan Lamar was still in English, from this small detail, Lu Zhengyue felt that Ning Zi was fully confident in this paper.

Of course, what he didn't know was that the main reason why he was so considerate was that this job was not troublesome for Ning Zi, who had March.

…

The simple exchange between the two affected Dominette Duncan, who was concentrating on the paper, and after all, his name was directly mentioned.

The mathematician, who had been the world's youngest Fields Medal winner for only five minutes, raised his head, glanced at Ning Jie with complicated and unspeakable eyes, and said faintly: "We did talk about this at the time, but Ning, after that You also suggested that I do research on the zero-point problem, saying that this research is easier to produce results, but there are currently no results in the direction that is easy to produce results, and you said that there is no paper in the direction that cannot be conquered in the short term."

Ning Zi shrugged and replied helplessly: "The issue of inspiration is indeed out of control. But you should know that what I said is the truth. In fact, we have advanced the research on the zero-point problem and should have it ready within half a year. Results. But inspiration is uncontrollable. If I said that the solution to this problem was really a flash of inspiration not long ago, you would believe it, right?"

Before Dominette Duncan could answer, Conan Lamar next to him responded very simply: "Of course I don't believe it. A moment of inspiration may be able to solve a certain proposition in this direction, such as the intermediate process. But as long as you look After reading the table of contents of the paper, you will know that it is impossible to solve this series of problems without long-term related thinking, such as the mathematical inference of multi-dimensional to low-dimensional jogging motion in the paper and the annotation of multiple rotation matrices.

It probably takes more than ten inspirations to solve this series of problems. Of course, I still can't judge whether your inference is correct. The most annoying thing is that you didn't give the proof process. I just looked for it, and you didn't cite any literature. So don’t tell me that these are all told to you by inspiration. If so, then your inspiration is terrible. Moreover, are you sure you can convince the reviewer with your conjecture? "

"Actually, this problem can be simplified as the representation and conversion of the same vector in different dimensions, um..." Ning Zi wanted to explain, but suddenly discovered that this part of the content was actually based on the content taught in March. So suddenly I didn't know what to say.

Because he suddenly discovered that this part of mathematical research did not seem to have advanced to this level in this world. In other words, he could not find relevant literature to explain why these results were so naturally given in the paper.

This also made Ning Zi suddenly realize that this was a big problem, and he directly used the arguments in the previous system for granted.

This problem has actually arisen before.

At that time, Fang Xu completed the research on the proposition, but the paper could not be published because Ning Ji did not write a paper specifically for Ning's split.

In other words, although there is certainly nothing wrong with the argumentation process of Ning Zhi's paper, the lack of a pre-explanatory paper will make reading and review difficult. Of course, he can also choose to add the argument process in the paper, but in that case the paper will be too long.

Because the problem that needs to be explained is more than just a lemma.

There will be at least six or seven lemmas that require prerequisite theoretical guidance.

If they were all written in one paper, Ning Zi probably estimated in his mind that the length of the entire paper would increase to six or seven hundred pages, which would not only be extremely difficult to read. But it is simply impractical, because it is difficult or even impossible to find suitable reviewers, because many of the directly cited theories contain different mathematical directions.

As we all know, in this era, versatile mathematicians like Hilbert are rarer than endangered animals. After all, mathematical research in this era is too divided, so if he puts everything together, it will be extremely difficult. trouble.

"You don't want to say this is simple, do you? Then ask why we can't understand it?"

Dominique Duncan glanced at Ning Jie, still using his signature resentful tone: "So are you planning to teach horse racing? In fact, you already have a complete proof of this conjecture, but it is limited by the length of the article. , so it was omitted? If I understood it correctly, this process should be a very important prerequisite theorem, but you directly obtained the result. So you called us here just to let us read an article that requires guessing your thoughts. paper?"

Lu Zhengyue, who was silently listening to the conversation between the three people, put on his reading glasses again, picked up the paper he had just put on the coffee table, and began to search for the questions the two talked about in the catalog, and then began to habitually obey the old man in his heart. , not only did he not see it as deeply as these young people, he also didn't see it as quickly as these young people.

Ning Zi glanced at the two colleagues silently, then put down March, picked up the paper and pen thrown on the coffee table, then quickly wrote a few formulas and a simple proof process, and then handed them to the two of them.

Of course, this posture was really uncomfortable, so Ning Zi wrote very briefly. While showing the manuscript paper to the two of them, he continued to explain: "P point represents the coordinates in a high-dimensional coordinate system, and D represents the coordinates of this point. In the conversion process, P^c represents the intermediate point coordinate system, P^w represents the low-dimensional coordinates, W represents the connecting line of the projection, and K represents the closed-chain subspace... Well, can you understand this?"

The two took the manuscript paper handed over by Ning Zi, listened to Ning Zi's explanation, their heads were squeezed together, and then their eyebrows were furrowed tightly. They looked up at each other from time to time, then raised their heads and shook their heads at Ning Zi.

Sure enough, it is still too abstract, which fully proves that mathematics has blind spots that students always find not difficult.

After all, these two people are already at the top of the modern mathematics pyramid. If they can't understand it, Ning Zi will find that he won't be able to pass this hurdle at all if he doesn't write six or seven detailed preliminary papers.

This is probably the tragedy of accidentally surpassing the times.

He was simply too happy today.

These people couldn't understand such a wonderful paper, and if they couldn't understand it, they would naturally lose the fun of sharing it.

So in order to share it with these people smoothly, he had to prepare a math paper first and prove all these mathematical tools, and then everyone could continue to have fun together.

"Okay, today's sharing will end here. I decided to listen to your opinions. I will provide the proof process of these issues as soon as possible, and then invite everyone to discuss this issue together."

Ning Zi waved her hand boredly and said.

"Well, let's take the paper back and study it first?" Dominette Duncan raised the manuscript paper in his hand and asked inquiringly.

Ning Zi thought for a moment, then shook her head.

It wasn’t that he was worried about Dominette Duncan and Conan Lamar, it was mainly because after they read the entire article, they found more content that should have been proved in detail but was omitted. He was afraid that more information would be added then. There's no way to explain it.

"Then...Okay! Although I don't know why your inspiration is so strange, but if you can really prove this theorem...wait, why do I feel that if this conclusion is correct, it can guide the solution of the Hodge conjecture?" Domini Duncan suddenly said.

Ning Jimoran, Dominette Duncan was right. This proposition was originally proposed to prove the Hodge conjecture. Although the problem was not solved, the method remained in the March database.

"Okay, don't think about it. Give me some time. Let's talk about this paper at the next sharing meeting." Ning Zi didn't want to explain, and directly showed off as a farewell gesture.

The three people looked at each other, then put down the papers in their hands and walked out of the office.

Academician Lu, who was walking at the end, looked back at Ning Zi and closed the door for him thoughtfully.

Ning Zi, who was left alone, stood up, returned to his desk, and found that Yue Yue had thoughtfully sent the preliminary paper to his computer through Penguin software...

Of course, these are the contents in its database, and it doesn't even need to consume computing power to process the copywriting. It just needs to be retrieved and the author's name is changed.

Ning Zi's judgment was correct, there were exactly seven chapters.

Ning Jie was silent and couldn't help complaining: "March, why didn't you discover this problem earlier?"

The kitten's expression was innocent, and then he gave an explanation that Ning Zi couldn't refute: "Meow, because these are not problems for me."

One person and one cat, looking at each other in silence.

Then Ning Zi asked another question on Penguin that would tremble the souls of countless mathematicians: "March, do you think there is a possibility? If we submit all seven papers at once, what will happen?" Make a lot of people go crazy right there?”

"Meow……"

Additional update for the Silver League boss 3/20)